Physical Review Letters

Phototaxis of many species of green algae relies upon directional sensitivity of their membrane-bound photoreceptors, which arises from the presence of a pigmented "eyespot" behind them that blocks light passing through the cell body from reaching the photoreceptor. A decade ago it was discovered that the spherical cell body of the alga Chlamydomonas reinhardtii acts as a lens to concentrate incoming light, and that in "eyeless" mutants of Chlamydomonas the consequence of that focused light reaching the photoreceptor from behind is a reversal in the sign of phototaxis relative to the wild type behavior. We present a quantitative theory of this sign reversal by completing a recent simplified analysis of lensing [Yang, et al., Phys. Rev. E 113, 022401 (2026)] and incorporating it into an adaptive model for Chlamydomonas phototaxis. This model shows that phototactic dynamics in the presence of lensing is subtle because of the existence of internal light caustics when the cellular index of refraction exceeds that of water. During each period of cellular rotation about its body-fixed axis, the photoreceptor receives two competing signals: a relatively long, slowly-varying signal from the direct illumination, and a stronger, shorter, rapidly-varying lensed signal. The reversal of the sign of phototaxis is then a consequence of the dominance of the flagellar photoresponse to the signal with the higher time derivative. These features lead to a quantitative understanding of phototaxis sign reversal, including bistability in the direction choice, a prediction that can be tested in single-cell tracking studies of mutant phototaxis.

We demonstrate that the global state of a Gene Regulatory Network [1] may be labeled by a few genes in spite of the fact that there are thousands of genes participating in it. For example, the expression values of only 3 genes are enough to discriminate between a tissue sample coming from a normal lung or a lung adenocarcinoma. We follow a pragmatic procedure, dependent on the sample set, but which is expected to become exact for large enough sets of samples. The proof relies on a scheme for the construction of perfect classification panels of genes [2], inspired by rough set theory [3].

Layers composed of lateral connections prevail in biological systems from subcellular membranes to epithelial sheets. This work presents a continuum framework to describe the effects of mechanical forces within a 3D curved layer with supporting lateral mesh. We provide detailed discussion on the emergence of stress anisotropy as a function of depth in different curvature settings, building on Lou et al. Phys. Rev. Lett. 130, 108401 (2023). We principally consider an epithelial monolayer to explain how the interplay between layer curvature and cell mechanics determines the stress anisotropy. We show that this can lead to irregular cellular shapes in 3D, including scutoid-like geometries. Our framework is general, and can be extended to a diverse set of biologically relevant systems.

Neural mass models such as the Jansen-Rit or Wendling systems provide a practical framework for representing and interpreting electro-physiological activity (1-6) in both local and global brain models (7, 8). However, they are only partly derived from first principles. While the post-synaptic potential dynamics are inferred from data and can be grounded on diffusion physics (9-11), Freemans "wave to pulse" (W2P) sigmoid function (12-14), used to transduce mean population membrane potential into firing rate, rests on a weaker theoretical standing. On the other hand, Montbrio et al (15, 16) derive an exact mean-field theory (MPR) from a quadratic integrate and fire neuron model under some simplifying assumptions, thereby connecting microscale neural mechanisms and meso/macroscopic phenomena. The MPR model can be seen to replace Freemans W2P sigmoid function with a pair of differential equations for the mean membrane potential and firing rate variables--a dynamical relation between firing rate and membrane potential--, providing a more fundamental interpretation of the semi-empirical NMM sigmoid parameters. In doing so, we show it sheds light on the mechanisms behind enhanced network response to weak but uniform perturbations. In the exact mean-field theory, intrinsic population connectivity modulates the steady-state firing rate W2P relation in a monotonic manner, with increasing self-connectivity leading to higher firing rates. This provides a plausible mechanism for the enhanced response of densely connected networks to weak, uniform inputs such as the electric fields produced by non-invasive brain stimulation. This new, dynamic W2P relation also endows the neural mass model with a form of "inertia", an intrinsic delay to external inputs that depends on, e.g., self-coupling strength and state of the system. Next, we complete the MPR model by adding the second-order equations for delayed post-synaptic currents and the coupling term with an external electric field, bringing together the MPR and the usual NMM formalisms into a unified exact mean-field theory (NMM2) displaying rich dynamical features. In the single population model, we show that the resonant sensitivity to weak alternating electric field is enhanced by increased self-connectivity and slow synapses. O_TEXTBOXSignificance Several decades of research suggest that weak electric fields influence neural processing. A long-standing question in the field is how networks of neurons process spatially uniform weak inputs that barely affect a single neuron but that produce measurable effects in networks. Answering this can help implement electric field coupling mechanisms in neural mass models of the whole brain, and better represent the impact of electrical stimulation or ephaptic communication. This issue can be studied using local detailed computational models, but the use of statistical mechanics methods can deliver "mean-field models" to simplify the analysis. Following the steps of Montbrio et al (15, 16), we show that the sensitivity to inputs such a weak alternating electric field can be modulated by the intrinsic self-connectivity of a neural population, and produce a more grounded set of equations for neural mass modeling to guide further work. C_TEXTBOX

Individual bacterial cells grow and divide stochastically. Yet they maintain their characteristic sizes across generations within a tightly controlled range. What rules ensure intergenerational stochastic homeostasis of individual cell sizes? Valuable clues have emerged from high-precision longterm tracking of individual statistically-identical Caulobacter crescentus cells as reported in [1, 2]: Intergenerational cell size homeostasis is an inherently stochastic phenomenon, follows Markovian or memory-free dynamics, and cells obey an intergenerational scaling law, which governs the stochastic map characterizing generational sequences of cell sizes. These observed emergent simplicities serve as essential building blocks of the data-informed principled theoretical framework we develop here. Our exact analytic fitting-parameter-free results for the predicted intergenerational stochastic map governing the precision kinematics of cell size homeostasis are remarkably well borne out by experimental data, including extant published data on other microorganisms, Escherichia coli and Bacillus subtilis. Furthermore, our framework naturally yields the general exact and analytic condition that is necessary and sufficient to ensure that stochastic homeostasis can be achieved and maintained. Significantly, this condition is more stringent than the known heuristic result from quasi-deterministic frameworks. In turn the fully stochastic treatment we present here extends and updates extant frameworks, and highlights the inherently stochastic behaviors of individual cells in homeostasis.

Efficient absorption of signaling molecules and carbohydrates through receptors on cell surfaces is crucial for various biological processes. While ubiquitous patterns of receptor distributions, including polar localization in rod-shaped cells, have been widely observed experimentally, their underlying evolutionary advantage is unclear. In this work, we study how spatial distributions of receptors on cell surfaces affect the total flux entering the cell. We innovate a method by which one can calculate the fluxes through all receptors using linear equations, which applies to arbitrarily shaped cells. Our theories recover previous results for spherical cells and further show that the flux through each receptor is spatially dependent in non-spherical cells. In particular, the fluxes are the highest near the poles in rod-shaped cells and the highest near the invagination in defective spherical cells. Surprisingly, we prove that the optimal receptor distribution on an arbitrarily shaped cell maximizing the total flux is precisely the charge density distribution on an ideal conductor of the same shape, which agrees with numerical simulations. Our work unveils the evolutionary origin of receptor localizations.

Biomolecular condensates are viscoelastic, and their mechanical properties are intimately related to their biological functions. However, the connection between microscopic networks formed by intermolecular crosslinks and viscoelasticity is still elusive. Here, we model biomolecular condensates as random crosslinked polymer solutions to elucidate how random connectivity fundamentally alters their viscoelasticity. We decompose the entire solution into multiple tree networks and demonstrate that for networks with size n, their spectra of relaxation rates{lambda} exhibit a power-law scaling pn({lambda}) [~]{lambda} -1/3 with a lower cutoff{lambda} min [~] n-3/2. By integrating all networks, we show that for the entire solution, random crosslinks generate an abundance of soft modes involving multiple linear polymers with a flat spectrum of relaxation rates. The soft modes cause anomalous linear frequency scaling of the dynamic modulus, in particular, they significantly boost the low-frequency storage modulus relative to uncrosslinked systems. Our predictions agree quantitatively with the experimental data from distinct biomolecular condensates.

Recent experimental investigations into Hydra regeneration revealed a remarkable phenomenon: the morphological transformation of a tissue fragment from the incipient spherical configuration to a tube-like structure - the hallmark of a mature Hydra - has the dynamical characteristics of a first-order phase-transition, with calcium field fluctuations within the tissue playing an essential role. This morphological transition was shown to be generated by activation over an energy barrier within an effective potential that underlies morphogenesis. Inspired by this intriguing insight, we propose a novel mechanism where stochastic fluctuations drive the emergence of morphological patterns. Thus, the inherent fluctuations determine the nature of the dynamics and are not incidental noise in the background of the otherwise deterministic dynamics. Instead, they play an important role as a driving force that defines the attributes of the pattern formation dynamics and the nature of the transition itself. Here, we present a simple model that captures the essence of this novel mechanism for morphological pattern formation. Specifically, we consider a one-dimensional tissue arranged as a closed contour embedded in a two-dimensional space, where the local curvature of the contour is coupled to a non-negative scalar field. An effective temperature parameter regulates the strength of the fluctuations in the system. The tissue exhibits fluctuations near a circular shape at sufficiently low coupling strengths, but as the coupling strength exceeds some critical value, the circular state becomes unstable. The nature of the transition to the new state, namely whether it is a first-order-like or a second-order-like transition, depends on the temperature and the effective cutoff on the wavelength of the spatial variations in the system. It is also found that entropic barriers separate the various metastable states of the system.

The idea of self-organized signal processing in the cerebral cortex has become a focus of research since Beggs and Plentz 1 reported avalanches in local field potential recordings from organotypic cultures and acute slices of rat somatosensory cortex. How the cortex intrinsically organizes signals remains unknown. A current hypothesis was proposed by the condensed matter physicists Bak, Tang, and Wiesenfeld 2 when they conjectured that if neuronal avalanche activity followed inverse power law distributions, then brain activity may be set around phase transitions within self-organized signals. We asked if we would observe self-organized signals in an isolated slice of our data driven detailed simulation of the mouse primary motor cortex? If we did, would we observe avalanches with power-law distributions in size and duration and what would they look like? Our results demonstrate that a brief unstructured stimulus (100ms, 57A current) to a small subset of neurons (about 181 of more than 10,000) in a simulated mouse primary motor cortex slice results in self-organized and self-sustained avalanches with power-law size and duration distributions and values similar to those reported from in vivo and in vitro experiments. We observed 4 cross-layer and cross-neuron population patterns, 3 of which displayed a dominant rhythmic component. Avalanches were each composed of one or more of the 4 population patterns.

The complex spatiotemporal flow patterns in living tissues, driven by active forces, have many of the characteristics associated with inertial turbulence even though the Reynolds number is extremely low. Analyses of experimental data from two-dimensional epithelial monolayers in combination with agent-based simulations show that cell division and apoptosis lead to directed cell motion for hours, resulting in rapid topological transitions in neighboring cells. These transitions in turn generate both long ranged and long lived clockwise and anticlockwise vortices, which gives rise to turbulent-like flows. Both experiments and simulations show that at long wavelengths the wave vector (k) dependent energy spectrum E(k) {approx} k-5/3, coinciding with the Kolmogorov scaling in fully developed inertial turbulence. Using theoretical arguments and simulations, we show that long-lived vortices lead to long-time tails in the velocity auto-correlation function, Cv(t) [~] t-1/2, which has the same structure as in classical 2D fluids but with a different scaling exponent.

Fluid-filled biological cavities are ubiquitous, but their collective dynamics has remained largely unexplored from a physical perspective. Based on experimental observations in early embryos, we propose a model where a cavity forms through the coarsening of myriad of pressurized micrometric lumens, that interact by ion and fluid exchanges through the intercellular space. Performing extensive numerical simulations, we find that hydraulic fluxes lead to a self-similar coarsening of lumens in time, characterized by a robust dynamic scaling exponent. The collective dynamics is primarily controlled by hydraulic fluxes, which stem from lumen pressures differences and are dampened by water permeation through the membrane. Passive osmotic heterogeneities play, on the contrary, a minor role on cavity formation but active ion pumping can largely modify the coarsening dynamics: it prevents the lumen network from a collective collapse and gives rise to a novel coalescence-dominated regime exhibiting a distinct scaling law. Interestingly, we prove numerically that spatially biasing ion pumping may be sufficient to position the cavity, suggesting a novel mode of symmetry breaking to control tissue patterning. Providing generic testable predictions, our model forms a comprehensive theoretical basis for hydro-osmotic interaction between biological cavities, that shall find wide applications in embryo and tissue morphogenesis. Author summaryThe formation of a single biological cavity, or lumen, in tissues and embryos has been widely studied experimentally but the collective dynamics of multiple lumens has received much less attention. Here, we focus on a particular type of lumens, which are located at the adhesive side of cells and can therefore interact directly through the intercellular space, as recently observed in the very first stages of embryogenesis. We propose a generic model to describe the hydraulic and osmotic exchanges between lumens themselves, and with the surrounding cellular medium. Lumens are pressurized by a surface tension, which leads naturally to their coarsening into a single final cavity through hydraulic exchanges. With extensive numerical simulations and mean-field theory we predict that such coarsening dynamics follows a robust scaling law, that barely depends on concentration heterogeneities between lumens. On the contrary, active osmotic pumping largely influences the collective dynamics by favoring lumen coalescence and by biasing the position of the final cavity. Our theoretical work highlights the essential role of hydraulic and osmotic flows in morphogenesis.

Recent studies have shown that neural representation and processing are widely distributed in the brains of behaving animals [1, 2, 3, 4]. These observations challenge functional specialization as a central tenet of Neuroscience, which refers to the notion that distinct brain regions are dedicated to specific aspects of cognition such as working memory or subjective decision-making. Here we develop the concept of bifurcation in space to mechanistically account for the emergence of functional specialization that is compatible with distributed neural coding in a large-scale neo-cortex. Our theory starts with a departure from the canonical local circuit principle [5] by highlighting differences between cortical areas in the form of experimentally quantified heterogeneities of synaptic excitation and inhibition. We investigated connectome-based modelling of a multiregional cortex for both macaque monkeys and mice, as well as a generative model of a spatially embedded neocortex. During working memory in a simulated delayed response task, surprisingly, we found an inverted-V-shaped pattern of neuronal timescales across the cortical hierarchy as a signature of functional modularity, in sharp contrast to an increasing pattern of timescales during the resting state, as reported previously [6]. Furthermore, our model cortex simultaneously and robustly displays a plethora of bifurcations in space and their associated rich repertoire of timescale profiles across a large-scale cortex; the corresponding functionally defined modules (spatial attractors) could potentially subserve various internal mental processes. This work yields several specific experimentally testable predictions, including an inverted-V pattern of timescales, a measure of comparison between functional modules and structural modules defined by the graph theory, and a new plot for revealing bifurcation in space in neural activity recorded from animals performing different tasks that engage various functional modules. We propose that bifurcation in space, resulting from the connectome and macroscopic gradients of neurobiological properties across the cortex, represents a fundamental principle for understanding the brains functional specialization and modular organization.

Material renewability in active living systems, such as in cells and tissues, can drive the large-scale patterning of forces, with distinctive phenotypic consequences. This is especially significant in the cell cytoskeleton, where multiple species of myosin bound to actin, apply differential contractile stresses and undergo differential turnover, giving rise to patterned force channeling. Here we study the dynamical patterning of stresses that emerge in a hydrodynamic description of a renewable active actomyosin elastomer comprising two myosin species. Our analytical framework also holds for an actomyosin elastomer with a single myosin species. We find that a uniform active contractile elastomer spontaneously segregates into spinodal stress patterns, followed by a finite-time collapse into tension carrying singular structures that display self-similar scaling and caustics. Our numerical analysis carried out in 1D, shows that these singular structures move and merge, and gradually result in a slow coarsening dynamics. We discuss the implications of our findings to the emergence of stress fibers and the spatial patterning of actomyosin. Our study suggests, that with state-dependent turnover of crosslinkers and myosin, the in vivo cytoskeleton can navigate through the space of material parameters to achieve a variety of functional phenotypes.

Clathrin-mediated endocytosis (CME), the major cellular entry pathway, starts when clathrin assembles on the plasma membrane into clathrin-coated pits (CCPs). Two populations of CCPs are detected within the same cell: productive CCPs that invaginate and pinch off, forming clathrin-coated vesicles (CCVs) [1, 2], and abortive CCPs [3, 4, 5] that prematurely disassemble. The mechanisms of gating between these two populations and their relations to the functions of dozens of early-acting endocytic accessory proteins (EAPs) [5, 6, 7, 8, 9] have remained elusive. Here, we use experimentally-guided modeling to integrate the clathrin machinery and membrane mechanics in a single dynamical system. We show that the split between the two populations is an emergent property of this system, in which a switch between an Open state and a Closed state follows from the competition between the chemical energy of the clathrin basket and the mechanical energy of membrane bending. In silico experiments revealed an abrupt transition between the two states that acutely depends on the strength of the clathrin basket. This critical strength is lowered by membrane-bending EAPs [10, 11, 12]. Thus, CME is poised to be shifted between abortive and productive events by small changes in membrane curvature and/or coat stability. This model clarifies the workings of a putative endocytic checkpoint whose existence was previously proposed based on statistical analyses of the lifetime distributions of CCPs [4, 13]. Overall, a mechanistic framework is established to elucidate the diverse and redundant functions of EAPs in regulating CME progression.

Over the half century since the renormalization group (RG) brought about deep understanding of critical phenomena in condensed matter physics, it has been claimed that diverse social, engineered, astrophysical, and biological systems operate close to criticality. However, these systems do not afford the neat phase diagrams and exquisite control available in condensed matter physics. How can one assess proximity to criticality when control parameters are unknown, difficult to manipulate experimentally, and fluctuating in response to changing environmental or internal conditions? Here we meet this challenge with a rigorous theoretical framework and data-analytic strategy for measuring proximity to criticality from observed system dynamics. We developed a temporal RG, well-suited to commonly measured time series, and an information theoretic quantification of proximity to criticality that is independent of model parameterization. After benchmarking our approach on diverse ground-truth cases, we apply it to recordings of spiking activity in the mammalian brain, addressing a long-standing controversy. We show that brain dynamics shift closer to criticality during wakefulness and shift away during deep sleep.

We investigate the target search process by proteins locating specific target sites along DNA - a phenomenon fundamental to biological functions such as gene regulation, transcription, replication, recombination, and gene-editing technologies. This process proceeds through a repetitive sequence of stochastic motions: consisting of one-dimensional (1D) sliding along the DNA contour interspersed with detachment and three-dimensional (3D) excursions in the bulk, and then reattachment to a random location on DNA. Recognizing this sequence of random events as analogous to the resetting processes widely studied in statistical physics, we employ a first-passage-renewal framework and derive general expressions for both the mean and fluctuations of the total search time. Our results are completely generic and do not depend on the detailed microscopic dynamics of either the 1D or 3D phases. Quite interestingly, we find that intermittent detachment can not only accelerate the mean search but can also regulate fluctuations around it. Our analysis reveals a universal fluctuation inequality that links the variability and mean of the sliding time to the mean excursion time, thereby identifying the fundamental conditions under which target search process becomes efficient. Notably, we find that broad distributions of sliding times emerge as a universal characteristic for optimal search efficiency--a feature emanating from the slow dynamics along the DNA. Using the facilitated diffusion mechanism as a representative example, we validate the generality of our results. These findings provide a unified theoretical framework connecting stochastic search, resetting dynamics, and biological efficiency, while also highlighting the crucial role of DNA structure such as its contour length in modulating search performance.

In this paper we use the methods of theoretical physics to show how brain-like signals can be generated in a special surface network with the topological connectivity of the biological brain by exploiting its form. The network is required to have surface spin-half particles. We show that the signals thus generated carry information regarding their creation and can transfer and store this information to form memory structures in helical aligned surface spin-half particles present on the surfaces of the pathways traversed by the signals. Theoretical neuroscience is progressing strongly with novel representations of the brain, enhanced by the increase of computational power now available. New methods to explore complex brain events and the structures for storing memories as engrams are emerging. However, there are major conceptual theoretical problems that remain unaddressed. Current theoretical methods are very capable of reacting to experimental results and modelling both neural signalling and structure. Yet they still fall short to throw light on how the brain creates its own information code, or relate the variety of brain signals observed, or explain where and how memories are stored. We prove that current brain signal interpretations cannot carry information regarding their formation so that they cannot be used to understand how memories of events are related to signals. Thus, our results address these basic unresolved theoretical problems of neuroscience and suggest testable solutions. The memory structures of aligned spin-half particles suggested have not been observed in biological organisms as yet they but they have been observed in solid state physics and their existence is consistent with conventional understandings of neurobiology. All the results stated follow from the dynamical law for the network.

The spatiotemporal selectivity of neurons to sensory stimuli that underlie the center and surround receptive fields represents the anticommutative and, thus, symmetry that defines sensorimotor transformation. However, owing to the nonabelian nature of the irresponsiveness of neurons to sensory stimuli characterized by inexcitations, symmetry and, thus, transformation does not become apparent. Hence, a neuroscientific model that describes the precise mechanism of the nonabelian gauge group in the brain is unknown. Using quantum field theory, we show visuomotor transformation of natural images in which the superposition of opposite parallel cortical columns creates visual fields and annihilates motor fields. The creation and annihilation operators, magnetic and electric charged particles, are opposed inertia systems that act on each other by raising and lowering each others particles, leading to momentum-energy trade-offs, in our case, retinotopic gain and retinomotion loss, and vice versa. The magnetic charged particles K-, Cl+, Na-, intrinsic to a magnetic neuron, nabla, are predicted to exist opposite parallel to the electrically charged particles Na+, Cl-, K+ of the electrical pyramidal neuron in the neocortex. The implication is that the physical neocortex or electric brain is in concert with a nonphysical complex neocortex or magnetic brain that is hardly detectable but much alive and proactive.

We present a theory for the effects of osmotic pressure exerted by macromolecular crowders, on a double-stranded DNA (or any other semiflexible polymer) extended by tension. Our results predict DNA force extension curves. The lowest-order effect is a crowder-dependent compression that counteracts the external stretching force. This compression effect can collapse the polymer at a crowder-dependent critical force f*. This compression is dependent on crowder radius r and density phi, with higher densities and smaller radii having greater effects on the force-extension curve. At first order in perturbation theory we also find a fluctuation-dependent correction to the depletion volume, which can overwhelm the simple compression effect for large crowders, leading to expansion of the polymer.

Cell-scale curvature plays important roles in controlling cell and tissue behaviors. However, these roles have not been well quantified, and the underlying mechanisms remain elusive. We combine experiments with theory to study systematically the curvature-dependence of cell migration inside PDMS microcylinders. We find that persistence is positively correlated with speed, following the universal speed-persistence coupling relation, i.e., faster cells turn less. Cell migration inside microcylinders is anisotropic and depends on curvature in a biphasic manner. At small curvatures, as curvature increases, the average speed and anisotropy both increase, but surprisingly, the average persistence decreases. Whereas as the curvature increases over some threshold, cells detach from the surface, the average speed and anisotropy both decrease sharply but the average persistence increases. Moreover, interestingly, cells are found to leave paxillins along their trajectories (on curved but not planar surfaces), facilitating the assembly of focal adhesions of following cells. We propose a minimal model for the biphasic curvotaxis based on three mechanisms: the persistent random "noise", the bending penalty of stress fibers, and the cell-surface adhesion. The findings provide a novel and general perspective on directed cell migration in the widely existing curved microenvironment of cells in vivo.