📰 "Molecular-scale, nonlinear actomyosin binding dynamics drive population-scale adaptation and evolutionary convergence"
https://arxiv.org/abs/2603.17183 #Physics.Bio-Ph
#Actomyosin #Dynamics #Nlin.Ao
#Myosin #Force
Molecular-scale, nonlinear actomyosin binding dynamics drive population-scale adaptation and evolutionary convergence
Biological actuators -- from myosin motors to muscles -- follow Hill's model where a dimensionless parameter $α$ captures the nonlinear coupling between contraction rate and force generation. Our prior work identified a characteristic $α^* = 3.85 \pm 2.32$ across natural muscles and showed that $α^*$ optimizes a power-efficiency tradeoff, potentially explaining its prevalence in nature. However, those results reflected short-term actuation tasks whereas phenotypic distributions in $α$ emerge over evolutionary timescales. Here, we use numerical simulations of self-propelled agents to explore how nonlinear actomyosin actuation (parameterized by $α$) shapes population dynamics. Agents of different $α$ compete for resources and reproduce with slight mutations. Without mutations, resource availability drives populations in $α$ toward distinct behaviors: under abundance or scarcity, specialized $α$ survive. However, with mutations and selection, populations evolve toward distributions centered around the characteristic $α^*$ observed in nature. Further, we show that the mutation rate $δ$ governs a balance between adaptability and robustness: large $δ$ generates instability and extinction, small $δ$ prevents feedback, while intermediate $δ$ enables long-term adaptability while remaining robust to short-term noise. Our results suggest that nonlinear actuation provides a general understanding of energy management in actomyosin systems across a wide range of timescales, ranging from the task-specific to evolutionary. These insights may guide the rational design of active materials with adaptive properties.
📰 "Molecular-scale, nonlinear actomyosin binding dynamics drive population-scale adaptation and evolutionary convergence"
https://arxiv.org/abs/2603.17183 #Physics.Bio-Ph
#Actomyosin #Nlin.Ao
#MyosinMolecular-scale, nonlinear actomyosin binding dynamics drive population-scale adaptation and evolutionary convergence
Biological actuators -- from myosin motors to muscles -- follow Hill's model where a dimensionless parameter $α$ captures the nonlinear coupling between contraction rate and force generation. Our prior work identified a characteristic $α^* = 3.85 \pm 2.32$ across natural muscles and showed that $α^*$ optimizes a power-efficiency tradeoff, potentially explaining its prevalence in nature. However, those results reflected short-term actuation tasks whereas phenotypic distributions in $α$ emerge over evolutionary timescales. Here, we use numerical simulations of self-propelled agents to explore how nonlinear actomyosin actuation (parameterized by $α$) shapes population dynamics. Agents of different $α$ compete for resources and reproduce with slight mutations. Without mutations, resource availability drives populations in $α$ toward distinct behaviors: under abundance or scarcity, specialized $α$ survive. However, with mutations and selection, populations evolve toward distributions centered around the characteristic $α^*$ observed in nature. Further, we show that the mutation rate $δ$ governs a balance between adaptability and robustness: large $δ$ generates instability and extinction, small $δ$ prevents feedback, while intermediate $δ$ enables long-term adaptability while remaining robust to short-term noise. Our results suggest that nonlinear actuation provides a general understanding of energy management in actomyosin systems across a wide range of timescales, ranging from the task-specific to evolutionary. These insights may guide the rational design of active materials with adaptive properties.
📰 "Topology and higher-order global synchronization on directed and hollow simplicial and cell complexes"
https://arxiv.org/abs/2602.09715 #Cond-Mat.Stat-Mech
#Cond-Mat.Dis-Nn
#Physics.Soc-Ph
#Dynamics #Nlin.Ao
#Math-Ph
#Math.Mp
#Cell
Topology and higher-order global synchronization on directed and hollow simplicial and cell complexes
Higher-order networks encode the many-body interactions of complex systems ranging from the brain to biological transportation networks. Simplicial and cell complexes are ideal higher-order network representations for investigating higher-order topological dynamics where dynamical variables are not only associated with nodes, but also with edges, triangles, and higher-order simplices and cells. Global Topological Synchronization (GTS) refers to the dynamical state in which identical oscillators associated with higher-dimensional simplices and cells oscillate in unison. On standard unweighted and undirected complexes this dynamical state can be achieved only under strict topological and combinatorial conditions on the underlying discrete support. In this work we consider generalized higher-order network representations including directed and hollow complexes. Based on an in depth investigation of their topology defined by their associated algebraic topology operators and Betti numbers, we determine under which conditions GTS can be observed. We show that directed complexes always admit a global topological synchronization state independently of their topology and structure. However, we demonstrate that for directed complexes this dynamical state cannot be asymptotically stable. While hollow complexes require more stringent topological conditions to sustain global topological synchronization, these topologies can favor both the existence and the stability of global topological synchronization with respect to undirected and unweighted complexes.
📰 "Gardner volumes and self-organization in a minimal model of complex ecosystems"
https://arxiv.org/abs/2601.00707 #Q-Bio.Pe
#Dynamics #Nlin.Ao
#Math.Ds
#Matrix
Gardner volumes and self-organization in a minimal model of complex ecosystems
We study self-organization in a minimally nonlinear model of large random ecosystems. Populations evolve over time according to a piecewise linear system of ordinary differential equations subject to a non-negativity constraint resulting in discrete time extinction and revival events. The dynamics are generated by a random elliptic community matrix with tunable correlation strength. We show that, independent of the correlation strength, solutions of the system are confined to subsets of the phase space that can be cast as time-varying Gardner volumes from the theory of learning in neural networks. These volumes decrease with the diversity (i.e. the fraction of extant species) and become exponentially small in the long-time limit. Using standard results from random matrix theory, the changing diversity is then linked to a sequence of contractions and expansions in the spectrum of the community matrix over time, resulting in a sequence of May-type stability problems determining whether the total population evolves toward complete extinction or unbounded growth. In the case of unbounded growth, we show the model allows for a particularly simple nonlinear extension in which the solutions instead evolve towards a new attractor.
📰 "Epigenetic Control and Reprogramming-Induced Potential Landscapes of Gene Regulatory Networks: A Quantitative Theoretical Approach"
https://arxiv.org/abs/2512.24427 #Physics.Bio-Ph
#Q-Bio.Qm
#Dynamics #Q-Bio.Mn
#Nlin.Ao
#Nlin.Cd
#Cell
Epigenetic Control and Reprogramming-Induced Potential Landscapes of Gene Regulatory Networks: A Quantitative Theoretical Approach
We develop an extended Dynamical Mean Field Theory framework to analyze gene regulatory networks (GRNs) incorporating epigenetic modifications. Building on the Hopfield network model analogy to spin glass systems, our approach introduces dynamic terms representing DNA methylation and histone modification to capture their regulatory influence on gene expression. The resulting formulation reduces high-dimensional GRN dynamics to effective stochastic equations, enabling the characterization of both stable and oscillatory states in epigenetically regulated systems. This framework provides a tractable and quantitative method for linking gene regulatory dynamics with epigenetic control, offering new theoretical insights into developmental processes and cell fate decisions.
📰 "Stochastic Models of Neuronal Growth"
https://arxiv.org/abs/2205.10723 #Physics.Bio-Ph
#Q-Bio.Nc
#Nlin.Ao
#Actin
Stochastic Models of Neuronal Growth
Neuronal circuits arise as axons and dendrites extend, navigate, and connect to target cells. Axonal growth, in particular, integrates deterministic guidance from substrate mechanics and geometry with stochastic fluctuations generated by signaling, molecular detection, cytoskeletal assembly, and growth cone dynamics. A comprehensive quantitative description of this process remains incomplete. We review stochastic models in which Langevin dynamics and the associates Fokker-Planck equation capture axonal motion and turning under combined biases and noise. Paired with experiments, these models yield key parameters, including effective diffusion (motility) coefficients, speed and angle distributions, mean-square displacement, and mechanical measures of cell-substrate coupling, thereby linking single-cell biophysics and intercellular interactions to collective growth statistics and network formation. We further couple the Fokker-Planck description to a mechanochemical actin-myosin-clutch model and perform a linear stability analysis of the resulting dynamics. Routh--Hurwitz criteria identify regimes of steady extension, damped oscillations, and Hopf bifurcations that generate sustained limit cycles. Together, these results clarify the mechanisms that govern axonal guidance and connectivity and inform the design of engineered substrates and neuroprosthetic scaffolds aimed at enhancing nerve repair and regeneration.
📰 "Protein Drift-Diffusion in Membranes with Non-equilibrium Fluctuations arising from Gradients in Concentration or Temperature"
https://arxiv.org/abs/2506.22695 #Physics.Comp-Ph
#Physics.Bio-Ph
#Cond-Mat.Soft
#Mechanics #Q-Bio.Sc
#Nlin.Ao
#CellProtein Drift-Diffusion in Membranes with Non-equilibrium Fluctuations arising from Gradients in Concentration or Temperature
We investigate proteins within heterogeneous cell membranes where non-equilibrium phenomena arises from spatial variations in concentration and temperature. We develop simulation methods building on non-equilibrium statistical mechanics to obtain stochastic hybrid continuum-discrete descriptions which track individual protein dynamics, spatially varying concentration fluctuations, and thermal exchanges. We investigate biological mechanisms for protein positioning and patterning within membranes and factors in thermal gradient sensing. We also study the kinetics of Brownian motion of particles with temperature variations within energy landscapes arising from heterogeneous microstructures within membranes. The introduced approaches provide self-consistent models for studying biophysical mechanisms involving the drift-diffusion dynamics of individual proteins and energy exchanges and fluctuations between the thermal and mechanical parts of the system. The methods also can be used for studying related non-equilibrium effects in other biological systems and soft materials.
📰 "Active waves from non-reciprocity and cytoplasmic exchange"
https://arxiv.org/abs/2505.09740 #Physics.Flu-Dyn
#Physics.Bio-Ph
#Actomyosin #Nlin.Ps
Active waves from non-reciprocity and cytoplasmic exchange
Pattern formation in active biological matter typically arises from the feedback between chemical concentration fields and mechanical stresses. The actomyosin cortex of cells is an archetypal example of an active thin film that displays such patterns. Here, we show how pulsatory patterns emerge in a minimal model of the actomyosin cortex with a single stress-regulating chemical species that exchanges material with the cytoplasm via a linear turnover reaction. Deriving a low-dimensional amplitude-phase model, valid for a one-dimensional periodic domain and a spherical surface, we show that nonlinear waves arise from a secondary parity-breaking bifurcation that originates from the nonreciprocal interaction between spatial modes of the concentration field. Numerical analysis confirms these analytical predictions, and also reveals analogous pulsatory patterns on impermeable domains. Our study provides a generic route to the emergence of nonreciprocity-driven pulsatory patterns that can be controlled by both the strength of activity and the turnover rate.
📰 "Two-component model of a microtubule in a semi-discrete approximation"
https://arxiv.org/abs/2410.14297 #Physics.Bio-Ph
#Microtubule #Nlin.Ps
Two-component model of a microtubule in a semi-discrete approximation
In the present work, we study the nonlinear dynamics of a microtubule, an important part of the cytoskeleton. We use a two-component model of the relevant system. A crucial nonlinear differential equation is solved with semi-discrete approximation, yielding some localised modulated solitary waves called the breathers. A detailed estimation of the existing parameters is provided. The numerical investigation shows that the solutions are robust only if the carrier velocity of the breather wave is higher than its envelope velocity. That disproves the previously accepted solutions based on the equality of these velocities.
📰 "Travelling waves and wave pinning (polarity): Switching between random and directional cell motility"
https://arxiv.org/abs/2410.12213 #Q-Bio.Cb
#Nlin.Ps
#ActinBistability of travelling waves and wave-pinning states in a mass-conserved reaction-diffusion system: From bifurcations to implications for actin waves
Eukaryotic cells demonstrate a wide variety of dynamic patterns of filamentous actin (F-actin) and its regulators. Some of these patterns play important roles in cell functions, such as distinct motility modes, which motivate this study. We devise a mass-conserved reaction-diffusion model for active and inactive Rho-GTPase and F-actin in the cell cortex. The mass-conserved Rho-GTPase system promotes F-actin, which feeds back to inactivate the former. We study the model on a 1D periodic domain (edge of thin sheet-like cell) using bifurcation theory in the framework of spatial dynamics, complemented with numerical simulations. Among several discussed bifurcations, the analysis centers on the study of the codimension-2 long wavelength and finite wavenumber Hopf instability, in which we describe a rich structure of steady wave-pinning states (a.k.a. mesas, obeying the Maxwell construction), propagating coherent solutions (fronts and excitable pulses), and travelling and standing waves, all distinguished by mass conservation regimes and classified by domain sizes. Specifically, we highlight the unexpected conditions for bistability between steady wave-pinning and travelling wave states on moderate domain sizes, i.e., unfolding through domain length. These results uncover and exemplify possible mechanisms of coexistence, robustness, and transitions between distinct cellular motility modes, including directed migration, turning, and ruffling. More broadly, the results indicate that non-gradient reaction-diffusion models comprising mass conservation have distinct pattern formation mechanisms that motivate further investigations, such as the unfolding of codimension-3 instabilities and T-points.
Rxiv mechanobio
Rxiv cytoskeleton
Rxiv cytoskeleton