Morphomechanics: An Extended View

Abstract

Morphomechanics is based on the idea that living matter can mechanically self-organize into forms without the need for a pre-pattern, as recently supported by the physics of active matter. Here an extended view is proposed that integrates bioelectricity and differentiation waves as the mechanisms by which cells measure mechanical stress and couple morphogenesis and cell differentiation, respectively. Morphomechanics is a largely unexplored approach, which however could deeply transform our way of seeing nature.

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Morphomechanics: An Extended View
Marta Linde
Funding: No specific funding was received for this work.
Potential competing interests: No potential competing interests to declare.
Abstract
Morphomechanics is based on the idea that living matter can mechanically self-organize into forms without the need for
a pre-pattern, as recently supported by the physics of active matter. Here an extended view is proposed that integrates
bioelectricity and differentiation waves as the mechanisms by which cells measure mechanical stress and couple
morphogenesis and cell differentiation, respectively. Morphomechanics is a largely unexplored approach, which
however could deeply transform our way of seeing nature.
Marta Linde-Medinaa,*
Independent Researcher, Palma, Spain
a ORCID iD: 0000-0002-8141-6301
* E-mail: linde.m@outlook.com
Keywords: active liquid crystals, active matter, bioelectricity, differentiation waves, mechanical self-organization.
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Introduction
The idea of living matter as an active and intrinsically ordered entity begins to sound as a robust scientific statement.
Controversial from the very beginnings of embryology as a research field (Linde-Medina 2010; Linde-Medina 2020), it has
now opened a new avenue at the interface between physics and biology (Needleman and Dogic 2017). This emerging
field is concerned with the study of large ensembles of entities capable of transforming chemical energy into mechanical
work, called active matter. The definition includes biological systems across scales (e.g., cytoskeletal components, cells,
whole organisms) and some artificial systems. Some of the main experimental models are biopolymers and biofilms, from
a biological origin, and Janus particles, from an artificial origin (Schaller et al. 2010; Menzel 2015; Shankar et al. 2022).
Their distinguishing feature is that, as long as there is an energy supply, they are in permanent activity, i.e., at a far from
equilibrium state. This condition confers to them a rich variety of large-scale patterns and behaviors not available at
equilibrium (e.g., see Fig. 1 in Bär et al. 2020). Powered from within, they do not require an external factor that drives them
to a new state, like those formed by passive entities (e.g., Rayleigh–Bénard system), but they will do it spontaneously.
However, this intrinsic capacity of generating order can be externally harnessed for the system to acquire reproducibility
and robustness. This is an important point to design materials and to understand biological forms.
Contrary to previous models, the physics of active matter seems to capture the essence of the living (note that some
physical models widely applied to morphogenesis, as for example, the differential adhesion hypothesis [Cerchiari et al.
2015], assume the system is at equilibrium). In the future, it could provide the theoretical framework for understanding the
role of mechanical, molecular and electrical signals in the generation of biological forms, transforming our fragmented
views into a theory of embryogenesis (Beloussov 2012b). This paper is aimed to provide a grain of sand towards
achieving this.
At the core of morphomechanics
It has been shown that living matter behaves, to some extent, as a liquid crystal. Liquid crystals are materials formed by
rod-like particles (e.g., cytoskeletal filaments and cells under some circumstances) that can flow like a liquid and still keep
a long-range directional and/or orientational order, like a solid, hence the name. A characteristic feature of anisotropic
liquid crystals is the formation of topological defects, i.e., regions at which the long-range directional and/or orientational
order is disrupted (Doostmohammadi et al. 2018; Bär et al. 2020; Zhang et al. 2021a). These defects display characteristic
geometries depending if the rod-like particles are polarized (polar liquid crystals) or non-polarized (nematic liquid crystals)
(Fig. 1). Importantly, these defects are loci of high mechanical stress (Saw et al. 2017).
There is a growing evidence of the existence of topological defects in biological systems across length scales (Saw et al.
2018; Balasubramaniam et al. 2022). Remarkably, some studies have shown a correlation between topological defects
and some morphogenetic events, suggesting they could represent mechanical organizing centers. For example, in Hydra
regeneration, a pair of +1 defects mark the location of the prospective mouth and foot (i.e., the body axis). Furthermore,
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the position of the tentacles surrounding the mouth are specified by a pair of -1/2 defects at the base, and a +1 defect at
the prospective tip (Maroudas-Sacks et al. 2021) (Fig. 2). Topological defects could spatially coincide with the classical
organizers of early embryogenesis, traditionally defined in molecular terms only (Martínez-Arias and Steventon 2018).
Figure 1. Types of topological defects in polar and nematic liquid crystals (redrawn from Shankar et al. 2022).
The presence of topological defects in living systems indicates that the body of theoretical work developed for
understanding the behavior of liquid crystals can be useful to explain biological forms, once the activity component is
incorporated into the models. Hoffmann et al. (2022) have theoretically tested if topological defects can drive
morphogenesis. The authors have shown that a thin film of a confined active polar liquid crystal, which could represent a
cell monolayer, is unstable to the formation of protrusions at the location of +1 defects. This has been experimentally
observed in myoblast cultures (Guillamat et al. 2022). The forces leading to these out-of-plane protrusions only appear if
the liquid crystal is extensile (i.e., the entities extend along their long axis); if contractile (i.e., the entities contract along
their long axis), the film remains flat. Similarly, Nejad and Yeomans (2022) have shown that a transition from 2D to a 3D
nematic layer is only theoretically possible under extensile activity. According to the authors, this result stresses the
relevance of extensile forces as an underlying mechanism of epithelial morphogenesis. Modelled as a shell (i.e. a thin film
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with a spherical shape), +1/2 defects in a nematic crystal lead to the formation of protrusions and shell elongation –
resembling organoid elongation – under extensile and contractile activity, respectively.
Figure 2. Schematic illustration of the nematic orientation field formed by actin fibers in Hydra. Note the
correspondence between the topological defects and the body plan (redrawn from Maroudas-Sacks et
al. 2021).
The relevance of extensile forces for a layer to grow in a third dimension could help to better understand the evolution of
the metazoan body plan. It has been observed that some cell monolayers behave as extensile liquid crystals (e.g., neural
progenitor cells), whereas others are contractile (e.g., NIH 3T3 mouse embryonic fibroblasts). It has been observed that
Madin-Darby Canine Kidney (MDCK) cells switch from extensile to contractile activity when E-cadherin expression is
knocked out (Balasubramaniam et al. 2021). The results indicate that when these epithelial cells cannot attach to each
other, they strongly attach to the substratum and contract themselves, i.e., they behave like loose mesenchymal cells.
This leads to a contractile monolayer. However, when cells form an epithelium, the net forces from neighbors and
substrate interactions allow them to extend along their long axis, the monolayer is extensile.
A major transition during the evolution of the metazoan body plan leading to the eumetazoans was coincident with the
acquisition of the membrane protein Van Gogh/Strabismus and the enzyme peroxsidasin (Newman 2016). The former is
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involved in the planar cell polarity pathway, by which cells become anisotropic in shape. The latter is involved in the
formation of the basement membrane, i.e. true epithelial sheets. That is, the emergence of eumetazoans was coincident
with the capability of cells to form active nematic liquid crystals with extensile activity.
When activity at the lower scale is considered, matter is capable of mechanically self-organizing into forms without the
need for any external factor (e.g., a chemical or electrical pre-pattern). Under certain conditions, the active stresses
generated at topological defects can originate certain morphological motifs common in embryogenesis. At the cell scale,
however, the possibility of a response to topological defects could increase the capacity of living matter for mechanical
self-shaping. According to Beloussov and co-workers (Beloussov et al. 1994; Beloussov and Grabovsky 2003), this could
be accomplished as follows:
Whenever a change is produced in the amount of local stress applied to a cell or local region of tissue (regardless
of whether this change in force comes from a neighbouring part of the embryo or has been exerted by an
experimenter), the cells or tissue will respond by actively generating forces directed toward the restoration of the
initial stress value, but as a rule, overshooting it.
A cell (tissue) with fixed edges that is stretched or compressed by an external force will expand or contract, respectively,
in order to restore its initial stress value with an overshoot, i.e., it will exceed it. Generally, this overshoot will mechanically
perturb the surrounding cells and so on, thereby leading to sustained morphogenesis.
It has been theoretically demonstrated that the hyper-restoration hypothesis is part of a more general principle that
includes two other behaviors: growth response and stretch activation. In the former, the cell (tissue) behaves as expected
by hyper-restoration response, but without an overshoot. In the stretch activation, the cell (tissue) behaves opposite to the
hyper-restoration response: it will contract if stretched and expand if compressed. At the steady-state, it will remain at a
higher stress (Taber 2009). This generality has broadened the number of morphological motifs explained by mechanical
self-organization.
Morphomechanics provides a way for unifying the wide variety of cells behaviors observed in embryogenesis. They could
be classified into two categories: those that decrease mechanical stress, and those that increase it. Under stretching, cell
behaviors decreasing stress will be, for example: division, intercalation, growth, elongation or recruitment, and for
increasing it: contraction, migration, apoptosis or extrusion. Those cell behaviors decreasing stress under tension, will
increase it under compression, and vice versa. It has been shown that myoblasts are extruded at +1/2 defects in cultured
monolayers (Saw et al. 2017). This extrusion is due to the accumulation of high compressible stress at these defects. This
observation is in agreement with the morphomechanic view: cell extrusion under compression will restore the initial stress
value of the tissue.
Harnessing defects
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If not externally forced or trapped by a structural inhomogeneity, topological defects in passive liquid crystals tend to
disappear as they collide and annihilate to each other, and the long-range orientational order is eventually restored.
Contrarily, the addition of activity to these theoretical models has shown the formation of a chaotic flow of self-propelled
defects which are spontaneously and continually created and destroyed, a state called active turbulence. To construct
something upon it, either biological or artificial, it would be necessary to harness this potential of mechanical self-shaping.
Several ways of harnessing active turbulence have been proposed (e.g. Balasubramaniam et al. 2021; Shankar et al.
2022). Here, two techniques that would be present in biological systems will be briefly discussed. One of them is
confinement. Most of the studies on liquid crystals has been carried out in two-dimensions. In order to elucidate its
relevance for understanding biological forms, the approach has been extended to three-dimensional confinements. For
example, when confined to a spherical shape, an active nematic film of microtubules and molecular motors display four
+1/2 defects that oscillate between two tetrahedral configurations (Keber et al. 2014). The frequency of this oscillation can
be tuned by changing the concentration of ATP (i.e., its activity). By decreasing the surface tension of the vesicle that
encapsulated the film, these defects lead the formation of four filopodia-like protrusions (Fig. 3).
Figure 3. Filopodia-like protrusions formed at +1/2 defects in an active nematic film (redrawn from
Keber et al. 2014).
Another technique is activity patterning. Experimental and theoretical studies have shown that, when activity is confined to
a specific region, rather than homogeneously distributed, defects are created and trapped at these regions. Activity
patterns have been created by engineering light-sensitive cytoskeletal components. For example, kinesin motor proteins
form dimers capable of pulling on microtubules when binding to them. Ross et al (2019) engineered a molecule in which a
kinesin motor was fused to an optically-dimerizable iLID protein, i.e., kinesin dimers formed only upon illumination. An
activity pattern can be induced in a nematic system formed by microtubules and these light-activatable kinesin motors by
illuminating specific regions. By this technique, the authors controlled the formation, movement and fusion of topological
defects.
In another study, Zhang et al. (2021b) regulated the activity of a nematic system formed by actin filaments and light-
sensitive myosin motors. These engineered motors consisted in a myosin XI catalytic heads and a lever arm containing
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the light-sensitive LOV2 domain. This lever arm unfolds upon illumination, which increases the sliding velocity of the motor
protein on actin filaments. The authors have shown, theoretically and experimentally, that +1/2 defects created within an
activation area are deflected when they approach the boundaries, i.e. they are trapped. They have also shown how a low
activity stimulation can be used to guide the motion of +1/2 defects along desired trajectories. Activity patterning offers a
more direct way of regulating the formation and flow of topological defects than other techniques.
Measuring mechanical stress
Morphomechanics is based on the assumption that cells are capable of measuring the magnitude and duration of different
mechanical forces. Here it is suggested that they could compute these measurements by using electrical signals. The lipid
membrane is electrically charged in all cells. This charge results from a difference in the concentration of negatively (Cl
–)
and positively charged ions (Na+, Ca2+, K+) between its intracellular and extracellular side. Non-excitatory cells possess
an excess of negatively charged ions in their interior, i.e., a negative membrane voltage (Vmem). Among the cellular
components involved in the regulation of this voltage, it has been shown that cells possess mechanically activated ion
channels (Brohawn 2015; Kefauver et al. 2020; Richardson et al. 2022). These channels are pore-forming proteins
inserted in the cell membrane that change their configuration upon mechanical stimuli. This configurational change opens
the pore, which alters the Vmem by facilitating the influx of ions. Some of the identified channels are present in specific
tissues (e.g., PIEZO2: neural), but others have been found in a wide variety of tissues (e.g., PIEZO1) (Coste et al. 2010).
They are not only involved in the regulation of physiological conditions of adult tissues, but also in their embryonic
development (e.g., Nonomura et al. 2018; Shah et al. 2022). This is a relatively recent finding in vertebrates (Coste et al.
2010) so there is not too much detail about their number, structure, mechanism of activation or role in embryogenesis.
Here, some characteristics of these force-sensing molecules that may provide to cells the ability to finely measure and
respond to changes in their membrane mechanics will be commented.
Mechanically activated ion channels are primary transducers of mechanical stress as they are both directly and quickly
activated (on the millisecond timescale) by forces applied to the cell membrane. For example, PIEZO1 channels purified
and reconstituted in a double lipid bilayer are capable of generating electric currents when the membrane is mechanically
perturbed, i.e., they are directly activated by forces transmitted from the surrounding lipids (Coste et al. 2010). Although
there is a controversy about to what extent mechanically activated ion channels are intrinsically sensitive to mechanical
forces (force-from-lipids model) or they require the interaction of other cellular components (force-from-filament model),
present data seem to suggest these are not mutually exclusive mechanisms. A general view is emerging in which inherent
force-sensing ion channels can be modulated by other cellular components (Cox et al. 2019). For example, PIEZO1 is
more sensitive to mechanical pulling when attached to the extracellular matrix (Gaub and Muller 2017) (for other
modulators see Kefauver et al. 2020; Richardson et al. 2022).
These channels present differences in their activation profile, threshold and ion selectivity, which may be related to their
different structure. For example, PIEZO1 is activated by stretching, compression, shear or pillar deflection (forces applied
at the cell-matrix interface), whereas TRPV4 only generates rapid electrical currents by pillar deflection (Richardson et al.
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2022). They also display different activation thresholds. The pressure needed for half-maximal activation of OSCA
channels (OSCA1.1 an OSCA 1.2) is two-fold higher than PIEZO1, i.e., OSCA evoke high-threshold currents under
stretching (Murthy et al. 2018). In general terms, the evoked currents by mechanically activated ion channels are
proportional to the intensity of the applied force, so a higher change in the Vmem would be indicative of a higher change in
mechanical stress. PIEZO1 is a non-selective cation channel that allows the flow of Na+ and Ca2+. OSCA channels are
also non-selective cation channel with some chloride permeability and TREK channels are permeable to K+ (Kefauver et
al. 2020).
Using micro-patterned cultures of EpH4 mouse mammary epithelial cells, Silver et al. (2020) have shown how differences
in mechanical stress lead to the formation of a bioelectrical gradient in which cells located at areas of high tension are
more depolarized (more positive Vmen) than those located in areas of low tension. In a square culture, areas of high
tension form at the corners; in a sinusoidal culture, at convex areas (Gomez et al. 2010). This bioelectrical gradient was
generated by connexin-43 hemichannels, which opened preferentially at areas under tension. This change in Vmem gave
rise to an increase in cell proliferation via Yap/Taz signaling.
Differentiation waves: coupling morphogenesis and cell differentiation
There is a general agreement that mechanical forces are relevant in morphogenesis, however, it is considered they are
downstream gene regulatory networks, which are the drivers of this process. In an alternative view, a bioelectrical pre-
pattern is added on the top of molecular pre-patterns (Tseng and Levin 2013; Levin and Martyniuk 2018), but this new
layer of information would not alter the general view that pre-patterns are indispensable to generate a form.
When living matter is conceived as a mechanically active medium, common morphological motifs of embryos can arise by
mechanical interactions only, i.e., pre-patterns are dispensable (Taber 2008; Beloussov 2012b; Hoffmann et al. 2022).
Conjointly with a strong evidence in support of the capability of mechanical forces to change gene expression (e.g., Oses
et al. 2023), a different view emerges in which mechanical forces can drive morphogenesis and molecular pre-patterns
may be downstream rather than upstream them. Under this framework, pre-patterns would not provide instructions as
commonly assumed, but would harness the self-shaping potential of living tissues (Beloussov and Grabovsky 2007;
Doursat et al. 2012; Beloussov 2012a). It is important to stress that morphomechanics is focused on morphogenesis, and
therefore, it is compatible with the idea that gene regulatory networks can drive other developmental processes. According
to morphomechanics, morphogenesis and cell differentiation could be uncoupled.
There is some evidence in support of this idea. In the cnidarian Nematostella vectensis, it has been shown that the
invagination of the blastula during gastrulation is uncoupled from the differentiation of the resulting inner layer into
endoderm. This invagination is mediated by the apical constriction of cells at the animal pole via Wnt/Planar Cell Polarity.
Blocking this pathway, inhibits the invagination of the blastula, but not its differentiation into endoderm. Contrarily, blocking
Wnt/ß-catenin inhibited endodermal differentiation, but not tissue invagination (Kumburegama et al. 2011).
Gastruloids are three-dimensional cell aggregates capable of elongating and differentiating into the three germ layers and
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some of their derivatives after a pulse of Wnt activation, mimicking the spatiotemporal organization of a gastrula. When
they are cultured in suspension, this organization is reflected at the molecular level only, i.e., gastruloids express key
markers of specific tissues, but they do not reproduce the corresponding morphology (Beccari et al. 2018; van den Brink
and van 2021). For example, they express neural markers along the longitudinal axis, but these cells do not form a tube.
Cells expressing somite markers appears at both sides of the longitudinal axis and at the expected developmental time,
however they do not form somite-like structures (i.e., hollow epithelial spheres). That is, morphogenesis and cell
differentiation can be uncoupled in this system (Steventon et al. 2021).
Here it is suggested that these two processes could be coupled in embryonic development by the differentiation waves.
The latter are mechanical waves that travel throughout an epithelium. They are generated by a structure called the “cell
state splitter”, which is located at the apical side of epithelial cells (Gordon 1999; Gordon and Gordon 2016a; Gordon and
Gordon 2016b). This organelle consists of: a ring of microfilaments, a ring of intermediate filaments and a mat of
microtubules connecting both rings. The cell state splitter is a bistable structure that can display two states: contracted or
expanded. The former is mediated by the contraction of the microfilament ring. The latter, by the polymerization of
microtubules.
Before a differentiation wave starts, the contraction force exerted by the microfilament ring is in equilibrium with the
expansion force exerted by the microtubules. However, this equilibrium is unstable: an external force enhancing either the
contraction or the expansion of the cell state splitter will let it adopt the corresponding stable state. Once the cell state
splitter contracts or expands, it sends a signal to the nucleus that triggers the transcription of a set of genes (i.e., cell
differentiation). Triggering the same state to neighboring cells via cell-cell attachments, the initial response leads to the
formation of a mechanical wave of cell contraction/expansion that will travel throughout the epithelial sheet. At the same
time, the signal sent to the nucleus feedbacks to the cell state splitter, returning it to new equilibrium state. Now the cell is
ready to be part of another differentiation wave.
The intermediate filaments ensure the metastability of the system by buffering the cell state splitter from small random
fluctuations. The initial stimulus should be strong enough to be able to switch the cell state splitter to one of its stable
states. Each differentiation wave triggers the transcription of a different set of genes, and therefore, cells undergoing
different sequences of contraction and expansion waves will follow different cell fates (Gordon 1999; Gordon and Gordon
2016a; Gordon and Gordon 2016b).
Accordingly, differentiation waves (contractile or extensile) would be initiated at topological defects and will propagate
across the epithelium depending on the presence of other defects, as the same cell cannot participate in more than one
wave at a time. Cells at different locations of the embryo will receive different combinations of contraction and expansion
waves and at different timings. They could use this to know which set of genes to express and at what time.
Simultaneously, they will undergo different regimes of mechanical stress. Measuring the type, magnitude and duration of
these mechanical stimuli by the Vmem, they will know if they should restore their initial stress value – with or without
overshoot – or increase it, and which cell behavior to use to perform this task. This will lead to changes in shape.
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Bioelectrical waves traveling along the embryo have also been observed (Jaffe 2008). In case they were coincident, these
electrical waves could be caused by the differentiation waves. Differentiation waves expand as a transient, elastic cell
deformation that expands or contracts the cell state splitter, but these deformations could also stimulate, to some extent,
the mechanically activated ion channels. This would generate an electrical wave. In this case, these pairs of waves could
be related, at least, in four ways. Bioelectrical waves may be: 1) a side effect of the differentiation waves, without a
specific role; 2) provide redundant information for increasing robustness of the system; 3) provide additional information,
4) be part of the signal sent to the nucleus by the cell state splitter.
Coming back to Nematostella vectensis, Nguyen et al. (2022) have shown that both tissue invagination by apical
constriction (morphogenesis) and endoderm specification (cell differentiation) are mechanically coupled, as suggested in
the present work. This coupling would be mediated by the existence of a mechanically activable site (Y654) in the ß-
catenin molecule, which regulates endoderm specification (Nguyen et al. 2022). However, it is unknown if this coupling
involves a differentiation wave.
When mouse gastruloids are embedded in matrigel (an extracellular matrix surrogate), they are able to form trunk-like
structures with a morphologically recognizable neural tube, somites and a gut. i.e., they undergo both morphogenesis and
cell differentiation (Veenvliet et al. 2020). A key difference between embedded and non-embedded gastruloids is the lack
of an epithelium in the latter (Steventon et al. 2021). This system highlights the relevance of the epithelium in
morphogenesis, as expected from active nematics. As suggested in Hydra regeneration (Maroudas-Sacks et al. 2021),
cell movements during gastrulation could be guided by a nematic orientation field formed by the epithelium. The lack of
morphogenesis in suspended gastruloids would be expected as this field would be absent.
Discussion
Morphomechanics does not deny that genes have played a fundamental role in the emergence of biological forms. It does
not deny the existence of developmental programs. Morphomechanics challenges the common view that living matter
needs to be instructed to give rise to forms. This is the consequence of conceiving it as a passive and non-intrinsically
ordered entity, i.e., like a piece of “play doh” (Linde-Medina 2010; Linde-Medina 2020). In the standard view, it is thought
gene regulatory networks give form to living matter, they contain the blueprint of the organism. In an alternative view, this
blueprint is contained in a bioelectric code, which governs gene regulatory networks (Tseng and Levin 2013; Levin and
Martyniuk 2018).
When matter is formed not by passive, but active entities capable of transforming energy into mechanical work, large
scale patterns spontaneously arise from mechanical interactions only, without the need for an external factor (i.e., a pre-
pattern). In a liquid crystal state, rod-like active entities form flows with a large scale orientational order that is disrupted by
topological defects (Doostmohammadi et al. 2018; Bär et al. 2020; Zhang et al. 2021a). This defects are foci of active
mechanical stress able to lead morphogenesis (Hoffmann et al. 2022; Guillamat et al. 2022). The correlation in Hydra
regeneration between topological defects of different charges and its body plan suggests that nematic flows may
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constitute a morphogenetic field that guides embryogenesis (Maroudas-Sacks et al. 2021).
In a self-organizing system, patterns can emerge by random interactions of identical entities, but the addition of more
controllable conditions and heterogeneities would not annul this emergence, but rather would potentiate it (Doursat et al.
2012). Contrary to natural, non-living entities, cells can regulate the initial/boundary conditions and parameters of the laws
relevant to their material properties. Within the context of active nematics, for example, cells can regulate the number of
topological defects by modulating the level of activity (Saw et al. 2017). A patterned activity could also specify the location
in which a defect will appear, as well as its trajectory (Ross et al. 2019; Zhang et al. 2021b). The introduction of
heterogeneities in the type of activity (extensile or contractile) leads to phase separation (Balasubramaniam et al. 2021).
By harnessing self-organization using gene regulatory networks, cells could generate complex, functional forms in a
reproducible way (Beloussov and Grabovsky 2007; Doursat et al. 2012; Beloussov 2012a). However, these
developmental programs are not as usually conceived. In analogy with man-made artefacts, it is commonly thought that
gene regulatory networks (or bioelectrical signals) encode instructions to form an organism, they control the
spatiotemporal organization of cells. However, in self-organizing natural systems, there is not a central entity imposing
order, but it emerges from the collective interaction of entities at the lower level, in a bottom-up direction (e.g., a nematic
orientation field) (Doursat et al. 2012). To better understand this point, it may be helpful to compare artificial and natural
buildings. Artificial buildings are constructed by builders under the guidance of an architect (a centralized control), who
has designed a blueprint that contains the details about how the building will look like. Contrarily, in nature, social insects
construct complex buildings without following any blueprint or the instructions of an “architect”, but they emerge from the
collective interaction of insects (a decentralized control), which respond to some environmental cues in a specific way (low
level rules) (e.g., Theraulaz et al. 2003).
Organisms could be constructed this way. Like social insects, cells could also construct rules that guide their response to
environmental cues. According to morphomechanics, a tendency to restore their initial stress value – with or without an
overshoot –, or to increase it, depending on the magnitude and duration of the mechanical stimuli (Taber 2009), could
increase the ability of biological systems to mechanically self-organize. To achieve this, cells would need to measure the
magnitude and duration of different mechanical stimuli. Here, it is proposed they could perform this task by using their
mechanically activated ion channels, which directly transduce mechanical stimuli into changes in Vmem.
Under this framework, bioelectrics is not an “instructive driver of morphogenesis” (Levin 2021), but a mechanical
mechanism. As stressed by Levin and Martyniuk (2018), a main feature of a code is arbitrariness: the response triggered
by a signal is not a physical consequence, but something arbitrary. Borrowing an example from Levin and Martyniuk
(2018), exposure at a high temperature will lead to cell death as the physical consequence of protein denaturalization, i.e.,
heating destroys the three dimensional configuration that makes proteins functional. A specific value of Vmem could also
lead to cell death, but this response would not be physically connected. Cells interpret this signal as a cue to trigger
programed cell death. The same signal could evolve to trigger, for example, cell proliferation, i.e., the link between the
signal and the response is an evolutionary convention, and thus, a code.
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In morphomechanics, a change in V
mem is not arbitrary, but physically connected to a change in mechanical stress.
Alterations in Vmem inform to cells about their membrane mechanics. Bioelectric signals are part of the physical
mechanism underlying morphogenesis. However, the cell response to these changes could be arbitrary, an evolved rule.
Here it is important to stress that, according to Beloussov (2008; 2012a), the hyper-restoration response is not specifically
biological (i.e. arbitrary), but it can be understood as the extension of the Le Chatelier principle for active matter (i.e., at far
from equilibrium conditions).
Embryonic tissues would not remain in a liquid crystal state for the whole process of embryogenesis. They can undergo
unjamming-jamming transitions that will confer to them a solid-like state (Mongera et al. 2018). This transition gives rise to
a new set of patterning processes, e.g., differential strain. Differential strain is a phenomenon first described in the
inanimate realm (Alarcón et al. 2010) that has proven helpful for understanding embryonic development. It occurs when
two solid materials are physically connected, and one of them extends or shrinks with respect to the other. This creates
regularly spaced foci of high mechanical strain that lead to morphological changes. When an elastic material expands
faster than a rigid underground, it compresses itself, which leads to geometric buckling phenomena like the wrinkling gut
(Savin et al. 2011), the folded brain cortex (Tallinen et al. 2014), and the scoliotic spine (Crijns et al. 2017). When it
shrinks, the rigid underground is overstretched, which leads to the formation of regularly spaced cracks. Cracking has
been proposed to explain the fragmentation of the crocodile skin and the paraxial mesoderm into scales (Milinkovitch et al.
2013) and somites (Truskinovsky et al. 2014; Linde-Medina and Smit 2021), respectively.
Finally, the extensile activity that allows out-of-plane morphological changes, cell-cell attachments that propagate
mechanical and bioelectrical waves, the “fixed edges” condition necessary for a hyper-restoration response, the cell state
splitter that could couple morphogenesis and cell differentiation, all them are features of an epithelium. To better
understand embryogenesis, it would be necessary to elucidate what is the best way to conceive an embryonic tissue, i.e.,
the relationships between the epithelium, mesenchyme and extracellular matrix.
Acknowledgements
I am very grateful to Richard Gordon for his encouragement.
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