[Show abstract][Hide abstract] ABSTRACT: Genetics and biochemistry have defined the components and wiring of the signaling pathways that pattern the embryo. Among them, the transforming growth factor β (TGF-β) pathway has the potential to behave as a morphogen: in vitro experiments established that it can dictate cell fate in a concentration-dependent manner. How morphogens convey positional information in a developing embryo, when signal levels change with time, is less understood. Using integrated microfluidic cell culture and time-lapse microscopy, we demonstrate here that the speed of ligand presentation has a key and previously unexpected influence on TGF-β signaling outcomes. The response to a TGF-β concentration step is transient and adaptive: slowly increasing the ligand concentration diminishes the response, and well-spaced pulses of ligand combine additively, resulting in greater pathway output than with constant stimulation. Our results suggest that in an embryonic context, the speed of change of ligand concentration is an instructive signal for patterning.
[Show abstract][Hide abstract] ABSTRACT: Embryos allocate cells to the three germ layers in a spatially ordered sequence. Human embryonic stem cells (hESCs) can generate the three germ layers in culture; however, differentiation is typically heterogeneous and spatially disordered. We show that geometric confinement is sufficient to trigger self-organized patterning in hESCs. In response to BMP4, colonies reproducibly differentiated to an outer trophectoderm-like ring, an inner ectodermal circle and a ring of mesendoderm expressing primitive-streak markers in between. Fates were defined relative to the boundary with a fixed length scale: small colonies corresponded to the outer layers of larger ones. Inhibitory signals limited the range of BMP4 signaling to the colony edge and induced a gradient of Activin-Nodal signaling that patterned mesendodermal fates. These results demonstrate that the intrinsic tendency of stem cells to make patterns can be harnessed by controlling colony geometries and provide a quantitative assay for studying paracrine signaling in early development.
[Show abstract][Hide abstract] ABSTRACT: Cells send and receive signals through pathways that have been defined in great detail biochemically, and it is often presumed that the signals convey only level information. Cell signaling in the presence of noise is extensively studied but only rarely is the speed required to make a decision considered. However, in the immune system, rapidly developing embryos, and cellular response to stress, fast and accurate actions are required. Statistical theory under the rubric of "exploit-explore" quantifies trade-offs between decision speed and accuracy and supplies rigorous performance bounds and algorithms that realize them. We show that common protein phosphorylation networks can implement optimal decision theory algorithms and speculate that the ubiquitous chemical modifications to receptors during signaling actually perform analog computations. We quantify performance trade-offs when the cellular system has incomplete knowledge of the data model. For the problem of sensing the time when the composition of a ligand mixture changes, we find a nonanalytic dependence on relative concentrations and specify the number of parameters needed for near-optimal performance and how to adjust them. The algorithms specify the minimal computation that has to take place on a single receptor before the information is pooled across the cell.
Proceedings of the National Academy of Sciences 09/2013; · 9.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Early T-cell activation is selected by evolution to discriminate a few foreign peptides rapidly from a vast excess of self-peptides, and it is unclear in quantitative terms how this is possible. We show that a generic proofreading cascade supplemented by a single negative feedback mediated by the Src homology 2 domain phosphatase-1 (SHP-1) accounts quantitatively for early T-cell activation, including the effects of antagonists. Modulation of the negative feedback with SHP-1 concentration explains counterintuitive experimental observations, such as the nonmonotonic behavior of receptor activity on agonist concentration, the digital vs. continuous behavior on certain parameters, and the loss of response for high SHP-1 concentration. New experiments validate predictions on the nontrivial joint dependence on binding time and concentration for the relative effect of two antagonists: We explain why strong antagonists behave as partial agonists at low concentration and predict that the relative effect of antagonists can invert as their concentrations are varied. By focusing on the phenotype, our model quantitatively fits a body of experimental data with minimal variables and parameters.
Proceedings of the National Academy of Sciences 03/2013; 110(10):E888-97. · 9.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Quantitative models of development that consider all relevant genes typically are difficult to fit to embryonic data alone and have many redundant parameters. Computational evolution supplies models of phenotype with relatively few variables and parameters that allows the patterning dynamics to be reduced to a geometrical picture for how the state of a cell moves. The clock and wavefront model, that defines the phenotype of somitogenesis, can be represented as a sequence of two discrete dynamical transitions (bifurcations). The expression-time to space map for Hox genes and the posterior dominance rule are phenotypes that naturally follow from computational evolution without considering the genetics of Hox regulation.
Current opinion in genetics & development 09/2012; · 8.99 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The computational evolution of gene networks functions like a forward genetic screen to generate, without preconceptions, all networks that can be assembled from a defined list of parts to implement a given function. Frequently networks are subject to multiple design criteria that cannot all be optimized simultaneously. To explore how these tradeoffs interact with evolution, we implement Pareto optimization in the context of gene network evolution. In response to a temporal pulse of a signal, we evolve networks whose output turns on slowly after the pulse begins, and shuts down rapidly when the pulse terminates. The best performing networks under our conditions do not fall into categories such as feed forward and negative feedback that also encode the input-output relation we used for selection. Pareto evolution can more efficiently search the space of networks than optimization based on a single ad hoc combination of the design criteria.
[Show abstract][Hide abstract] ABSTRACT: A temperature independent period and temperature entrainment are two defining features of circadian oscillators. A default model of distributed temperature compensation satisfies these basic facts yet is not easily reconciled with other properties of circadian clocks, such as many mutants with altered but temperature compensated periods. The default model also suggests that the shape of the circadian limit cycle and the associated phase response curves (PRC) will vary since the average concentrations of clock proteins change with temperature. We propose an alternative class of models where the twin properties of a fixed period and entrainment are structural and arise from an underlying adaptive system that buffers temperature changes. These models are distinguished by a PRC whose shape is temperature independent and orbits whose extrema are temperature independent. They are readily evolved by local, hill climbing, optimization of gene networks for a common quality measure of biological clocks, phase anticipation. Interestingly a standard realization of the Goodwin model for temperature compensation displays properties of adaptive rather than distributed temperature compensation.
[Show abstract][Hide abstract] ABSTRACT: The TGF-β pathway plays a vital role in development and disease and regulates transcription through a complex composed of receptor-regulated Smads (R-Smads) and Smad4. Extensive biochemical and genetic studies argue that the pathway is activated through R-Smad phosphorylation; however, the dynamics of signaling remain largely unexplored. We monitored signaling and transcriptional dynamics and found that although R-Smads stably translocate to the nucleus under continuous pathway stimulation, transcription of direct targets is transient. Surprisingly, Smad4 nuclear localization is confined to short pulses that coincide with transcriptional activity. Upon perturbation, the dynamics of transcription correlate with Smad4 nuclear localization rather than with R-Smad activity. In Xenopus embryos, Smad4 shows stereotyped, uncorrelated bursts of nuclear localization, but activated R-Smads are uniform. Thus, R-Smads relay graded information about ligand levels that is integrated with intrinsic temporal control reflected in Smad4 into the active signaling complex.
Proceedings of the National Academy of Sciences 06/2012; 109(28):E1947-56. · 9.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Developmental signaling networks are composed of dozens of components whose interactions are very difficult to quantify in an embryo. Geometric reasoning enumerates a discrete hierarchy of phenotypic models with a few composite variables whose parameters may be defined by in vivo data. Vulval development in the nematode Caenorhabditis elegans is a classic model for the integration of two signaling pathways; induction by EGF and lateral signaling through Notch. Existing data for the relative probabilities of the three possible terminal cell types in diverse genetic backgrounds as well as timed ablation of the inductive signal favor one geometric model and suffice to fit most of its parameters. The model is fully dynamic and encompasses both signaling and commitment. It then predicts the correlated cell fate probabilities for a cross between any two backgrounds/conditions. The two signaling pathways are combined additively, without interactions, and epistasis only arises from the nonlinear dynamical flow in the landscape defined by the geometric model. In this way, the model quantitatively fits genetic experiments purporting to show mutual pathway repression. The model quantifies the contributions of extrinsic vs. intrinsic sources of noise in the penetrance of mutant phenotypes in signaling hypomorphs and explains available experiments with no additional parameters. Data for anchor cell ablation fix the parameters needed to define Notch autocrine signaling.
Proceedings of the National Academy of Sciences 03/2012; 109(15):5568-75. · 9.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: During vertebrate embryogenesis, the expression of Hox genes that define anterior-posterior identity follows general rules: temporal colinearity and posterior prevalence. A mathematical measure for the quality or fitness of the embryonic pattern produced by a gene regulatory network is derived. Using this measure and in silico evolution we derive gene interaction networks for anterior-posterior (AP) patterning under two developmental paradigms. For patterning during growth (paradigm I), which is appropriate for vertebrates and short germ-band insects, the algorithm creates gene expression patterns reminiscent of Hox gene expression. The networks operate through a timer gene, the level of which measures developmental progression (a candidate is the widely conserved posterior morphogen Caudal). The timer gene provides a simple mechanism to coordinate patterning with growth rate. The timer, when expressed as a static spatial gradient, functions as a classical morphogen (paradigm II), providing a natural way to derive the AP patterning, as seen in long germ-band insects that express their Hox genes simultaneously, from the ancestral short germ-band system. Although the biochemistry of Hox regulation in higher vertebrates is complex, the actual spatiotemporal expression phenotype is not, and simple activation and repression by Hill functions suffices in our model. In silico evolution provides a quantitative demonstration that continuous positive selection can generate complex phenotypes from simple components by incremental evolution, as Darwin proposed.
Development 07/2010; 137(14):2385-95. · 6.60 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Many promoters in eukaryotes have nucleosome-depleted regions (NDRs) containing transcription factor binding sites. However, the functional significance of NDRs is not well understood. Here, we examine NDR function in two cell cycle-regulated promoters, CLN2pr and HOpr, by varying nucleosomal coverage of the binding sites of their activator, Swi4/Swi6 cell-cycle box (SCB)-binding factor (SBF), and probing the corresponding transcriptional activity in individual cells with time-lapse microscopy. Nucleosome-embedded SCBs do not significantly alter peak expression levels. Instead, they induce bimodal, "on/off" activation in individual cell cycles, which displays short-term memory, or epigenetic inheritance, from the mother cycle. In striking contrast, the same SCBs localized in NDR lead to highly reliable activation, once in every cell cycle. We further demonstrate that the high variability in Cln2p expression induced by the nucleosomal SCBs reduces cell fitness. Therefore, we propose that the NDR function in limiting stochasticity in gene expression promotes the ubiquity and conservation of promoter NDR. PAPERCLIP:
[Show abstract][Hide abstract] ABSTRACT: Budding yeast cells irreversibly commit to a new division cycle at a regulatory transition called Start. This essential decision-making step involves the activation of the SBF/MBF transcription factors. SBF/MBF promote expression of the G1 cyclins encoded by CLN1 and CLN2. Cln1,2 can activate their own expression by inactivating the Whi5 repressor of SBF/MBF. The resulting transcriptional positive feedback provides an appealing, but as yet unproven, candidate for generating irreversibility of Start. Here, we investigate the logic of the Start regulatory module by quantitative single-cell time-lapse microscopy, using strains in which expression of key regulators is efficiently controlled by changes of inducers in a microfluidic chamber. We show that Start activation is ultrasensitive to G1 cyclin. In the absence of CLN1,2-dependent positive feedback, we observe that Start transit is reversible, due to reactivation of the Whi5 transcriptional repressor. Introduction of the positive feedback loop makes Whi5 inactivation and Start activation irreversible, which therefore guarantees unidirectional entry into S phase. A simple mathematical model to describe G1 cyclin turn on at Start, entirely constrained by empirically measured parameters, shows that the experimentally measured ultrasensitivity and transcriptional positive feedback are necessary and sufficient dynamical characteristics to make the Start transition a bistable and irreversible switch. Our study thus demonstrates that Start irreversibility is a property that arises from the architecture of the system (Whi5/SBF/Cln2 loop), rather than the consequence of the regulation of a single component (e.g., irreversible protein degradation).
[Show abstract][Hide abstract] ABSTRACT: Metazoan organisms can 'scale', that is, maintain similar proportions regardless of size. Ben-Zvi et al. use experiments in Xenopus to support a quantitative model that explains morphological scaling as the result of scaling of a gradient of bone morphogenetic protein (BMP) signals. We believe that the evidence for scaling in Xenopus is misinterpreted, and that their model for embryonic patterning disagrees with prior data. The experiments they present supporting their model admit alternative interpretations.
[Show abstract][Hide abstract] ABSTRACT: In eukaryotic genomes, nucleosomes function to compact DNA and to regulate access to it both by simple physical occlusion and by providing the substrate for numerous covalent epigenetic tags. While competition with other DNA-binding factors and action of chromatin remodeling enzymes significantly affect nucleosome formation in vivo, nucleosome positions in vitro are determined by steric exclusion and sequence alone. We have developed a biophysical model, DNABEND, for the sequence dependence of DNA bending energies, and validated it against a collection of in vitro free energies of nucleosome formation and a set of in vitro nucleosome positions mapped at high resolution. We have also made a first ab initio prediction of nucleosomal DNA geometries, and checked its accuracy against the nucleosome crystal structure. We have used DNABEND to design both strong and weak histone- binding sequences, and measured the corresponding free energies of nucleosome formation. We find that DNABEND can successfully predict in vitro nucleosome positions and free energies, providing a physical explanation for the intrinsic sequence dependence of histone-DNA interactions.
Nucleic Acids Research 07/2009; 37(14):4707-22. · 8.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Phase-locking (frequency entrainment) of an oscillator, in which a periodic extrinsic signal drives oscillations at a frequency different from the unperturbed frequency, is a useful property for study of oscillator stability and structure. The cell cycle is frequently described as a biochemical oscillator; however, because this oscillator is tied to key biological events such as DNA replication and segregation, and to cell growth (cell mass increase), it is unclear whether phase locking is possible for the cell cycle oscillator. We found that forced periodic expression of the G(1) cyclin CLN2 phase locks the cell cycle of budding yeast over a range of extrinsic periods in an exponentially growing monolayer culture. We characterize the behavior of cells in a pedigree using a return map to determine the efficiency of entrainment to the externally controlled pulse. We quantify differences between mothers and daughters and how synchronization of an expanding population differs from synchronization of a single oscillator. Mothers only lock intermittently whereas daughters lock completely and in a different period range than mothers. We can explain quantitative features of phase locking in both cell types with an analytically solvable model based on cell size control and how mass is partitioned between mother and daughter cells. A key prediction of this model is that size control can occur not only in G(1), but also later in the cell cycle under the appropriate conditions; this prediction is confirmed in our experimental data. Our results provide quantitative insight into how cell size is integrated with the cell cycle oscillator.
Proceedings of the National Academy of Sciences 05/2009; 106(16):6632-7. · 9.81 Impact Factor