ArticlePDF Available

A guide to ERK dynamics, part 1: mechanisms and models

Authors:

Abstract

Extracellular signal-regulated kinase (ERK) has long been studied as a key driver of both essential cellular processes and disease. A persistent question has been how this single pathway is able to direct multiple cell behaviors, including growth, proliferation, and death. Modern biosensor studies have revealed that the temporal pattern of ERK activity is highly variable and heterogeneous, and critically, that these dynamic differences modulate cell fate. This two-part review discusses the current understanding of dynamic activity in the ERK pathway, how it regulates cellular decisions, and how these cell fates lead to tissue regulation and pathology. In part 1, we cover the optogenetic and live-cell imaging technologies that first revealed the dynamic nature of ERK, as well as current challenges in biosensor data analysis. We also discuss advances in mathematical models for the mechanisms of ERK dynamics, including receptor-level regulation, negative feedback, cooperativity, and paracrine signaling. While hurdles still remain, it is clear that higher temporal and spatial resolution provide mechanistic insights into pathway circuitry. Exciting new algorithms and advanced computational tools enable quantitative measurements of single-cell ERK activation, which in turn inform better models of pathway behavior. However, the fact that current models still cannot fully recapitulate the diversity of ERK responses calls for a deeper understanding of network structure and signal transduction in general.
Review Article
A guide to ERK dynamics, part 1: mechanisms
and models
Abhineet Ram* Devan Murphy* Nicholaus DeCuzzi, Madhura Patankar, Jason Hu, Michael Pargett
and John G. Albeck
Department of Molecular and Cellular Biology, University of California, Davis, U.S.A.
Correspondence: John Albeck ( jgalbeck@ucdavis.edu)
Extracellular signal-regulated kinase (ERK) has long been studied as a key driver of both
essential cellular processes and disease. A persistent question has been how this single
pathway is able to direct multiple cell behaviors, including growth, proliferation, and
death. Modern biosensor studies have revealed that the temporal pattern of ERK activity
is highly variable and heterogeneous, and critically, that these dynamic differences modu-
late cell fate. This two-part review discusses the current understanding of dynamic activ-
ity in the ERK pathway, how it regulates cellular decisions, and how these cell fates lead
to tissue regulation and pathology. In part 1, we cover the optogenetic and live-cell
imaging technologies that rst revealed the dynamic nature of ERK, as well as current
challenges in biosensor data analysis. We also discuss advances in mathematical models
for the mechanisms of ERK dynamics, including receptor-level regulation, negative feed-
back, cooperativity, and paracrine signaling. While hurdles still remain, it is clear that
higher temporal and spatial resolution provide mechanistic insights into pathway circuitry.
Exciting new algorithms and advanced computational tools enable quantitative measure-
ments of single-cell ERK activation, which in turn inform better models of pathway behav-
ior. However, the fact that current models still cannot fully recapitulate the diversity of
ERK responses calls for a deeper understanding of network structure and signal trans-
duction in general.
Introduction
The extracellular signal-regulated kinase (ERK) pathway (Figure 1) plays a widespread role in the
development and physiology of animals [1]. ERK is a member of the mitogen-activated protein kinase
(MAPK) family, which is found in all eukaryotes. Among the MAPK family, ERK1 (MAPK3) and
ERK2 (MAPK1) have received a disproportionate amount of attention, owing to their overlapping and
essential involvement in many processes that impact human health. Other ERK paralogs, including
ERK3, ERK4, ERK5, and other MAPK family members including the JNK and p38 kinases, also play
signicant roles in these processes. Nonetheless, we focus here on developments in understanding the
regulation of ERK1/2 activity, which is required for the proliferation of cancer cells, the formation of
memory by neurons, and morphological changes in development, among many other examples. For
more than two decades, it has been recognized that the frequency, duration, and amplitude of ERK
activation are important in determining its effect on the cell [2]. Under some circumstances, ERK acti-
vation is more dynamic than that of JNK and p38 [3]. However, other studies have observed pulsatile
JNK and p38 activities in response to cell stresses [47], suggesting this form of behavior is a
common theme for MAPK pathways. Collectively, these dynamic behaviors appear to arise from the
regulatory topology of the respective MAPK cascades, which contain numerous feedback loops [4,8].
Several early studies laid the conceptual groundwork for understanding the importance of ERK
dynamics. In the 1990s, observations from several groups rst established a relationship between
ligand stimulation, the timing and duration of ERK activity, and cell fate [9]. Manipulating ERK
*Co-first authors.
Version of Record published:
1 December 2023
Received: 9 July 2023
Revised: 2 November 2023
Accepted: 6 November 2023
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1887
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
Figure 1. The central ERK signaling pathway.
Initiation of the MAPK/ERK pathway begins with ligand binding of tyrosine receptor kinases (RTKs). This begins the
phosphorylation cascade and activation of the core MAPK/ERK pathway consisting of RAS, RAF, MEK, and ERK (orange box,
individual isoforms are listed). Active ERK can translocate to the nucleus, where it stimulates gene expression, or dimerize and
phosphorylate cytoplasmic substrates. Depending on ERK dynamics, several gene expression programs can be activated,
including cell cycle, cell survival, and ligand production (pathways bolded and specic genes listed in the box within the
nucleus). Outside the nucleus, ERK regulates cytoplasmic proteins involved in cell growth, metabolism, and differentiation.
Pathway termination is regulated by numerous phosphatases (PP2A and DUSPs), as well as several negative feedback loops
mediated by ERK phosphorylation. For a comprehensive discussion of additional molecular details see [1]. TF, transcription
factors.
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY).1888
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
activation patterns by different growth factors, receptor expression levels, or oncogenic mutants led to alternate
cell fates [10]. In parallel, Ferrell et al. [11] showed that MAPK activation occurs in a highly switch-like
manner in individual Xenopus oocytes. These results demonstrated that a pathways output does not necessarily
operate as a simple linear response to stimuli, but instead is shaped heavily by feedback, especially when
viewed at the single-cell level [12]. Finally, it was found that the regulatory structure for a number of ERK
target genes can make them sensitive to the duration of ERK activity [1315]. Together, these concepts form
the overarching framework for dynamics-based information encoding and decoding by the ERK pathway. In
this review, we focus on the unique dynamic behavior observed for ERK and examine how it arises from the
biochemical organization of the pathway. In a companion review, we look further into the impact of ERK
dynamics on downstream processes and cell phenotypes.
Mathematical models have played an essential role in the study of ERK, providing a way to test questions
that are not accessible experimentally and to explore possible mechanisms for dynamic behavior. In
general, the ux of proteinprotein interactions and modications in the pathway can be represented as a
system of ordinary differential equations (ODEs), which simulate pathway dynamics under different condi-
tions. Historically, Ferrell and colleagues used such models to understand how MAPK pathways could
exhibit the observed non-linear responses without explicit cooperativity and positive feedback [12]. This
behavior is termed zero-order ultrasensitivity and occurs in MAPK systems when both the kinase and com-
peting phosphatase molecules available are limited enough to become saturated [16]. Subsequently, the
question of how transient ERK behavior arises under constant stimuli led to an expansion of MAPK
models. Early evidence implicated the internalization of the epidermal growth factor receptor (EGFR) [17],
but it was also argued that the transient assembly of signaling complexes at the EGFR could explain the
observed transient kinetics [18]. Multiple models then explored the possibility of oscillations in activity due
to feedback phosphorylation [19,20]. Orton et al. [21] elegantly summarized the early mathematical models
of MAPK signaling, and the eld of MAPK modeling continues to evolve, exploring the complex effects of
feedback and more subtle concepts such as buffering of ERK by its substrates [22]. The concepts of transi-
ent, oscillatory, and excitatory behavior remain actively studied, especially with regard to distinguishing
between true oscillations and pulsatile responses excited by uctuating external stimulus. Throughout this
review, we discuss the relevant mathematical models that can be used to understand the dynamic operation
of the ERK pathway.
Forms of dynamic ERK activity
Experimentally observed ERK dynamics can be grouped into several major categories (Box 1), including sus-
tained, transient, peak with sustain, oscillatory, sporadic, and complex. These categories are not always clearly
distinct, but they provide a useful framework for discussing ERK activity over time. In early studies, the PC-12
rat pheochromocytoma cell line served as a useful model system, as it responds with ligand-specic ERK
dynamics: sustained activity to NGF stimulation and transient activity to EGF [23]. Importantly, these dynam-
ics have phenotypic consequences resulting in cell proliferation and differentiation, respectively. At the time,
population-level assays, such as immunoblots, were only able to provide rough estimates of ERK patterns, such
as sustained activation lasting several hours, or transient activation peaking at 20 min before returning to
baseline [9,10,24,25]. More complex ERK dynamics such as oscillations were postulated [19] but only became
clearly observable with the development of uorescent ERK biosensors [26,27]. These reporters are briey sum-
marized in the following section and have been reviewed in depth elsewhere [28].
Using live-cell reporters, Pertz and colleagues re-examined the classic PC-12 system, conrming the original
ndings from Marshall et al. but also uncovering substantial cell-to-cell variation [29]. This variation is
extremely broad; Ryu et al. found both sustained and transiently responding cells at different proportions
within any population of PC-12 cells, regardless of EGF or NGF stimulation. Further intricacies were revealed
in the form of oscillations [30] and sporadic pulses [31,32] in growth factor-stimulated cells. The cell-to-cell
variation also found in these systems made it clear why these diverse ERK activity forms were not measurable
in immunoblot studies; because they occur asynchronously between cells, they are blurred in the average of
thousands of cells in an immunoblot sample. In addition to distinguishing single-cell variation, live-cell assays
also provide much greater time resolution, allowing dynamics to be closely tracked on the scale of minutes for
many hours or even days, in contrast with the small number of time points typically captured in an
immunoblot.
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1889
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
BOX 1. Field Guide to Dynamic ERK Signaling
(A)
(B)
(C)
(D)
(E)
(F)
(G)
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY).1890
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
The subcellular distribution of active ERK within a cell is also an important facet of ERK dynamics. ERK
sequestration to different subcellular regions can be a mechanism to regulate interactions between ERK and its
substrates, altering the subset of targets that are phosphorylated [33,34]. For example, ERK translocation from
the cytoplasm to the nucleus appears to be required for the phosphorylation of some substrates, such as the
transcription factor ELK1 and subsequent induction of gene expression [35]. ERK biosensors localized to the
plasma membrane and endosomes have begun to uncover examples of distinct subcellular ERK activity pat-
terns. Within a particular cell, activity at the plasma membrane can be sustained, in contrast with the transient
activation observed in the cytosol and nucleus [36]. However, complexities in the subcellular milieu remain yet
to be fully resolved. ERK translocation is not necessarily required for the phosphorylation of ERK substrates
within the nucleus [37,38]. It is possible for ERK to interact with and phosphorylate its substrates irrespective
of their bulk localization because both ERK and its substrates such as ELK1 or FOS can shuttle between
nucleus and cytosol on the scale of minutes [3943]. Thus, even with the biosensors now available and the
elegant work already performed, it must be recognized that interactions over space and time create many
complex possibilities for the ERK signaling system [8]. Further work is still needed to resolve the full temporal
and subcellular features of ERK activity dynamics.
Advances in measuring ERK activity and remaining
challenges
ERK dynamics are most easily detected by uorescent protein-based ERK activity reporters (i.e. biosensors)
which have recently been reviewed in detail [28]. The main categories of reporter include FRET-based (EKAR
series), translocation-based (ERK-KTR; ERK-FP fusions), and degradation-based (FIRE) (outlined in Table 1).
While the FRET-based ERK sensor has undergone many generations of improvements, the ERK-KTR, ERK-FP
and FIRE reporters remain essentially unchanged (Table 1). Furthermore, as each reporter type has advantages
and disadvantages, the choice of reporter used is critical when studying live-cell ERK activity. For instance,
FRET-based ERK reporters are spectrally limited to uorescent proteins (FPs) capable of FRET, such as
CFP/YFP. Alternatively, translocation-based reporters use only a single FP of any color, providing much more
exibility to combine with other reporters or uorescent markers [3,44]. Additional markers to distinguish the
nucleus from cytosol are still needed to quantify translocation reporters, and cells with complex three-
dimensional or dynamic shapes can be a signicant challenge to accurately quantify. Reporters also vary in the
timescale of ERK activity changes they can detect, with FRET reporters showing the fastest responses, followed
closely by translocation-based reporters, and degradation reporters being the slowest. While rapid reporter
responses are needed to accurately distinguish closely grouped pulses of ERK activity, the slow responses of a
degradation-based reporter can be very useful for measuring the integrated activity of ERK over time
[31,45,46].
In most cases, the specicity of ERK reporters is high, as judged by the ability of either MEK or ERK inhibitors
to eliminate their signal. However, one notable exception is the tendency of FRET and translocation-based repor-
ters to show a non-ERK-specic increase in activity late in the cell cycle. This non-specic response is attributable
to the fact that the ERK substrate sequences used in many of the existing reporters can also be phosphorylated by
cyclin-dependent kinases (CDKs) that are most active in the G2 and M phases [32], causing a slow increase in
reporter signal that is resistant to MEK or ERK inhibitors and rapidly disappears following cell division [47]. In
our experience, the onset of this non-specic activity varies between cell lines; some cells show an increase in
non-specicsignal12 h prior to mitosis while others show a much longer period of accumulation. A recent set
of FRET-based reporters derived from the EKAR-EV reporter, EKAR-EN4 and EKAR-EN5, addressed this
problem by mutating two residues in the target phosphorylation sequence to eliminate the CDK afnity [48].
An ongoing challenge for accurate reporter readouts lies in quantifying the intensity of ERK activity. This is an
inherently difcult problem, as ERK activityat any given time is not a uniform parameter across the cell. In add-
ition to spatial variability, different endogenous substrates can be phosphorylated to different extents, depending
on the afnity of the substrate-kinase interaction [49]. Thus, any individual reporter is inherently limited to a
single perspectiveon ERK activity, while the set of endogenous ERK substrates represents multiple perspectives.
Combining multiple ERK reporters in the same cell has been a useful exercise to show how the same pulse of
ERK activity can be received differently by alternate targets [5052]. These studies show that FRET and transloca-
tion-based ERK reporters agree in large part, but they also reveal subtle differences in on-rate and off-rate.
Another key difference is in the measured amplitude of ERK activity. Dual readouts highlight systematic
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1891
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
Table 1 Genetically Encoded ERK activity Biosensors grouped based on their sensing modality
Reporter
Type
Reporter
name
(aliases)
Subcellular
Resolution
of ERK
activity Dynamic Range
Response Time
(approx.) Sensitivity Fluorescent Protein(s)
Cell Shape
Sensitivity
CDK
Sensitivity Reference
FP-fused
ERK
FP-ERK
(BFP-ERK,
(GFP-ERK)
No + 3min + BFP, GFP * Yes No [52,79,185]
Degron FIRE No +++ 150 min +++ mVenus * No No [31]
Kinase
Translocation
Reporter
(KTR)
ERK-KTR
(ERKKTR,
ERKTR)
No ++++ 3 min +++ Clover * Yes Yes [3]
Forster
Resonance
Energy
Transfer
(FRET)
EKAR Yes + 1 min ++ mVenus, mCerulean No Yes [27]
EKAREV
(EKARev,
EKAR-EV)
Yes ++ 1 min ++ YPet, ECFP No Yes [181]
EKAR2G1 Yes + 1 min + cp173Venus, cp227mTFP1 No Yes [182]
EKAR-TVV Yes ++ 1 min ++ cp173Venus-Venus, mTurquoise No Yes [53,182]
RAB-
EKARev
Yes ++ 5 min NA ddRFP-A, ddRFP-B No Unknown [183]
FPX-EKAR Yes + (50% of EKARev) 5 min + Red-ddFP, Green-ddFP, ddFP (B) No Unknown [184]
EKAR3 Yes + 1 min ++ YPet, mTurquoise2 No Yes [50]
EKAR4 Yes +++ 1 min ++ ECFP, YPet No No [36]
EKAR-EN4
(EKAREN4)
Yes +++ 1 min ++ ECFP, YPet No No [48]
EKAR-EN5
(EKAREN5)
Yes +++ 1 min +++ YPet, mTurquoise2 No No [48]
Fluorescent protein fused ERK (FP-ERK) translocates partially to the nucleus when phosphorylated by MEK allowing average cellular activity to be estimated by the nuclear to cytosolic fluorescence ratio. The
Degron reporter (FIRE) is stabilized upon phosphorylation by ERK such that its fluorescence indicates ERK activity on a scale of 3-12 hours. Upon phosphorylation, KTR reporters shift in their preference for nuclear
import vs. export allowing their nuclear vs. cytosolic ratio to reflect the average cellular ERK activity on the scale of minutes. FRET reporters shift in conformation upon phosphorylation by ERK allowing the ratio of
fluorescent protein intensities to reflect subcellular ERK activity on the scale of minutes. Subcellular resolution of ERK activity: yes indicates the capability for the reporter to be localized to different subcellular
compartments and to therefore reflect the activity of a specific region. Response Time: an estimate of time from ERK activation to apparent localization/fluorescence change. Cell Shape Sensitivity: the apparent
read-out of translocation-based reporters can be shifted independently of ERK by changes in cell shape. Cyclin Dependent Kinase (CDK) sensitivity: Some reporters can be phosphorylated independently of ERK
by Cyclin Dependent Kinases.
* any fluorescent protein can be theoretically used.
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY).1892
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
differences in dynamic range between reporters. For example, the FRET reporter EKAR3 shows greater sensitivity
than ERK-KTR to small ERK activity changes but saturates easily [51]. While the dynamic range of FRET-based
reporters has increased [48,53], a head-to-head comparison between the newest FRET reporters and translocation
reporters to assess their relative advantages has not yet been performed. Altogether, these differences emphasize
the caveat that the amplitude of ERK reporter signals must be interpreted with caution and not as an absolute
linear measurement. We discuss these quantitative issues in more depth in Box 2.
BOX 2. Rigor and Challenges in Quantication
and Analysis
Reporter Calibration For true quantitative measurements of ERK activity, two problems must be
dealt with. First, the reporter signal itself must have its linear range of response characterized.
This can be done by western blotting, to relate the fraction of the reporter in its phosphorylated
form to its readout detected by FRET [83,158]. When performed carefully, reporter signals can be
interpreted quantitatively, relative to the maximal signal, and any non-linear regions of the
readout can be identied. Second, the reporter readout must be linked to the level of ERK activity
in the cell. This calibration can be approached by relating ERK FRET readouts to immunoblots on
parallel samples that measure the fraction of ERK phosphorylation or endogenous ERK substrate
phosphorylation. However, a crucial caveat is that ERK reporters indicate not simply ERK activity,
but instead the balance of ERK activity relative to any phosphatase activity on the reporters ERK
target site. The rapid reversibility of reporter signals upon ERK inhibition indicates high cellular
phosphatase activity, and it seems reasonable that these phosphatases are the same ones that
act on endogenous ERK substrates. However, this assumption has not been established experi-
mentally. Any change in this phosphatase activity will affect the relationship between ERK activity
and the observed reporter signal. This complicating factor can be approached by mathematically
modeling both ERK and phosphatase effects on the reporter, or by empirically determining the
relationship between phosphorylated ERK and the reporter signal [83]. While often overlooked,
phosphatase activity may be one of the main drivers of heterogeneity in observed ERK readouts,
both within and between cell types.
Quantifying features in time series data Once live-cell data is collected, one must choose the
appropriate technique to mathematically describe, or featurize, the time-dependent signal of
ERK activity. Several mathematical methods are available to extract information from time series
data [159]. Pulse detection algorithms identify peaks of signal activity and then quantify para-
meters such as signal amplitude, pulse duration, or frequency (Figure 2A)[160,161]. Other
methods include Fourier and wavelet transformation [162,163], which decompose time series
measurements into simpler components (which, added together, reconstruct the original signal).
With any of these methods, the challenge lies in identifying the information that is most relevant
for the cellular process under study, whether it be the amplitude, duration, average, or another
aspect of ERK activity. Typically, it is necessary to experiment with more than one method to
quantify the relationship of interest.
Clustering cells by dynamics Parsing cells with similar reporter activity is often necessary as a
rst step during analysis. This task is not trivial as cellular kinetic data frequently have overlapping
distributions, and thus determining the appropriate number of clusters is often arbitrary. A critical
consideration is whether to predene the number of clusters or allow the algorithm to determine
the nal number of groupings. There are many clustering functions to choose from, including
K-means clustering, hierarchical clustering, K-nearest neighbor, and other deep learning-based
methods. Another important consideration is which distance metric to use; dynamic time warping
has proved to be one useful approach, which allows signals that are similar in shape but have dif-
ferent timing to be grouped together [164]. Each of these approaches require signicant user
input which must be guided by awareness of algorithm limitations and the structure of the data.
As a result, clustering can be challenging to implement in exploratory research.
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1893
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
Deep learning and neural networks offer a more sophisticated approach to classify dynamic
signaling behaviors. Rather than directly breaking down signals into unique characteristics, neural
networks are trained to recognize distinguishing features in the data. A recent example of this is
CODEX, which can recognize dynamic prototypesfor signal behavior that can be used to group
similarly behaving cells [157]. This method allows a computer to learn which patterns distinguish
signal activity between specied categories, such as treatment conditions. Although these
methods allow for analysis of large, multidimensional datasets, it can be difcult for humans to
understand the abstract patterns that the algorithms learn. CODEX resolves this issue by provid-
ing prototypical time trajectories for each of the categories it identies. An additional advantage
is that CODEX can be used on datasets where multiple biosensors are measured in the same
cell. Thus, with the increasing size and complexity of reporter datasets, deep learning methods
provide an attractive tool to facilitate data interpretation.
Another current challenge lies in extracting meaningful information from the hundreds or thousands of cells
that are interrogated in a typical live-cell imaging experiment. The rst step in this process is the extraction of
ERK activity tracesfrom image datasets, which can now be performed automatically using various segmenta-
tion and tracking algorithms [5456]. While this step was often rate-limiting in the past, advances in computa-
tional image analysis have made it routine. In particular, machine learning software such as StarDist and
CellPose have greatly increased the reliability of automated cell recognition [57,58]. Tracking algorithms, such
as uTrack [59] and EllipTrack [60], link cells from one image frame to the next, creating a time-series vector
for each cell. Typically, it is possible to track over 90% of cells in each experiment; however, tracking efciency
is reduced by abnormal cell morphology, over-conuency, fast migration, or cell death. Despite these limita-
tions, recent studies have used data from thousands or even hundreds of thousands of cells to draw statistically
well-supported conclusions. Subsequent challenges emerge in the analysis of high-content time-series data,
which we briey discuss in Box 2.
Modeling the mechanisms driving dynamics
The question of how different forms of ERK dynamics are generated at the molecular level has captured scien-
tic interest for at least 30 years [9]. Approaches to this question have spanned structural analysis, subcellular
localization, and mass-action kinetic modeling [33,6166]. Many mechanistic details can shape the dynamic
behavior of ERK, and here we group these mechanisms into several overarching concepts and discuss the evolu-
tion of mathematical models that explore these factors. Computational models play an increasingly essential
role in this question because the complexity of multiple layers of regulation makes it difcult or impossible to
predict system behavior from intuition alone. A major caveat that applies across these studies is that many
mathematical models pre-date the ability to track ERK activity in live cells. Consequently, many published
models, although intended to represent a prototypical cell, have been t only to population-average data, which
does not always accurately represent the true behavior of any individual cell. Thus, conclusions from models
must be interpreted with caution in cases where it is unknown how single cells differ from the mean.
Predominance of RTKs in setting ERK dynamics
From the earliest studies of ERK signaling, it was observed that ligands for different receptor tyrosine kinases
(RTKs) can specify distinct activity kinetics [24]. These receptor-specic patterns can be attributed either to
differential binding of adaptor and RAS-family G proteins to the receptor [67], or to differences in the kinetics
of receptor dimerization, internalization, degradation, and recycling [9,68]. Dimerized EGFR molecules
perform autophosphorylation of their partners, which targets them for internalization by both clathrin-
mediated and clathrin-independent mechanisms [69,70]. Although the receptor may continue to signal from
endosomal compartments of the cell, this internalization ultimately results in EGFR inactivation and transient
ERK activation (Box 1B) [68,71]. Numerous mathematical models of ERK signaling have incorporated the
mechanisms of receptor processing as a focus of regulation [21,61,7278]. These models enabled the explor-
ation of how receptor internalization rates determine the duration of ERK activity and predict responses to dif-
ferent EGF levels.
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY).1894
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
The importance of receptor kinetics is underscored by converging evidence that ERK activity tracks very
closely with RTK activity. When ERK activity is stimulated by light-induced optogenetic constructs upstream
of RAS, the activity follows the intensity of light stimulation with very little lag or adaptation [79,80]. This
memorylessbehavior is surprising given that several downstream negative feedback loops (detailed in the next
section) are operative under these conditions and would be expected to complicate the signal dynamics.
However, a strong correlation between upstream initiation and ERK output has been observed in multiple
(A)
(B)
Figure 2. Feedback mutants and regulators of ERK pulse dynamics.
(A) Dynamic features of ERK activity and genes that have been shown to positively or negatively regulate them. This list is
curated from experiments where ERK activity features were measured after knockdown or knockout (KD/KO) of respective
genes. KD/KO of positive regulators resulted in a net decrease or delay of ERK activity, while KD/KO of negative regulators
resulted in a net increase or acceleration of ERK activity. Most experiments were performed at single-cell resolution [81], or
from western blot experiments (indicated in bold) [2]. (B) Comparison of experimental techniques to investigate the strength of
negative feedback. Left: ERK inhibits both MEK and RAF. Middle: Experimental knockdown of Raf weakens negative feedback
from ERK; however, signaling from RAF to MEK will also be disrupted. Right: Feedback-insensitive mutants only weaken the
negative feedback from ERK, and allow for wild-type RAF to MEK signaling.
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1895
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
systems, regardless of whether the signaling is initiated at the level of RAS or the intracellular domain of RTKs
[81]. Further corroborating this concept are data showing that ERK activity terminates within seconds to
minutes upon RTK inhibition [50,73], and that ERK activity tracks dynamically with receptor phosphorylation
across different receptors [82].
A further line of evidence for the importance of receptors in dynamics is that oncogenic or activating muta-
tions in proteins downstream of the receptor, including RAS, RAF, or MEK, generally promote sustained ERK
activity in single cells (Box 1A) [52,83]. In contrast, manipulating the activity of the receptors results in
changes in pulse frequency. Together, these data argue that the tendency toward transient or sustained activity
of ERK is primarily a reection of the activation and deactivation of the ligand-bound receptor, in at least
several commonly studied cell types. However, under more atypical experimental conditions, the regulation of
EGFR internalization can result in surprising behavior. Under conditions in which EGF is slowly ramped to
high concentrations, receptors become down-regulated and fail to activate ERK [84]. This adaptation persists
for hours, and even withdrawal of EGF for several hours and subsequent re-stimulation does not elicit ERK
activation. Thus, receptor-level regulation also acts as a noise lter to reduce spurious ERK activity in the face
of incremental or gradual ligand changes. More generally, this study implies that an important area to rene
models of EGFR internalization and feedback is in the response to complex but physiologically relevant stimu-
lation patterns that deviate from simple bolus treatments.
It is also important to note that while studies of ERK activation and dynamics have focused heavily on recep-
tor tyrosine kinase signaling, ERK can be activated in a number of other ways. G protein-coupled receptor
(GPCR) signaling activates ERK through arrestin [85], a key regulatory scaffold protein that binds to GPCR
tails upon activation, and through arrestin-independent mechanisms [86]. Ligands for different GPCRs can
generate distinct ERK and Protein Kinase B (AKT) activity responses [87]. Protein kinase C is also capable of
activating RAF [88], as are cellular oscillations of calcium [89], providing additional inputs to ERK signaling.
Physiologically, it is likely that cells simultaneously receive multiple stimuli, and understanding the dynamics
induced by these combinations at the single-cell level is an underexplored area for further study.
Additional regulation by downstream negative feedback loops
Another essential feature of ERK regulation is an intricate negative feedback structure. Active ERK can nega-
tively regulate several upstream targets, including EGFR [90], MEK1 [91], RAF [92], or SOS [93,94]. Still
another level of negative feedback is the ERK-mediated transcriptional induction of phosphatase genes, such as
the dual specicity phosphatases (DUSPs) and MAPK phosphatases (MKPs) [95]. Increased expression of
DUSPs and MKPs leads to dephosphorylation of the MAP kinases, reducing their activity. The net result of
these seemingly redundant negative feedback mechanisms is a strong tendency of ERK activity to fall sharply
within 1530 min after its peak activation, even independently of the receptor internalization described above,
to enforce the transient pulse shape observed in many cell types (Box 1B). In contrast, systems with weaker col-
lective negative feedback show sustained signaling (Box 1A) [20,61,67]. Studies combining both modeling and
experiments have built a consensus that negative feedback loops vary in their relative importance, explaining
the diverse ERK dynamics found across different cell types [72,96,97].
One of the most thorough efforts to deconvolve feedback mechanisms in ERK dynamics was a pathway-wide
RNAi screen of 50 MAPK genes by Dessauges et al. [81]. With its large-scale and detailed analysis employing
optogenetic stimulation at different points in the pathway, this landmark study provided two important conclu-
sions. First, a number of subtle changes in ERK dynamics resulted from knocking down certain genes, includ-
ing CRAF, RSK2, PP2A, and PLCG1 (Figure 2A), several of which are involved in negative feedback. Some of
these knockdowns led to increased oscillatory behavior, while others moderately increased ERK amplitude.
Second, this study underscores the remaining challenge of disentangling highly redundant signaling systems. In
many cases, ERK activation was not affected by the knockdown of core pathway genes such as ERK2, GRB2, or
SOS2, likely because additional isoforms of these proteins maintained their function. Perhaps most strikingly,
the authors found that even this extensive dataset was still insufcient to fully specify a multi-feedback compu-
tational model. Thus, the redundancy of negative feedback loops continues to be a formidable challenge for
both experiments and modeling.
While computational models can capture basic ERK kinetics using one or more of these feedback loops
[19,72,76,98], it is difcult to verify that these models capture the underlying biology. Due to the redundancy
of feedback circuitry (Figure 2B, left), isolating single feedback loops is experimentally difcult. Simple knock-
down or overexpression experiments are often limited in their ability to test feedback loop functions because
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY).1896
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
they would change both the forward and the feedback effects of the protein within the loop (Figure 2B,
middle). Ideally, feedback nodes could be isolated experimentally by replacing the proteins involved with
feedback-insensitive versions (Figure 2B, right). Such isolation would require either editing multiple sequences
in endogenous genes or expressing a mutated protein while simultaneously knocking out the endogenous
protein, both of which would be highly time-consuming. The closest examples to date ablate specic feedback
loops via phospho-insensitive RAF [92,99,100] or SOS mutations [93,101]. Consequently, current computa-
tional models likely suffer from overtting due to the large number of loops in the system and limited experi-
mental data to constrain these parameters. Future experiments aimed at accurately disentangling individual
feedback nodes, without altering the proteins forward signaling activity, will rene models and improve predic-
tion performance.
In addition to simply terminating pathway activation, negative feedback plays an important role in producing
linear ERK responses that are robust to noise [64,102]. Because ERK inhibits upstream pathway components,
the system takes on the topology of a negative feedback amplier, a design frequently used in engineering to
stabilize system output and reduce sensitivity to environmental perturbations. Acting in this fashion, pathway
inputs that would normally saturate ERK output instead show a graded linear response over a wide range of
stimuli [64,102]. Finally, another function of negative feedback is that it can render the amount of ERK activity
output insensitive to the total ERK protein level [103]. Together, these studies highlight the importance of
negative feedback in setting the system-level inputoutput properties of ERK activity and the need for models
to represent the multiple feedback loops accurately. A simplied interpretation that reconciles many of the
existing observations is that negative feedback loops within the RAFMEKERK cascade act on the scale of
seconds or minutes and provide linearity and robustness to the inputoutput behavior of this module, while
feedback at the receptor level varies the input to the cascade on a longer time scale, creating the overall form of
the dynamics. However, this concept has yet to be fully tested, both computationally and experimentally.
Pulsatile and oscillatory behavior due to cooperativity
In many systems, the ERK cascade exhibits evidence of cooperativity - that is, a steeply non-linear response
curve to ligands that tends toward full activation once stimulated [12,104,105]. In experiments using single-cell
assays, ERK activity often transitions rapidly from fully off to maximally active, with few intermediate responses
observed [12,32]. Cooperativity is important in allowing the ERK pathway to act as an excitable system in
which activity can propagate spatially, either within a cell or from cell to cell. This form of activity is referred
to as a trigger wave, and has been observed in various types of monolayer cultures, both in vitro and in vivo
[106109]. In the slime mold Dictyostelium, the RAS-linked signaling network displays excitability that allows
regions of RAS activity to propagate within individual cells [110].
The most comprehensive study of cooperative MAPK behavior has been carried out in Xenopus oocytes,
where cooperative activation is driven by positive feedback from MAPK to the MAPKKK Mos [11,111].
However, in other systems, the source of cooperativity has been more difcult to identify denitively. It has
been suggested that the requirement for dual phosphorylation of MEK and ERK enables cooperative behavior
of the cascade, and modeling of these effects shows that they are sufcient to create switch-like behavior or
oscillations in ERK/MAPK activity (e.g. Box 1D) [63]. Another potentially important positive feedback occurs
at the level of SOS, a guanine nucleotide exchange factor that mediates RAS activation by RTKs [112,113]. SOS
has two binding sites for RAS one at which it catalyzes guanine nucleotide exchange on RAS, and one at
which GTP-bound RAS binds and allosterically enhances exchange activity at the rst site. This allostery
creates a positive feedback loop, which has been proposed as the source of cooperative ERK activation in mam-
malian cells [104]. However, the observations that optogenetic stimulation either at the receptor level or the
SOS level fail to elicit cooperative activation of ERK suggest that these mechanisms alone are insufcient for
cooperativity [81]. Thus, similar to the situation of redundant negative feedbacks, there remains substantial dif-
culty in unambiguously establishing contributions of individual positive feedback mechanisms in most cell
types examined to date.
Despite the ambiguity in the molecular mechanism, it is likely that some combination of negative feedback
and cooperativity underlies the oscillatory or highly pulsatile behavior that has been observed for ERK in
various systems [30,114]. The rst demonstration of such a possibility used a model in which high cooperativity
(also known as ultrasensitivity) was coupled to negative feedback from ERK to RAF to produce oscillatory
behavior [19]. A number of other models have conrmed that such combinations can produce oscillatory
behavior. In a more recent example, Kochańczyk et al. [115] constructed a MAPK pathway model with one
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1897
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
positive feedback from Ras to SOS, and three negative feedbacks from ERK acting on MEK, RAF, and SOS.
They found that the positive feedback from Ras to SOS allows for bistable pathway activation, and the negative
feedback from ERK to SOS then refashions the networks bistable behavior into oscillatory patterns of ERK
activation. In this model, negative feedback from ERK to MEK and RAF primarily modulates the shape of ERK
activity pulses. Finally, similar models are supported by additional work from Arkun and Yesemi [116], who
argue that bistability and switch-like behavior arise from positive feedback from Ras to SOS, but add that
internal negative feedback from phosphatases allows for dampened oscillations.
Signal amplication and regulation through scaffold proteins
MAPK activity dynamics can also be shaped by the assembly of signaling complexes via scaffold proteins,
which simultaneously interact with multiple MAPK pathway components. Scaffolds can control both the
spatial distribution and activation of ERK within the cell and the temporal characteristics of activity by facili-
tating kinase-substrate interactions or shielding kinases from dephosphorylation [117119]. Scaffolds in the
MAPK pathway were initially found to be essential for S. cerevisiae pheromone responses, where Ste5 was
identied as a tether for multiple MAP kinases and later recognized for its role in shaping both graded and
switch-like signaling [120122]. Multicellular organisms lack obvious homologs of Ste5, but have other genes
that may play similar functions. KSR1 homologs were rst identied in Drosophila and C. elegans as positive
regulators of the MAPK pathway [123,124]. KSR1 is a pseudokinase with homology to RAF whose catalytic
activity has been debated; however, it was found to be capable of forming a complex with CRAF, MEK, and
ERK [125127]. Deletion of KSR1 in mouse embryonic broblasts reduces the intensity and duration of ERK
activation [128]. In single cells, Dessauges et al. [81] demonstrate that KSR1 positively regulates ERK activitys
amplitude, baseline, and adaptation (drop rate) but not its oscillations (Figure 2A). Another protein, SHOC2,
promotes the interaction of RAS and RAF, and enhances the intensity of ERK activation [129]. Further com-
plicating our understanding, experimental and computational evidence suggest that overexpression of some
scaffolds can actually hinder MAPK activation, suggesting that optimal concentrations of scaffolds are required
for efcient signaling [119,132]. Therefore, while KSR1, SHOC2, and other potential scaffolds such as IQGAP
and MP-1 contribute to the strength and duration of ERK signaling [132,133], their signicance relative to
other regulators in generating the differences in ERK dynamics between cell types or between individual cells
remains largely unexplored. Additional modeling analysis of pathway-wide datasets [81] could be used to
address this gap.
Autocrine/paracrine signaling as a source of sporadic pulses
While feedback and cooperativity can explain regular oscillations in ERK activity, irregular patterns of pulses
(Box 1E,F) indicate a strong source of variability. Several lines of evidence suggest that autocrine and para-
crine signaling through EGFR plays a dominant role in driving irregular pulsatile dynamics. Epithelial cells
secrete numerous EGFR ligands [134], each eliciting distinct ERK activities. For example, high-afnity
ligands, such as transforming growth factor α(TGF-α) rarely escape capture by the secreting cells own recep-
tors, and thus act primarily as an autocrine signal [135]. Lower-afnity ligands such as Amphiregulin
(AREG) can diffuse more broadly to stimulate surrounding cells. The release of these ligands is controlled by
matrix metalloproteinases (MMPs) on the cell surface that cleave the membrane anchor motif to release the
soluble mature forms into the extracellular space [136]. MMPs are in turn stimulated by ERK activity, which
effectively forms a positive feedback loop that operates across intracellular and extracellular compartments
[32,137]. In addition to canonical EGFR ligands, other growth factors, including those from the broblast
growth factor (FGF) family or G-protein coupled receptor (GPCR) ligands stimulate ERK and act in a para-
crine manner [87,138,139]. The combination of these different ligands and the irregular timing of their
release create a dynamically evolving microenvironment for the neighboring cells.
An additional layer of complexity arises from the fact that different EGFR ligands can trigger distinct pat-
terns of ERK activity even though they signal through the same receptor. Freed et al. [66] examined ligand-
specic EGFR dimer interactions and found that high-afnity ligands such as EGF or TGF-αcreate highly
stable EGFR dimers, whereas low-afnity ligands such as Epiregulin and Epigen (EREG and EPGN) form
weakly bound asymmetric dimers. The varying stability of these complexes results in differences in internaliza-
tion rate, effectively altering the strength of a key negative feedback. Strong EGFR binders (e.g. heparin-binding
EGF-like growth factor, betacellulin) target all EGFRs for lysosomal degradation and attenuate the signal [140].
As a result, EGFR molecules bound to EREG and EPGN are less subject to internalization and drive more
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY).1898
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
sustained ERK signaling [140]. Furthermore, differences in ligand dissociation from internalized EGFR allows
the receptors to be recycled to the plasma membrane surface rather than broken down, permitting rapid
re-activation by ligand and the potential for sustained ERK activation [140,141]. This multitude of activation
mechanisms further diversies the ERK responses that result from paracrine stimulation.
In in vivo imaging studies, some form of dynamic ERK pulses, resembling those described in cell culture,
have been observed in every case where single-cell resolution was available. The patterns of pulses vary depend-
ing on the tissue and organism. Examples of focal points of ERK activity that radially spread to neighboring
cells include the mouse epidermis [107] and Drosophila embryonic epithelium [142]. In some cases, ERK activ-
ity only travels limited distances (34 cell diameters), suggesting that propagation is limited by diffusion of the
ligand. However, in regenerating sh scales, wound healing, or cultured MDCK epithelial cells, waves of ERK
activation travel much farther, spreading out across dozens of cell layers. In these cases, ERK activity causes
shedding of EGFR ligands via MMPs, allowing for continued propagation of the wave [106108,143]. Other
cell systems show rapid, sporadic patterns of well-dened pulses with limited spatial correlation, suggesting
multiple overlapping sources [31,32]. At the extreme end of this continuum, cells containing oncogenic muta-
tions show a complex and seemingly stochastic pattern of ERK activity without clearly separated pulses, which
has been linked to increased secretion of AREG, a paracrine EGFR ligand [48,52,144]. In nearly all of these
cases, EGFR inhibition eliminates ERK pulses, conrming the importance of receptor-level regulation of these
patterns and dynamics. Thus, paracrine ligand secretion underlies a variety of highly dynamic ERK behavior.
Several mathematical models have been developed to simulate the propagation of ERK activation between
cells [32]. For instance, a spring model was used to investigate ERK-driven collective cell migration. In this
model, ERK activity increases the length of each cell and subsequently changes cell density and decreases
myosin light chain (MLC) phosphorylation. The model indicates that as ERK waves propagate through cells,
MLC dephosphorylation is sufcient for collective cell migration in the opposite direction of the ERK wave,
whereas cell density is not sufcient [143]. This model was restricted to observations in a one-dimensional
monolayer. Therefore, the spring model was transformed into a continuum model, which allows for a two-
dimensional analysis that accurately represents the 2D epithelial cell movement. The continuum model averages
the heterogenous and noisy properties of individual cells in order to successfully recapitulate tissue-level
dynamics driven by single cells [145]. Finally, biophysical models further our understanding of how monolayer
mechanics coupled to ERK translate to polarity changes and active cell migration [146].
Cell states create variability in ERK responses
Another prominent feature of ERK activation revealed by biosensors is cell-to-cell variation in activity pat-
terns. Even in cases where genetically identical cells respond to controlled spatial differences in stimulating
ligands, there is substantial divergence in the timing and intensity of ERK activation. Studies investigating
this phenomenon have found that the variation can be accounted for by pre-existing differences in cell state,
also termed extrinsic noise, rather than true stochastic behavior of the pathway, or intrinsic noise[147].
This nding is consistent with results from several other signaling pathways [148]andconrmed by a recent
study measuring dozens of cell state parameters, including local cell density, cell shape, and expression of
various non-pathway markers [149]. The latter study demonstrated that cell state, as indicated by factors such
as calreticulin, Sec13, and cell density may exert an even larger effect on a given cellsERKactivation(aswell
as for many other signaling pathways) as compared with different concentrations of EGF. This concept helps
to explain a disparate set of ndings that ERK pathway activation depends strongly on actin cytoskeletal pro-
trusions [150], the presence of caveolin pits in the plasma membrane [151], and the rate of glycolysis [152]. If
all of these non-canonicalmechanisms each impact ERK activation, the pathway can be considered not only
as an output of growth factor stimulation, but also as an integrated index of both intracellular and extracellu-
lar factors.
Conclusion
The diversity of ERK dynamics helps to explain how this ubiquitous pathway plays a variety of cell-specic
roles in controlling cell proliferation, differentiation, and migration. Collectively, the work highlighted here
demonstrates that ERK activation dynamics are well positioned to provide acute sensing of the extracellular
microenvironment, allowing cells to respond in unique ways to paracrine signals, cell density, and the extracel-
lular matrix. When connected to pathway outputs, such as gene expression, that are selectively responsive to
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1899
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
different dynamic patterns, the ERK pathway makes it possible for the cell to continuously adjust its state and
behavior based on its physical context. In the companion review, we consider the outputside of this function,
exploring how dynamics regulate gene expression. We also examine the potential for pharmacological inhibitors
of the ERK pathway to promote different cellular functions depending on how they affect ERK dynamics.
Fully understanding and exploiting the ERK signaling codewill depend on accurate quantitative models.
The rich history of pathway models that we discuss here has provided an excellent start in capturing the main
mechanisms driving dynamic ERK activity. Nonetheless, as the most recent work shows, a complete model that
accurately predicts the effects of pharmacological and genetic perturbations remains some distance away [81].
While existing models provide the conceptual building blocks to understand how dynamic behaviors arise,
many cell systems contain several of these mechanisms operating together. As noted above, predictive models
of highly redundant systems are challenging to validate, especially when relatively few experiments precisely
dissect of the component mechanisms. Furthermore, even in the absence of mutations, genetically identical
cells can diverge in their dynamics due to variations in the copy numbers of pathway proteins [153]. Such vari-
ation can explain the observed differences between cell types in an organism, and the heterogeneity of cells
within the same tissue. Fully modeling these differences would require information on the hundreds of para-
meters (i.e. protein concentrations) that vary between contexts, which remains experimentally challenging.
The new technologies highlighted here, including improvements in biosensors, image processing, and large
dataset analysis, will likely be critical in overcoming the remaining obstacles. Machine learning is an exploding
eld that has rapidly expanded into biology. From predicting protein structure, cell segmentation, and improv-
ing CRISPR guide RNA design, neural networks have pushed the boundaries of many elds [154156].
Recently, convolutional neural networks have been used to identify ERK patterns and characterize signaling
motifs in single cells [81,157]. These newer models are able to recognize objective and abstract patterns in
large-scale data; therefore, they are an approach that may fully connect signaling, gene expression, and cell
fates. Future work should be aimed at creating a model that connects network topology and the functional and
phenotypic consequences of signal propagation. Specically, how do the positive regulators of the pathway
shape the spatial and temporal activation and deactivation of ERK? What features of the pathway are most
important for regulation, and which are redundant? Furthermore, how important is the pathway topology for
generating dynamic patterns of gene expression? Although it is unlikely there will be one universal model that
represents all aspects of the pathway, future computational models can likely succeed in capturing the majority
of the signaling network circuitry and simulating the full range of dynamic behaviors of ERK.
Competing Interests
The authors declare that there are no competing interests associated with the manuscript.
Funding
This work was supported by National Institutes of Health grants R35GM139621, R01HL151983, and
R01GM115650, by the Department of Defense Neurobromatosis Research Program grant W81XWH-16-1-0085,
and by the American Association for Cancer Research Stand Up To Cancer Innovative Research Grant
SU2C-AACR-IRG-01-16. Stand up to Cancer (SU2C) is a program of the Entertainment Industry Foundation.
Research grants are administered by the American Association for Cancer Research, the scientic partner of
SU2C.
Open Access
Open access for this article was enabled by the participation of University of California in an all-inclusive Read &
Publish agreement with Portland Press and the Biochemical Society under a transformative agreement with UC.
CRediT Author Contribution
John Albeck: Conceptualization, Writing original draft, Writing review and editing. Abhineet Ram: Writing
original draft, Writing review and editing. Devan Murphy: Writing original draft, Writing review and
editing. Nicholaus DeCuzzi: Writing original draft, Writing review and editing. Madhura Patankar: Writing
review and editing. Jason Hu: Visualization. Michael Pargett: Writing review and editing.
Acknowledgements
We would like to thank Nont Kosaisawe for helpful discussions. All gures were created with BioRender.com.
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY).1900
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
Abbreviations
A431, epidermoid carcinoma cell line; AREG, amphiregulin; BRAF, v-Raf murine sarcoma viral oncogene
homolog B1; CRAF, RAF proto-oncogene serine/threonine-protein kinase; CRISPR, clustered regularly
interspaced short palindromic repeats; DMEM, Dulbeccos Modied Eagle Medium; DUSPs, dual specicity
phosphatases; EGF, epidermal growth factor; EGFR, epidermal growth factor receptor; EKAR, extracellular
signal-regulated kinase activity reporter; EPGN, Epigen; EREG, Epiregulin; ERK, extracellular signal-regulated
kinase; ERK2, mitogen-activated protein kinase coded by MAPK1 gene; ERK-FP, extracellular signal-regulated
kinase-fusion protein; ERK-KTR, extracellular signal-regulated kinase translocation reporter; FBS, fetal bovine
serum; FGF, broblast growth factor; FIRE, uorescent InsP3-responsive element; FRET, uorescence resonance
energy transfer; Fus3P, the mitogen-activated protein kinases promoting G1 arrest (S. Cervevisiae); G proteins,
guanine nucleotide-binding proteins; GPCR, G-protein coupled receptors; GRB2, growth factor receptor bound
protein 2; GTP, guanosine triphosphate; H1395, human lung adenocarcinoma epithelial cell line; H1666, human
bronchoalveolar carcinoma epithelial cell; HEK293T, human kidney epithelial cell line; HeLa, human cervical cell
line from Henrietta lacks; HMT-3255 S1, human breast epithelial cells; HRAS, Harvey rat sarcoma viral oncogene
homolog; IGF-1, insulin-like growth factor 1; IMP, insulin-like growth factor 2 messenger RNA-binding proteins;
KSR, kinase suppressor of Ras; MAPK, mitogen-activated protein kinase; MAPKKK, mitogen activates protein
kinase kinase kinase; MCF10A, human breast epithelial cell line; MDCK, Madin-Derby canine kidney; MEF,
mouse embryonic broblasts; MEK, mitogen-activated protein kinase kinase; MKPs, MAPK phosphatases; MLC,
myosin light chain; MMPs, matrix metalloproteinases; MP-1, MEK Parter 1; NCK2, noncatalytic region of tyrosine
kinase, Beta; NGF, nerve growth factor; NIH3T3, broblast cell line; NRK-52E, rat kidney epithelial cell lines;
ODE, ordinary differential equation; PC-12, rat pheochromocytoma cells; PEA-15, phosphoprotein enriched in
astrocytes; PKC, creatine phosphokinase; PLCG1, phospholipase C, Gamma 1; PP2A, protein phosphatase 2A;
PTK2, protein tyrosine kinase 2; RAF, rapid accelerated brosarcoma; Rap1, Ras-proximate-1; RAPGEF1, Rap
guanine nucleotide exchange factor 1; RAS, rat sarcoma virus; RASGPR1, RAS guanyl-releasing protein 1; RKIP,
Raf kinase inhibitory protein; RNA, ribonucleic acid; RNAi, RNA interference; RRAS, Ras-related protein R-Ras;
RSK2, ribosomal protein S6 kinase 2; RTK, receptor tyrosine kinases; Shc1, SHC adaptor protein 1; SHOC2,
Soc-2 suppressor of clear homolog; SNAP-β2AR, self-labeling protein tag-β2-adrenergic receptor; SOS, son of
sevenless; SPRY, Sprouty; TGFα, transforming growth factor alpha; TrkA, tropomyosin receptor kinase A;
YWHAG, 14-3-3 protein gamma protein; YWHAZ, tyrosine 3 monooxygenase activation protein zeta.
References
1 Lavoie, H., Gagnon, J. and Therrien, M. (2020) ERK signalling: a master regulator of cell behaviour, life and fate. Nat. Rev. Mol. Cell Biol. 21, 607632
https://doi.org/10.1038/s41580-020-0255-7
2 Ebisuya, M., Kondoh, K. and Nishida, E. (2005) The duration, magnitude and compartmentalization of ERK MAP kinase activity: mechanisms for
providing signaling specicity. J. Cell Sci. 118, 29973002 https://doi.org/10.1242/jcs.02505
3 Regot, S., Hughey, J.J., Bajar, B.T., Carrasco, S. and Covert, M.W. (2014) High-sensitivity measurements of multiple kinase activities in live single cells.
Cell 157, 17241734 https://doi.org/10.1016/j.cell.2014.04.039
4 Miura, H., Kondo, Y., Matsuda, M. and Aoki, K. (2018) Cell-to-cell heterogeneity in p38-mediated cross-inhibition of JNK causes stochastic cell death.
Cell Rep. 24, 26582668 https://doi.org/10.1016/j.celrep.2018.08.020
5 Hanson, R.L. and Batchelor, E. (2022) Coordination of MAPK and p53 dynamics in the cellular responses to DNA damage and oxidative stress. Mol.
Syst. Biol. 18, e11401 https://doi.org/10.15252/msb.202211401
6 Van Valen, D.A., Kudo, T., Lane, K.M., Macklin, D.N., Quach, N.T., DeFelice, M.M. et al. (2016) Deep learning automates the quantitative analysis of
individual cells in live-cell imaging experiments. PLoS Comput. Biol. 12, e1005177 https://doi.org/10.1371/journal.pcbi.1005177
7Bradeld, C.J., Liang, J.J., Ernst, O., John, S.P., Sun, J., Ganesan, S. et al. (2023) Biphasic JNK signaling reveals distinct MAP3K complexes licensing
inammasome formation and pyroptosis. Cell Death Differ. 30, 589604 https://doi.org/10.1038/s41418-022-01106-9
8 Kholodenko, B.N., Hancock, J.F. and Kolch, W. (2010) Signalling ballet in space and time. Nat. Rev. Mol. Cell Biol. 11, 414426 https://doi.org/10.
1038/nrm2901
9 Wells, A., Welsh, J.B., Lazar, C.S., Wiley, H.S., Gill, G.N. and Rosenfeld, M.G. (1990) Ligand-induced transformation by a noninternalizing epidermal
growth factor receptor. Science 247, 962964 https://doi.org/10.1126/science.2305263
10 Marshall, C.J. (1995) Specicity of receptor tyrosine kinase signaling: transient versus sustained extracellular signal-regulated kinase activation. Cell 80,
179185 https://doi.org/10.1016/0092-8674(95)90401-8
11 Ferrell, Jr, J.E. and Machleder, E.M. (1998) The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. Science 280, 895898
https://doi.org/10.1126/science.280.5365.895
12 Huang, C.Y. and Ferrell, Jr, J.E. (1996) Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc. Natl Acad. Sci. U.S.A. 93, 1007810083
https://doi.org/10.1073/pnas.93.19.10078
13 Murphy, L.O., Smith, S., Chen, R.-H., Fingar, D.C. and Blenis, J. (2002) Molecular interpretation of ERK signal duration by immediate early gene
products. Nat. Cell Biol. 4, 556564 https://doi.org/10.1038/ncb822
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1901
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
14 Murphy, L.O., MacKeigan, J.P. and Blenis, J. (2004) A network of immediate early gene products propagates subtle differences in mitogen-activated
protein kinase signal amplitude and duration. Mol. Cell. Biol. 24, 144153 https://doi.org/10.1128/MCB.24.1.144-153.2004
15 Cook, S.J., Aziz, N. and McMahon, M. (1999) The repertoire of fos and jun proteins expressed during the G1 phase of the cell cycle is determined by
the duration of mitogen-activated protein kinase activation. Mol. Cell. Biol. 19, 330341 https://doi.org/10.1128/MCB.19.1.330
16 Ferrell, Jr, J.E. and Ha, S.H. (2014) Ultrasensitivity part III: cascades, bistable switches, and oscillators. Trends Biochem. Sci. 39, 612618 https://doi.
org/10.1016/j.tibs.2014.10.002
17 Wiley, H.S., Herbst, J.J., Walsh, B.J., Lauffenburger, D.A., Rosenfeld, M.G. and Gill, G.N. (1991) The role of tyrosine kinase activity in endocytosis,
compartmentation, and down-regulation of the epidermal growth factor receptor. J. Biol. Chem. 266, 1108311094 https://doi.org/10.1016/
s0021-9258(18)99131-3
18 Kholodenko, B.N., Demin, O.V., Moehren, G. and Hoek, J.B. (1999) Quantication of short term signaling by the epidermal growth factor receptor.
J. Biol. Chem. 274, 3016930181 https://doi.org/10.1074/jbc.274.42.30169
19 Kholodenko, B.N. (2000) Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades.
Eur. J. Biochem. 267, 15831588 https://doi.org/10.1046/j.1432-1327.2000.01197.x
20 Brightman, F.A. and Fell, D.A. (2000) Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF
signalling in PC12 cells. FEBS Lett. 482, 169174 https://doi.org/10.1016/s0014-5793(00)02037-8
21 Orton, R.J., Sturm, O.E., Vyshemirsky, V., Calder, M., Gilbert, D.R. and Kolch, W. (2005) Computational modelling of the
receptor-tyrosine-kinase-activated MAPK pathway. Biochem. J 392, 249261 https://doi.org/10.1042/BJ20050908
22 Ahmed, S., Grant, K.G., Edwards, L.E., Rahman, A., Cirit, M., Goshe, M.B. et al. (2014) Data-driven modeling reconciles kinetics of ERK
phosphorylation, localization, and activity states. Mol. Syst. Biol. 10, 718 https://doi.org/10.1002/msb.134708
23 Cowley, S., Paterson, H., Kemp, P. and Marshall, C.J. (1994) Activation of MAP kinase kinase is necessary and sufcient for PC12 differentiation and
for transformation of NIH 3T3 cells. Cell 77, 841852 https://doi.org/10.1016/0092-8674(94)90133-3
24 Muroya, K., Hattori, S. and Nakamura, S. (1992) Nerve growth factor induces rapid accumulation of the GTP-bound form of p21ras in rat
pheochromocytoma PC12 cells. Oncogene 7, 277281 PMID:1549349
25 Nguyen, T.T., Scimeca, J.C., Filloux, C., Peraldi, P., Carpentier, J.L. and Van Obberghen, E. (1993) Co-regulation of the mitogen-activated protein
kinase, extracellular signal-regulated kinase 1, and the 90-kDa ribosomal S6 kinase in PC12 cells. Distinct effects of the neurotrophic factor, nerve
growth factor, and the mitogenic factor, epidermal growth factor. J. Biol. Chem. 268, 98039810 https://doi.org/10.1016/S0021-9258(18)98418-8
26 Green, H.M. and Alberola-Ila, J. (2005) Development of ERK activity sensor, an in vitro, FRET-based sensor of extracellular regulated kinase activity.
BMC Chem. Biol. 5,1https://doi.org/10.1186/1472-6769-5-1
27 Harvey, C.D., Ehrhardt, A.G., Cellurale, C., Zhong, H., Yasuda, R., Davis, R.J. et al. (2008) A genetically encoded uorescent sensor of ERK activity.
Proc. Natl Acad. Sci. U.S.A. 105, 1926419269 https://doi.org/10.1073/pnas.0804598105
28 Nakamura, A., Goto, Y., Kondo, Y. and Aoki, K. (2021) Shedding light on developmental ERK signaling with genetically encoded biosensors.
Development 148, dev199767 https://doi.org/10.1242/dev.199767
29 Ryu, H., Chung, M., Dobrzyn
ski, M., Fey, D., Blum, Y., Lee, S.S. et al. (2015) Frequency modulation of ERK activation dynamics rewires cell fate. Mol.
Syst. Biol. 11, 838 https://doi.org/10.15252/msb.20156458
30 Shankaran, H., Ippolito, D.L., Chrisler, W.B., Resat, H., Bollinger, N., Opresko, L.K. et al. (2009) Rapid and sustained nuclearcytoplasmic ERK
oscillations induced by epidermal growth factor. Mol. Syst. Biol. 5, 332 https://doi.org/10.1038/msb.2009.90
31 Albeck, J.G., Mills, G.B. and Brugge, J.S. (2013) Frequency-modulated pulses of ERK activity transmit quantitative proliferation signals. Mol. Cell 49,
249261 https://doi.org/10.1016/j.molcel.2012.11.002
32 Aoki, K., Kumagai, Y., Sakurai, A., Komatsu, N., Fujita, Y., Shionyu, C. et al. (2013) Stochastic ERK activation induced by noise and cell-to-cell
propagation regulates cell density-dependent proliferation. Mol. Cell 52, 529540 https://doi.org/10.1016/j.molcel.2013.09.015
33 Nakakuki, T., Birtwistle, M.R., Saeki, Y., Yumoto, N., Ide, K., Nagashima, T. et al. (2010) Ligand-specic c-Fos expression emerges from the
spatiotemporal control of ErbB network dynamics. Cell 141, 884896 https://doi.org/10.1016/j.cell.2010.03.054
34 Wortzel, I. and Seger, R. (2011) The ERK cascade: distinct functions within various subcellular organelles. Genes Cancer 2, 195209 https://doi.org/10.
1177/1947601911407328
35 Brunet, A., Roux, D., Lenormand, P., Dowd, S., Keyse, S. and Pouysségur, J. (1999) Nuclear translocation of p42/p44 mitogen-activated protein kinase
is required for growth factor-induced gene expression and cell cycle entry. EMBO J. 18, 664674 https://doi.org/10.1093/emboj/18.3.664
36 Keyes, J., Ganesan, A., Molinar-Inglis, O., Hamidzadeh, A., Zhang, J., Ling, M. et al. (2020) Signaling diversity enabled by Rap1-regulated plasma
membrane ERK with distinct temporal dynamics. eLife 9, e57410 https://doi.org/10.7554/eLife.57410
37 Wilson, M.Z., Ravindran, P.T., Lim, W.A. and Toettcher, J.E. (2017) Tracing information ow from Erk to target gene induction reveals mechanisms of
dynamic and combinatorial control. Mol. Cell 67, 757769.e5 https://doi.org/10.1016/j.molcel.2017.07.016
38 Raman, M., Chen, W. and Cobb, M.H. (2007) Differential regulation and properties of MAPKs. Oncogene 26, 31003112 https://doi.org/10.1038/sj.
onc.1210392
39 Malnou, C.E., Salem, T., Brockly, F., Wodrich, H., Piechaczyk, M. and Jariel-Encontre, I. (2007) Heterodimerization with Jun family members regulates
c-Fos nucleocytoplasmic trafc. J. Biol. Chem. 282, 3104631059 https://doi.org/10.1074/jbc.M702833200
40 Costa, M., Marchi, M., Cardarelli, F., Roy, A., Beltram, F., Maffei, L. et al. (2006) Dynamic regulation of ERK2 nuclear translocation and mobility in living
cells. J. Cell Sci. 119, 49524963 https://doi.org/10.1242/jcs.03272
41 Pouysségur, J., Volmat, V. and Lenormand, P. (2002) Fidelity and spatio-temporal control in MAP kinase (ERKs) signalling. Biochem. Pharmacol. 64,
755763 https://doi.org/10.1016/s0006-2952(02)01135-8
42 Lavaur, J., Bernard, F., Trilieff, P., Pascoli, V., Kappes, V., Pagès, C. et al. (2007) A TAT-DEF-Elk-1 peptide regulates the cytonuclear trafcking of
Elk-1 and controls cytoskeleton dynamics. J. Neurosci. 27, 1444814458 https://doi.org/10.1523/JNEUROSCI.2279-07.2007
43 Salinas, S., Briançon-Marjollet, A., Bossis, G., Lopez, M.-A., Piechaczyk, M., Jariel-Encontre, I. et al. (2004) SUMOylation regulates nucleo-cytoplasmic
shuttling of Elk-1. J. Cell Biol. 165, 767773 https://doi.org/10.1083/jcb.200310136
44 Kudo, T., Jeknic
, S., Macklin, D.N., Akhter, S., Hughey, J.J., Regot, S. et al. (2018) Live-cell measurements of kinase activity in single cells using
translocation reporters. Nat. Protoc. 13, 155169 https://doi.org/10.1038/nprot.2017.128
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY).1902
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
45 Benary, M., Bohn, S., Lüthen, M., Nolis, I.K., Blüthgen, N. and Loewer, A. (2020) Disentangling pro-mitotic signaling during cell cycle progression using
time-resolved single-cell imaging. Cell Rep. 31, 107514 https://doi.org/10.1016/j.celrep.2020.03.078
46 Brandt, R., Sell, T., Lüthen, M., Uhlitz, F., Klinger, B., Riemer, P. et al. (2019) Cell type-dependent differential activation of ERK by oncogenic KRAS in
colon cancer and intestinal epithelium. Nat. Commun. 10, 2919 https://doi.org/10.1038/s41467-019-10954-y
47 Gerosa, L., Chidley, C., Fröhlich, F., Sanchez, G., Lim, S.K., Muhlich, J. et al. (2020) Receptor-driven ERK pulses recongure MAPK signaling and
enable persistence of drug-adapted BRAF-mutant melanoma cells. Cell Syst 11, 478494.e9 https://doi.org/10.1016/j.cels.2020.10.002
48 Ponsioen, B., Post, J.B., Buissant des Amorie, J.R., Laskaris, D., van Ineveld, R.L., Kersten, S. et al. (2021) Quantifying single-cell ERK dynamics in
colorectal cancer organoids reveals EGFR as an amplier of oncogenic MAPK pathway signalling. Nat. Cell Biol. 23, 377390 https://doi.org/10.1038/
s41556-021-00654-5
49 Burkhard, K.A., Chen, F. and Shapiro, P. (2011) Quantitative analysis of ERK2 interactions with substrate proteins: roles for kinase docking domains and
activity in determining binding afnity. J. Biol. Chem. 286, 24772485 https://doi.org/10.1074/jbc.M110.177899
50 Sparta, B., Pargett, M., Minguet, M., Distor, K., Bell, G. and Albeck, J.G. (2015) Receptor level mechanisms are required for epidermal growth factor
(EGF)-stimulated extracellular signal-regulated kinase (ERK) activity pulses. J. Biol. Chem. 290, 2478424792 https://doi.org/10.1074/jbc.M115.
662247
51 Gillies, T.E., Pargett, M., Minguet, M., Davies, A.E. and Albeck, J.G. (2017) Linear integration of ERK activity predominates over persistence detection in
Fra-1 regulation. Cell Syst. 5, 549563.e5 https://doi.org/10.1016/j.cels.2017.10.019
52 Aikin, T.J., Peterson, A.F., Pokrass, M.J., Clark, H.R. and Regot, S. (2020) MAPK activity dynamics regulate non-cell autonomous effects of oncogene
expression. eLife 9, e60541 https://doi.org/10.7554/eLife.60541
53 Vandame, P., Spriet, C., Riquet, F., Trinel, D., Cailliau-Maggio, K. and Bodart, J.-F. (2014) Optimization of ERK activity biosensors for both ratiometric
and lifetime FRET measurements. Sensors 14, 11401154 https://doi.org/10.3390/s140101140
54 Pargett, M., Gillies, T.E., Teragawa, C.K., Sparta, B. and Albeck, J.G. (2017) Single-cell imaging of ERK signaling using uorescent biosensors. Methods
(Frangi, A., Schnabel, J., Davatzikos, C., Alberola-López, C. and Fichtinger, G. eds), Mol. Biol. 1636,3559 https://doi.org/10.1007/
978-1-4939-7154-1_3
55 Blum, Y., Fritz, R.D., Ryu, H. and Pertz, O. (2017) Measuring ERK activity dynamics in single living cells using FRET biosensors. Methods Mol. Biol.
1487, 203221 https://doi.org/10.1007/978-1-4939-6424-6_15
56 Bray, M.-A. and Carpenter, A.E. (2015) Cellproler tracer: exploring and validating high-throughput, time-lapse microscopy image data. BMC
Bioinformatics 16, 368 https://doi.org/10.1186/s12859-015-0759-x
57 Schmidt, U., Weigert, M., Broaddus, C. and Myers, G. (2018) Cell Detection with Star-Convex Polygons. In: Medical Image Computing and Computer
Assisted Intervention MICCAI 2018. MICCAI 2018. Lecture Notes in Computer Science, vol. 11071. Springer, Cham https://doi.org/10.1007/978-3-
030-00934-2_30
58 Stringer, C., Wang, T., Michaelos, M. and Pachitariu, M. (2021) Cellpose: a generalist algorithm for cellular segmentation. Nat. Methods 18, 100106
https://doi.org/10.1038/s41592-020-01018-x
59 Jaqaman, K., Loerke, D., Mettlen, M., Kuwata, H., Grinstein, S., Schmid, S.L. et al. (2008) Robust single-particle tracking in live-cell time-lapse
sequences. Nat. Methods 5, 695702 https://doi.org/10.1038/nmeth.1237
60 Tian, C., Yang, C. and Spencer, S.L. (2020) Elliptrack: a global-local cell-tracking pipeline for 2D uorescence time-lapse microscopy. Cell Rep. 32,
107984 https://doi.org/10.1016/j.celrep.2020.107984
61 Sasagawa, S., Ozaki, Y.-I., Fujita, K. and Kuroda, S. (2005) Prediction and validation of the distinct dynamics of transient and sustained ERK activation.
Nat. Cell Biol. 7, 365373 https://doi.org/10.1038/ncb1233
62 Filippi, S., Barnes, C.P., Kirk, P.D.W., Kudo, T., Kunida, K., McMahon, S.S. et al. (2016) Robustness of MEK-ERK dynamics and origins of cell-to-cell
variability in MAPK signaling. Cell Rep. 15, 25242535 https://doi.org/10.1016/j.celrep.2016.05.024
63 Markevich, N.I., Hoek, J.B. and Kholodenko, B.N. (2004) Signaling switches and bistability arising from multisite phosphorylation in protein kinase
cascades. J. Cell Biol. 164, 353359 https://doi.org/10.1083/jcb.200308060
64 Sturm, O.E., Orton, R., Grindlay, J., Birtwistle, M., Vyshemirsky, V., Gilbert, D. et al. (2010) The mammalian MAPK/ERK pathway exhibits properties of a
negative feedback amplier. Sci. Signal. 3, ra90 https://doi.org/10.1126/scisignal.2001212
65 Lemmon, M.A., Freed, D.M., Schlessinger, J. and Kiyatkin, A. (2016) The dark side of cell signaling: positive roles for negative regulators. Cell 164,
11721184 https://doi.org/10.1016/j.cell.2016.02.047
66 Freed, D.M., Bessman, N.J., Kiyatkin, A., Salazar-Cavazos, E., Byrne, P.O., Moore, J.O. et al. (2017) EGFR ligands differentially stabilize receptor dimers
to specify signaling kinetics. Cell 171, 683695.e18 https://doi.org/10.1016/j.cell.2017.09.017
67 Kao, S., Jaiswal, R.K., Kolch, W. and Landreth, G.E. (2001) Identication of the mechanisms regulating the differential activation of the mapk cascade
by epidermal growth factor and nerve growth factor in PC12 cells. J. Biol. Chem. 276, 1816918177 https://doi.org/10.1074/jbc.M008870200
68 Sorkin, A. and Goh, L.K. (2008) Endocytosis and intracellular trafcking of ErbBs. Exp. Cell Res. 314, 30933106 https://doi.org/10.1016/j.yexcr.2008.
08.013
69 Sigismund, S., Argenzio, E., Tosoni, D., Cavallaro, E., Polo, S. and Di Fiore, P.P. (2008) Clathrin-mediated internalization is essential for sustained EGFR
signaling but dispensable for degradation. Dev. Cell 15, 209219 https://doi.org/10.1016/j.devcel.2008.06.012
70 Jiang, X., Huang, F., Marusyk, A. and Sorkin, A. (2003) Grb2 regulates internalization of EGF receptors through clathrin-coated pits. Mol. Biol. Cell 14,
858870 https://doi.org/10.1091/mbc.e02-08-0532
71 Burke, P., Schooler, K. and Wiley, H.S. (2001) Regulation of epidermal growth factor receptor signaling by endocytosis and intracellular trafcking. Mol.
Biol. Cell 12, 18971910 https://doi.org/10.1091/mbc.12.6.1897
72 Chen, W.W., Schoeberl, B., Jasper, P.J., Niepel, M., Nielsen, U.B., Lauffenburger, D.A. et al. (2009) Input-output behavior of ErbB signaling pathways
as revealed by a mass action model trained against dynamic data. Mol. Syst. Biol. 5, 239 https://doi.org/10.1038/msb.2008.74
73 Kleiman, L.B., Maiwald, T., Conzelmann, H., Lauffenburger, D.A. and Sorger, P.K. (2011) Rapid phospho-turnover by receptor tyrosine kinases impacts
downstream signaling and drug binding. Mol. Cell 43, 723737 https://doi.org/10.1016/j.molcel.2011.07.014
74 Schoeberl, B., Eichler-Jonsson, C., Gilles, E.D. and Müller, G. (2002) Computational modeling of the dynamics of the MAP kinase cascade activated by
surface and internalized EGF receptors. Nat. Biotechnol. 20, 370375 https://doi.org/10.1038/nbt0402-370
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1903
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
75 Hendriks, B.S., Orr, G., Wells, A., Wiley, H.S. and Lauffenburger, D.A. (2005) Parsing ERK activation reveals quantitatively equivalent contributions from
epidermal growth factor receptor and HER2 in human mammary epithelial cells. J. Biol. Chem. 280, 61576169 https://doi.org/10.1074/jbc.
M410491200
76 Wiley, H.S., Shvartsman, S.Y. and Lauffenburger, D.A. (2003) Computational modeling of the EGF-receptor system: a paradigm for systems biology.
Trends Cell Biol. 13,4350 https://doi.org/10.1016/s0962-8924(02)00009-0
77 Santos, S.D.M., Verveer, P.J. and Bastiaens, P.I.H. (2007) Growth factor-induced MAPK network topology shapes Erk response determining PC-12 cell
fate. Nat. Cell Biol. 9, 324330 https://doi.org/10.1038/ncb1543
78 Starbuck, C. and Lauffenburger, D.A. (1992) Mathematical model for the effects of epidermal growth factor receptor trafcking dynamics on broblast
proliferation responses. Biotechnol. Prog. 8, 132143 https://doi.org/10.1021/bp00014a007
79 Toettcher, J.E., Weiner, O.D. and Lim, W.A. (2013) Using optogenetics to interrogate the dynamic control of signal transmission by the Ras/Erk module.
Cell 155, 14221434 https://doi.org/10.1016/j.cell.2013.11.004
80 Johnson, H.E., Goyal, Y., Pannucci, N.L., Schüpbach, T., Shvartsman, S.Y. and Toettcher, J.E. (2017) The spatiotemporal limits of developmental Erk
signaling. Dev. Cell 40, 185192 https://doi.org/10.1016/j.devcel.2016.12.002
81 Dessauges, C., Mikelson, J., Dobrzyn
ski, M., Jacques, M.-A., Frismantiene, A., Gagliardi, P.A. et al. (2022) Optogenetic actuator - ERK biosensor
circuits identify MAPK network nodes that shape ERK dynamics. Mol. Syst. Biol. 18, e10670 https://doi.org/10.15252/msb.202110670
82 Kiyatkin, A., van Alderwerelt van Rosenburgh, I.K., Klein, D.E. and Lemmon, M.A. (2020) Kinetics of receptor tyrosine kinase activation dene ERK
signaling dynamics. Sci. Signal. 13, eaaz5267 https://doi.org/10.1126/scisignal.aaz5267
83 Gillies, T.E., Pargett, M., Silva, J.M., Teragawa, C.K., McCormick, F. and Albeck, J.G. (2020) Oncogenic mutant RAS signaling activity is rescaled by the
ERK/MAPK pathway. Mol. Syst. Biol. 16, e9518 https://doi.org/10.15252/msb.20209518
84 Krause, H.B., Bondarowicz, H., Karls, A.L., McClean, M.N. and Kreeger, P.K. (2021) Design and implementation of a microuidic device capable of
temporal growth factor delivery reveal ltering capabilities of the EGFR/ERK pathway. APL Bioeng. 5, 046101 https://doi.org/10.1063/5.0059011
85 Luttrell, L.M., Roudabush, F.L., Choy, E.W., Miller, W.E., Field, M.E., Pierce, K.L. et al. (2001) Activation and targeting of extracellular signal-regulated
kinases by β-arrestin scaffolds. Proc. Natl Acad. Sci. U.S.A. 98, 24492454 https://doi.org/10.1073/pnas.041604898
86 OHayre, M., Eichel, K., Avino, S., Zhao, X., Steffen, D.J., Feng, X. et al. (2017) Genetic evidence that β-arrestins are dispensable for the initiation of
β2-adrenergic receptor signaling to ERK. Sci. Signal. 10, eaal3395 https://doi.org/10.1126/scisignal.aal3395
87 Chavez-Abiega, S., Grönloh, M.L.B., Gadella, T.W.J., Bruggeman, F.J. and Goedhart, J. (2022) Single-cell imaging of ERK and Akt activation dynamics
and heterogeneity induced by G-protein-coupled receptors. J. Cell Sci. 135, jcs259685 https://doi.org/10.1242/jcs.259685
88 Kolch, W., Heidecker, G., Kochs, G., Hummel, R., Vahidi, H., Mischak, H. et al. (1993) Protein kinase C alpha activates RAF-1 by direct phosphorylation.
Nature 364, 249252 https://doi.org/10.1038/364249a0
89 Kupzig, S., Walker, S.A. and Cullen, P.J. (2005) The frequencies of calcium oscillations are optimized for efcient calcium-mediated activation of Ras
and the ERK/MAPK cascade. Proc. Natl Acad. Sci. U.S.A. 102, 75777582 https://doi.org/10.1073/pnas.0409611102
90 Li, X., Huang, Y., Jiang, J. and Frank, S.J. (2008) ERK-dependent threonine phosphorylation of EGF receptor modulates receptor downregulation and
signaling. Cell. Signal. 20, 21452155 https://doi.org/10.1016/j.cellsig.2008.08.006
91 Catalanotti, F., Reyes, G., Jesenberger, V., Galabova-Kovacs, G., de Matos Simoes, R., Carugo, O. et al. (2009) A Mek1Mek2 heterodimer determines
the strength and duration of the Erk signal. Nat. Struct. Mol. Biol. 16, 294303 https://doi.org/10.1038/nsmb.1564
92 Ritt, D.A., Monson, D.M., Specht, S.I. and Morrison, D.K. (2010) Impact of feedback phosphorylation and Raf heterodimerization on normal and mutant
B-Raf signaling. Mol. Cell. Biol. 30, 806819 https://doi.org/10.1128/MCB.00569-09
93 Corbalan-Garcia, S., Yang, S.S., Degenhardt, K.R. and Bar-Sagi, D. (1996) Identication of the mitogen-activated protein kinase phosphorylation sites on
human Sos1 that regulate interaction with Grb2. Mol. Cell. Biol. 16, 56745682 https://doi.org/10.1128/MCB.16.10.5674
94 Kamioka, Y., Yasuda, S., Fujita, Y., Aoki, K. and Matsuda, M. (2010) Multiple decisive phosphorylation sites for the negative feedback regulation of SOS1
via ERK. J. Biol. Chem. 285, 3354033548 https://doi.org/10.1074/jbc.M110.135517
95 Amit, I., Citri, A., Shay, T., Lu, Y., Katz, M., Zhang, F. et al. (2007) A module of negative feedback regulators denes growth factor signaling. Nat.
Genet. 39, 503512 https://doi.org/10.1038/ng1987
96 Cirit, M., Wang, C.-C. and Haugh, J.M. (2010) Systematic quantication of negative feedback mechanisms in the extracellular signal-regulated kinase
(ERK) signaling network. J. Biol. Chem. 285, 3673636744 https://doi.org/10.1074/jbc.M110.148759
97 Orton, R.J., Sturm, O.E., Gormand, A., Wolch, W. and Gilbert, D.R. (2008) Computational modelling reveals feedback redundancy within the epidermal
growth factor receptor/extracellular-signal regulated kinase signalling pathway. IET Syst. Biol. 2, 173183 https://doi.org/10.1049/iet-syb:20070066
98 Kocieniewski, P. and Lipniacki, T. (2013) MEK1 and MEK2 differentially control the duration and amplitude of the ERK cascade response. Phys. Biol. 10,
035006 https://doi.org/10.1088/1478-3975/10/3/035006
99 Brummer, T., Naegele, H., Reth, M. and Misawa, Y. (2003) Identication of novel ERK-mediated feedback phosphorylation sites at the C-terminus of
B-Raf. Oncogene 22, 88238834 https://doi.org/10.1038/sj.onc.1207185
100 Dougherty, M.K., Müller, J., Ritt, D.A., Zhou, M., Zhou, X.Z., Copeland, T.D. et al. (2005) Regulation of Raf-1 by direct feedback phosphorylation. Mol.
Cell 17, 215224 https://doi.org/10.1016/j.molcel.2004.11.055
101 Saha, M., Carriere, A., Cheerathodi, M., Zhang, X., Lavoie, G., Rush, J. et al. (2012) RSK phosphorylates SOS1 creating 14-3-3-docking sites and
negatively regulating MAPK activation. Biochem. J. 447, 159166 https://doi.org/10.1042/BJ20120938
102 Nunns, H. and Goentoro, L. (2018) Signaling pathways as linear transmitters. eLife 7, e33617 https://doi.org/10.7554/eLife.33617
103 Fritsche-Guenther, R., Witzel, F., Sieber, A., Herr, R., Schmidt, N., Braun, S. et al. (2011) Strong negative feedback from Erk to Raf confers robustness
to MAPK signalling. Mol. Syst. Biol. 7, 489 https://doi.org/10.1038/msb.2011.27
104 Das, J., Ho, M., Zikherman, J., Govern, C., Yang, M., Weiss, A. et al. (2009) Digital signaling and hysteresis characterize ras activation in lymphoid
cells. Cell 136, 337351 https://doi.org/10.1016/j.cell.2008.11.051
105 Altan-Bonnet, G. and Germain, R.N. (2005) Modeling T cell antigen discrimination based on feedback control of digital ERK responses. PLoS Biol. 3,
e356 https://doi.org/10.1371/journal.pbio.0030356
106 De Simone, A., Evanitsky, M.N., Hayden, L., Cox, B.D., Wang, J., Tornini, V.A. et al. (2021) Control of osteoblast regeneration by a train of Erk activity
waves. Nature 590, 129133 https://doi.org/10.1038/s41586-020-03085-8
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY).1904
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
107 Hiratsuka, T., Fujita, Y., Naoki, H., Aoki, K., Kamioka, Y. and Matsuda, M. (2015) Intercellular propagation of extracellular signal-regulated kinase
activation revealed by in vivo imaging of mouse skin. eLife 4, e05178 https://doi.org/10.7554/eLife.05178
108 Lin, S., Hirayama, D., Maryu, G., Matsuda, K., Hino, N., Deguchi, E. et al. (2022) Redundant roles of EGFR ligands in the ERK activation waves during
collective cell migration. Life Sci. Alliance 5, e202101206 https://doi.org/10.26508/lsa.202101206
109 Ogura, Y., Wen, F.-L., Sami, M.M., Shibata, T. and Hayashi, S. (2018) A switch-like activation relay of EGFR-ERK signaling regulates a wave of cellular
contractility for epithelial invagination. Dev. Cell 46, 162172.e5 https://doi.org/10.1016/j.devcel.2018.06.004
110 Huang, C.-H., Tang, M., Shi, C., Iglesias, P.A. and Devreotes, P.N. (2013) An excitable signal integrator couples to an idling cytoskeletal oscillator to
drive cell migration. Nat. Cell Biol. 15, 13071316 https://doi.org/10.1038/ncb2859
111 Ferrell, Jr, J.E. (1999) Building a cellular switch: more lessons from a good egg. Bioessays 21, 866870 https://doi.org/10.1002/(SICI)1521-1878
(199910)21:10<866::AID-BIES9>3.0.CO;2-1
112 Gureasko, J., Galush, W.J., Boykevisch, S., Sondermann, H., Bar-Sagi, D., Groves, J.T. et al. (2008) Membrane-dependent signal integration by the Ras
activator Son of sevenless. Nat. Struct. Mol. Biol. 15, 452461 https://doi.org/10.1038/nsmb.1418
113 Margarit, S.M., Sondermann, H., Hall, B.E., Nagar, B., Hoelz, A., Pirruccello, M. et al. (2003) Structural evidence for feedback activation by Ras.GTP of
the Ras-specic nucleotide exchange factor SOS. Cell 112, 685695 https://doi.org/10.1016/s0092-8674(03)00149-1
114 Shankaran, H. and Wiley, H.S. (2010) Oscillatory dynamics of the extracellular signal-regulated kinase pathway. Curr. Opin. Genet. Dev. 20, 650655
https://doi.org/10.1016/j.gde.2010.08.002
115 Kochan
czyk, M., Kocieniewski, P., Kozłowska, E., Jaruszewicz-Błon
ska, J., Sparta, B., Pargett, M. et al. (2017) Relaxation oscillations and hierarchy of
feedbacks in MAPK signaling. Sci. Rep. 7, 38244 https://doi.org/10.1038/srep38244
116 Arkun, Y. and Yasemi, M. (2018) Dynamics and control of the ERK signaling pathway: sensitivity, bistability, and oscillations. PLoS ONE 13, e0195513
https://doi.org/10.1371/journal.pone.0195513
117 Park, S.-H., Zarrinpar, A. and Lim, W.A. (2003) Rewiring MAP kinase pathways using alternative scaffold assembly mechanisms. Science 299,
10611064 https://doi.org/10.1126/science.1076979
118 Witzel, F., Maddison, L. and Blüthgen, N. (2012) How scaffolds shape MAPK signaling: what we know and opportunities for systems approaches. Front.
Physiol. 3, 475 https://doi.org/10.3389/fphys.2012.00475
119 Levchenko, A., Bruck, J. and Sternberg, P.W. (2000) Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling
and reduce its threshold properties. Proc. Natl Acad. Sci. U.S.A. 97, 58185823 https://doi.org/10.1073/pnas.97.11.5818
120 Choi, K.Y., Satterberg, B., Lyons, D.M. and Elion, E.A. (1994) Ste5 tethers multiple protein kinases in the MAP kinase cascade required for mating in S.
cerevisiae.Cell 78, 499512 https://doi.org/10.1016/0092-8674(94)90427-8
121 Marcus, S., Polverino, A., Barr, M. and Wigler, M. (1994) Complexes between STE5 and components of the pheromone-responsive mitogen-activated
protein kinase module. Proc. Natl Acad. Sci. U.S.A. 91, 77627766 https://doi.org/10.1073/pnas.91.16.7762
122 Takahashi, S. and Pryciak, P.M. (2008) Membrane localization of scaffold proteins promotes graded signaling in the yeast MAP kinase cascade. Curr.
Biol. 18, 11841191 https://doi.org/10.1016/j.cub.2008.07.050
123 Kornfeld, K., Hom, D.B. and Horvitz, H.R. (1995) The ksr-1 gene encodes a novel protein kinase involved in Ras-mediated signaling in C. elegans.Cell
83, 903913 https://doi.org/10.1016/0092-8674(95)90206-6
124 Sundaram, M. and Han, M. (1995) The C. elegans ksr-1 gene encodes a novel Raf-related kinase involved in Ras-mediated signal transduction. Cell 83,
889901 https://doi.org/10.1016/0092-8674(95)90205-8
125 Yu, W., Fantl, W.J., Harrowe, G. and Williams, L.T. (1998) Regulation of the MAP kinase pathway by mammalian Ksr through direct interaction with MEK
and ERK. Curr. Biol. 8,5664 https://doi.org/10.1016/s0960-9822(98)70020-x
126 Morrison, D.K. (2001) KSR: a MAPK scaffold of the Ras pathway? J. Cell Sci. 114, 16091612 https://doi.org/10.1242/jcs.114.9.1609
127 Nguyen, A., Burack, W.R., Stock, J.L., Kortum, R., Chaika, O.V., Afkarian, M. et al. (2002) Kinase suppressor of Ras (KSR) is a scaffold which facilitates
mitogen-activated protein kinase activation in vivo.Mol. Cell. Biol. 22, 30353045 https://doi.org/10.1128/MCB.22.9.3035-3045.2002
128 Kortum, R.L. and Lewis, R.E. (2004) The molecular scaffold KSR1 regulates the proliferative and oncogenic potential of cells. Mol. Cell. Biol. 24,
44074416 https://doi.org/10.1128/MCB.24.10.4407-4416.2004
129 Sieburth, D.S., Sun, Q. and Han, M. (1998) SUR-8, a conserved Ras-binding protein with leucine-rich repeats, positively regulates Ras-mediated
signaling in C. elegans. Cell 94, 119130 https://doi.org/10.1016/s0092-8674(00)81227-1
130 Li, W., Han, M. and Guan, K.L. (2000) The leucine-rich repeat protein SUR-8 enhances MAP kinase activation and forms a complex with Ras and Raf.
Genes Dev. 14, 895900 https://doi.org/10.1101/gad.14.8.895
131 Matsunaga-Udagawa, R., Fujita, Y., Yoshiki, S., Terai, K., Kamioka, Y., Kiyokawa, E. et al. (2010) The scaffold protein Shoc2/SUR-8 accelerates the
interaction of Ras and Raf. J. Biol. Chem. 285, 78187826 https://doi.org/10.1074/jbc.M109.053975
132 Roy, M., Li, Z. and Sacks, D.B. (2005) IQGAP1 is a scaffold for mitogen-activated protein kinase signaling. Mol. Cell. Biol. 25, 79407952 https://doi.
org/10.1128/MCB.25.18.7940-7952.2005
133 Teis, D., Wunderlich, W. and Huber, L.A. (2002) Localization of the MP1-MAPK scaffold complex to endosomes is mediated by p14 and required for
signal transduction. Dev. Cell 3, 803814 https://doi.org/10.1016/s1534-5807(02)00364-7
134 Shi, T., Niepel, M., McDermott, J.E., Gao, Y., Nicora, C.D., Chrisler, W.B. et al. (2016) Conservation of protein abundance patterns reveals the regulatory
architecture of the EGFR-MAPK pathway. Sci. Signal. 9, rs6 https://doi.org/10.1126/scisignal.aaf0891
135 DeWitt, A., Iida, T., Lam, H.-Y., Hill, V., Wiley, H.S. and Lauffenburger, D.A. (2002) Afnity regulates spatial range of EGF receptor autocrine ligand
binding. Dev. Biol. 250, 305316 https://doi.org/10.1006/dbio.2002.0807
136 Löffek, S., Schilling, O. and Franzke, C.-W. (2011) Biological role of matrix metalloproteinases: a critical balance. Eur. Respir. J. 38, 191208
https://doi.org/10.1183/09031936.00146510
137 Kajanne, R., Miettinen, P., Mehlem, A., Leivonen, S.-K., Birrer, M., Foschi, M. et al. (2007) EGF-R regulates MMP function in broblasts through MAPK
and AP-1 pathways. J. Cell. Physiol. 212, 489497 https://doi.org/10.1002/jcp.21041
138 Tany, R., Goto, Y., Kondo, Y. and Aoki, K. (2022) Quantitative live-cell imaging of GPCR downstream signaling dynamics. Biochem. J. 479, 883900
https://doi.org/10.1042/BCJ20220021
© 2023 The Author(s). This is an open access article published by Portland Press Limited on behalf of the Biochemical Society and distributed under the Creative Commons Attribution License 4.0 (CC BY). 1905
Biochemical Journal (2023) 480 18871907
https://doi.org/10.1042/BCJ20230276
Downloaded from http://portlandpress.com/biochemj/article-pdf/480/23/1887/952239/bcj-2023-0276.pdf by guest on 07 December 2023
139 Simon, C.S., Rahman, S., Raina, D., Schröter, C. and Hadjantonakis, A.-K. (2020) Live visualization of ERK activity in the mouse blastocyst reveals
lineage-specic signaling dynamics. Dev. Cell 55, 341353.e5 https://doi.org/10.1016/j.devcel.2020.09.030
140 Roepstorff, K., Grandal, M.V., Henriksen, L., Knudsen, S.L.J., Lerdrup, M., Grøvdal, L. et al. (2009) Differential effects of EGFR ligands on endocytic
sorting of the receptor. Trafc10, 11151127 https://doi.org/10.1111/j.1600-0854.2009.00943.x
141 Waterman, H., Sabanai, I., Geiger, B. and Yarden, Y. (1998) Alternative intracellular routing of ErbB receptors may determine signaling potency. J. Biol.
Chem. 273, 1381913827 https://doi.org/10.1074/jbc.273.22.13819
142 Valon, L., Davidovic
, A., Levillayer, F., Villars, A., Chouly, M., Cerqueira-Campos, F. et al. (2021) Robustness of epithelial sealing is an emerging property
of local ERK feedback driven by cell elimination. Dev. Cell 56, 17001711.e8 https://doi.org/10.1016/j.devcel.2021.05.006
143 Aoki, K., Kondo, Y., Naoki, H., Hiratsuka, T., Itoh, R.E. and Matsuda, M. (2017) Propagating wave of ERK activation orients collective cell migration. Dev.
Cell 43, 305317.e5 https://doi.org/10.1016/j.devcel.2017.10.016
144 Davies, A.E., Pargett, M., Siebert, S., Gillies, T.E., Choi, Y., Tobin, S.J. et al. (2020) Systems-level properties of EGFR-RAS-ERK signaling amplify local
signals to generate dynamic gene expression heterogeneity. Cell Syst 11, 161175.e5 https://doi.org/10.1016/j.cels.2020.07.004
145 Asakura, Y., Kondo, Y., Aoki, K. and Naoki, H. (2021) Hierarchical modeling of mechano-chemical dynamics of epithelial sheets across cells and tissue.
Sci. Rep. 11, 4069 https://doi.org/10.1038/s41598-021-83396-6
146 Boocock, D., Hino, N., Ruzickova, N., Hirashima, T. and Hannezo, E. (2020) Theory of mechanochemical patterning and optimal migration in cell
monolayers. Nat. Phys. 17, 267274 https://doi.org/10.1038/s41567-020-01037-7
147 Selimkhanov, J., Taylor, B., Yao, J., Pilko, A., Albeck, J., Hoffmann, A. et al. (2014) Systems biology. Accurate information transmission through
dynamic biochemical signaling networks. Science 346, 13701373 https://doi.org/10.1126/science.1254933
148 Cheong, R., Rhee, A., Wang, C.J., Nemenman, I. and Levchenko, A. (2011) Information transduction capacity of noisy biochemical signaling networks.
Science 334, 354358 https://doi.org/10.1126/science.1204553
149 Kramer, B.A., Sarabia del Castillo, J. and Pelkmans, L. (2022) Multimodal perception links cellular state to decision making in single cells. Science 377,
642648 https://doi.org/10.1126/science.abf4062
150 Yang, J.-M., Bhattacharya, S., West-Foyle, H., Hung, C.-F., Wu, T.-C., Iglesias, P.A. et al. (2018) Integrating chemical and mechanical signals through
dynamic coupling between cellular protrusions and pulsed ERK activation. Nat. Commun. 9, 4673 https://doi.org/10.1038/s41467-018-07150-9
151 Kortum, R.L., Fernandez, M.R., Costanzo-Garvey, D.L., Johnson, H.J., Fisher, K.W., Volle, D.J. et al. (2014) Caveolin-1 is required for kinase suppressor
of Ras 1 (KSR1)-mediated extracellular signal-regulated kinase 1/2 activation, H-RasV12-induced senescence, and transformation. Mol. Cell. Biol. 34,
34613472 https://doi.org/10.1128/MCB.01633-13
152 Peeters, K., Van Leemputte, F., Fischer, B., Bonini, B.M., Quezada, H., Tsytlonok, M. et al. (2017) Fructose-1,6-bisphosphate couples glycolytic ux to
activation of Ras. Nat. Commun. 8, 922 https://doi.org/10.1038/s41467-017-01019-z
153 Niepel, M., Spencer, S.L. and Sorger, P.K. (2009) Non-genetic cell-to-cell variability and the consequences for pharmacology. Curr. Opin. Chem. Biol.
13, 556561 https://doi.org/10.1016/j.cbpa.2009.09.015
154 Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O. et al. (2021) Highly accurate protein structure prediction with AlphaFold.
Nature 596, 583589 https://doi.org/10.1038/s41586-021-03819-2
155 Meijering, E. (2012) Cell segmentation: 50 years down the road [Life Sciences]. IEEE Signal Process. Mag. 29, 140145 https://doi.org/10.1109/MSP.
2012.2204190
156 Kim, H.K., Min, S., Song, M., Jung, S., Choi, J.W., Kim, Y. et al. (2018) Deep learning improves prediction of CRISPRCpf1 guide RNA activity. Nat.
Biotechnol. 36, 239241 https://doi.org/10.1038/nbt.4061
157 Jacques, M.-A., Dobrzyn
ski, M., Gagliardi, P.A., Sznitman, R. and Pertz, O. (2021) CODEX, a neural network approach to explore signaling dynamics
landscapes. Mol. Syst. Biol. 17, e10026 https://doi.org/10.15252/msb.202010026
158 Kosaisawe, N., Sparta, B., Pargett, M., Teragawa, C.K. and Albeck, J.G. (2021) Transient phases of OXPHOS inhibitor resistance reveal underlying
metabolic heterogeneity in single cells. Cell Metab. 33, 649665.e8 https://doi.org/10.1016/j.cmet.2021.01.014
159 Fulcher, B.D. and Jones, N.S. (2017) Hctsa: a computational framework for automated time-series phenotyping using massive feature extraction. Cell
Syst. 5, 527531.e3 https://doi.org/10.1016/j.cels.2017.10.001
160 Pargett, M. and Albeck, J.G. (2018) Live-cell imaging and analysis with multiple genetically encoded reporters. Curr. Protoc. Cell Biol. 78,
4.36.14.36.19 https://doi.org/10.1002/cpcb.38
161 Foreman, R. and Wollman, R. (2020) Mammalian gene expression variability is explained by underlying cell state. Mol. Syst. Biol. 16, e9146 https://doi.
org/10.15252/msb.20199146
162 Geva-Zatorsky, N., Dekel, E., Batchelor, E., Lahav, G. and Alon, U. (2010) Fourier analysis and systems identication of the p53 feedback loop. Proc.
Natl Acad. Sci. U.S.A. 107, 1355013555 https://doi.org/10.1073/pnas.1001107107
163 Kobrinsky, E., Mager, D.E., Bentil, S.A., Murata, S.-I., Abernethy, D.R. and Soldatov, N.M. (2005) Identication of plasma membrane macro- and
microdomains from wavelet analysis of FRET microscopy. Biophys. J. 88, 36253634 https://doi.org/10.1529/biophysj.104.054056
164 Strasen, J., Sarma, U., Jentsch, M., Bohn, S., Sheng, C., Horbelt, D. et al. (2018) Cell-specic responses to the cytokine TGFβare determined by
variability in protein levels. Mol. Syst. Biol. 14, e7733 https://doi.org/10.15252/msb.20177733
165 Lazzara, M.J., Lane, K.,