arXiv subjects

Yoichiro Mori

Publications and source records attributed to Yoichiro Mori.

At least 37 records · Page 2Linked to original sources

arXiv2022

Optimality of intercellular signaling: direct transport versus diffusion

Intercellular signaling has an important role in organism development, but not all communication occurs using the same mechanism. Here, we analyze the energy efficiency of intercellular signaling by two canonical mechanisms: diffusion of signaling molecules and direct transport mediated by signaling cellular protrusions. We show that efficient contact formation for direct transport can be established by an optimal rate of projecting protrusions, which depends on the availability of information about the location of the target cell. The optimal projection rate also depends on how signaling molecules are transported along the protrusion, in particular the ratio of the energy cost for contact formation and molecule synthesis. Also, we compare the efficiency of the two signaling mechanisms, under various model parameters. We find that the direct transport is favored over the diffusion when transporting a large amount of signaling molecules. There is a critical number of signaling molecules at which the efficiency of the two mechanisms are the same. The critical number is small when the distance between cells is far, which helps explain why protrusion-based mechanisms are observed in long-range cellular communications.

q-bio.QM↗

arXiv2022

Evolutionary Dynamics Within and Among Competing Groups

Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible for profound transitions in evolutionary history, including the origin of cellular life, multi-cellular life, and even societies. Here we synthesize a growing literature that extends evolutionary game theory to describe multilevel evolutionary dynamics, using nested birth-death processes and partial differential equations to model natural selection acting on competition within and among groups of individuals. We apply this theory to analyze how mechanisms known to promote cooperation within a single group -- including assortment, reciprocity, and population structure -- alter evolutionary outcomes in the presence of competition among groups. We find that population structures most conducive to cooperation in multi-scale systems may differ from those most conducive within a single group. Likewise, for competitive interactions with a continuous range of strategies we find that among-group selection may fail to produce socially optimal outcomes, but it can nonetheless produce second-best solutions that balance individual incentives to defect with the collective incentives for cooperation. We conclude by describing the broad applicability of multi-scale evolutionary models to problems ranging from the production of diffusible metabolites in microbes to the management of common-pool resources in human societies.

q-bio.PE↗

arXiv2022

Well-posedness and applications of classical elastohydrodynamics for a swimming filament

We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in $\mathbb{R}^3$. The hydrodynamics are described by resistive force theory, and the fiber elasticity is governed by Euler-Bernoulli beam theory. Our aim is twofold: (1) Serve as a starting point for developing the mathematical analysis of filament elastohydrodynamics, particularly the analytical treatment of an inextensibility constraint, and (2) As an application, prove conditions on internal fiber forcing that allow a free-ended filament to swim. Our analysis of fiber swimming speed is supplemented with a numerical optimization of the internal fiber forcing, as well as a novel numerical method for simulating an inextensible swimmer.

math.AP↗

arXiv2022

Selfish optimization and collective learning in populations

A selfish learner seeks to maximize their own success, disregarding others. When success is measured as payoff in a game played against another learner, mutual selfishness typically fails to produce the optimal outcome for a pair of individuals. However, learners often operate in populations, and each learner may have a limited duration of interaction with any other individual. Here, we compare selfish learning in stable pairs to selfish learning with stochastic encounters in a population. We study gradient-based optimization in repeated games like the prisoner's dilemma, which feature multiple Nash equilibria, many of which are suboptimal. We find that myopic, selfish learning, when distributed in a population via ephemeral encounters, can reverse the dynamics that occur in stable pairs. In particular, when there is flexibility in partner choice, selfish learning in large populations can produce optimal payoffs in repeated social dilemmas. This result holds for the entire population, not just for a small subset of individuals. Furthermore, as the population size grows, the timescale to reach the optimal population payoff remains finite in the number of learning steps per individual. While it is not universally true that interacting with many partners in a population improves outcomes, this form of collective learning achieves optimality for several important classes of social dilemmas. We conclude that naïve learning can be surprisingly effective in populations of individuals navigating conflicts of interest.

q-bio.PE↗

arXiv2022

Long-Time Behavior of a PDE Replicator Equation for Multilevel Selection in Group-Structured Populations

In many biological systems, natural selection acts simultaneously on multiple levels of organization. This scenario typically presents an evolutionary conflict between the incentive of individuals to cheat and the collective incentive to establish cooperation within a group. Generalizing previous work on multilevel selection in evolutionary game theory, we consider a hyperbolic PDE model of a group-structured population, in which members within a single group compete with each other for individual-level replication; while the group also competes against other groups for group-level replication. We derive a threshold level of the relative strength of between-group competition such that defectors take over the population below the threshold while cooperation persists in the long-time population above the threshold. Under stronger assumptions on the initial distribution of group compositions, we further prove that the population converges to a steady state density supporting cooperation for between-group selection strength above the threshold. We further establish long-time bounds on the time-average of the collective payoff of the population, showing that the long-run population cannot outperform the payoff of a full-cooperator group even in the limit of infinitely-strong between-group competition. When the group replication rate is maximized by an intermediate level of within-group cooperation, individual-level selection casts a long shadow on the dynamics of multilevel selection: no level of between-group competition can erase the effects of the individual incentive to defect. We further extend our model to study the case of multiple types of groups, showing how the games that groups play can coevolve with the level of cooperation.

q-bio.PE↗

arXiv2021

A single-layer based numerical method for the slender body boundary value problem

Fluid flows containing dilute or dense suspensions of thin fibers are widespread in biological and industrial processes. To describe the motion of a thin immersed fiber, or to describe the forces acting on it, it is convenient to work with one-dimensional fiber centerlines and force densities rather than two-dimensional surfaces and surface tractions. Slender body theories offer ways to model and simulate the motion of immersed fibers using only one-dimensional data. However, standard formulations can break down when the fiber surface comes close to intersecting itself or other fibers. In this paper we introduce a numerical method for a recently derived three-dimensional slender body boundary value problem that can be stated entirely in terms of a one-dimensional distribution of forces on the centerline. The method is based on a new completed single-layer potential formulation of fluid velocity which removes the nullspace associated with the unmodified single layer potential. We discretize the model and present numerical results demonstrating the good conditioning and improved performance of the method in the presence of near-intersections. To avoid the modeling and numerical choices involved with free ends, we consider closed fibers.

math.NA↗

arXiv2021

Evolution of prosocial behavior in multilayer populations

Human societies include diverse social relationships. Friends, family, business colleagues, and online contacts can all contribute to one's social life. Individuals may behave differently in different domains, but success in one domain may engender success in another. Here, we study this problem using multilayer networks to model multiple domains of social interactions, in which individuals experience different environments and may express different behaviors. We provide a mathematical analysis and find that coupling between layers tends to promote prosocial behavior. Even if prosociality is disfavored in each layer alone, multilayer coupling can promote its proliferation in all layers simultaneously. We apply this analysis to six real-world multilayer networks, ranging from the socio-emotional and professional relationships in a Zambian community, to the online and offline relationships within an academic University. We discuss the implications of our results, which suggest that small modifications to interactions in one domain may catalyze prosociality in a different domain.

physics.soc-ph↗

arXiv2021

Asymptotic behavior of fronts and pulses of the bidomain model

The bidomain model is the standard model for cardiac electrophysiology. In this paper, we investigate the instability and asymptotic behavior of planar fronts and planar pulses of the bidomain Allen-Cahn equation and the bidomain FitzHugh-Nagumo equation in two spatial dimension. In previous work, it was shown that planar fronts of the bidomain Allen-Cahn equation can become unstable in contrast to the classical Allen-Cahn equation. We find that, after the planar front is destabilized, a rotating zigzag front develops whose shape can be explained by simple geometric arguments using a suitable Frank diagram. We also show that the Hopf bifurcation through which the front becomes unstable can be either supercritical or subcritical, by demonstrating a parameter regime in which a stable planar front and zigzag front can coexist. In our computational studies of the bidomain FitzHugh-Nagumo pulse solution, we show that the pulses can also become unstable much like the bidomain Allen-Cahn fronts. However, unlike the bidomain Allen-Cahn case, the destabilized pulse does not necessarily develop into a zigzag pulse. For certain choice of parameters, the destabilized pulse can disintegrate entirely. These studies are made possible by the development of a numerical scheme that allows for the accurate computation of the bidomain equation in a two dimensional strip domain of infinite extent.

math.DS↗

arXiv2020

The Peskin Problem with Viscosity Contrast

The Peskin problem models the dynamics of a closed elastic filament immersed in an incompressible fluid. In this paper, we consider the case when the inner and outer viscosities are possibly different. This viscosity contrast adds further non-local effects to the system through the implicit non-local relation between the net force and the free interface. We prove the first global well-posedness result for the Peskin problem in this setting. The result applies for medium size initial interfaces in critical spaces and shows instant analytic smoothing. We carefully calculate the medium size constraint on the initial data. These results are new even without viscosity contrast.

math.AP↗

arXiv2020

Accuracy of slender body theory in approximating force exerted by thin fiber on viscous fluid

We consider the accuracy of slender body theory in approximating the force exerted by a thin fiber on the surrounding viscous fluid when the fiber velocity is prescribed. We term this the slender body inverse problem, as it is known that slender body theory converges to a well-posed PDE solution when the force is prescribed and the fiber velocity is unknown. From a PDE perspective, the slender body inverse problem is simply the Dirichlet problem for the Stokes equations, but from an approximation perspective, nonlocal slender body theory exhibits high wavenumber instabilities which complicate analysis. Here we consider two methods for regularizing the slender body approximation: spectral truncation and the $δ$-regularization of Tornberg and Shelley (2004). For a straight, periodic fiber with constant radius $ε>0$, we explicitly calculate the spectrum of the operator mapping fiber velocity to force for both the PDE and the approximations. We show that the spectrum of the original slender body approximation agrees closely with the PDE solution at low wavenumbers but differs at high frequencies, allowing us to define a truncated approximation with a wavenumber cutoff $\sim1/ε$. For both the truncated and $δ$-regularized approximations, we obtain similar convergence results to the PDE solution as $ε\to0$: a fiber velocity with $H^1$ regularity gives $O(ε)$ convergence, while a fiber velocity with at least $H^2$ regularity yields $O(ε^2)$ convergence. Moreover, we determine the dependence of the $δ$-regularized error estimate on the regularization parameter $δ$.

math.AP↗

arXiv2020

An error bound for the slender body approximation of a thin, rigid fiber sedimenting in Stokes flow

We investigate the motion of a thin rigid body in Stokes flow and the corresponding slender body approximation used to model sedimenting fibers. In particular, we derive a rigorous error bound comparing the rigid slender body approximation to the classical PDE for rigid motion in the case of a closed loop with constant radius. Our main tool is the slender body PDE framework established by the authors and D. Spirn in [18,19], which we adapt to the rigid setting.

math.AP↗

arXiv2019

Theoretical justification and error analysis for slender body theory

Slender body theory facilitates computational simulations of thin fibers immersed in a viscous fluid by approximating each fiber using only the geometry of the fiber centerline curve and the line force density along it. However, it has been unclear how well slender body theory actually approximates Stokes flow about a thin but truly three-dimensional fiber, in part due to the fact that simply prescribing data along a one-dimensional curve does not result in a well-posed boundary value problem for the Stokes equations in $\mathbb{R}^3$. Here, we introduce a PDE problem to which slender body theory (SBT) provides an approximation, thereby placing SBT on firm theoretical footing. The slender body PDE is a new type of boundary value problem for Stokes flow where partial Dirichlet and partial Neumann conditions are specified everywhere along the fiber surface. Given only a 1D force density along a closed fiber, we show that the flow field exterior to the thin fiber is uniquely determined by imposing a fiber integrity condition: the surface velocity field on the fiber must be constant along cross sections orthogonal to the fiber centerline. Furthermore, a careful estimation of the residual, together with stability estimates provided by the PDE well-posedness framework, allow us to establish error estimates between the slender body approximation and the exact solution to the above problem. The error is bounded by an expression proportional to the fiber radius (up to logarithmic corrections) under mild regularity assumptions on the 1D force density and fiber centerline geometry.

math.AP↗

arXiv2019

Theoretical justification and error analysis for slender body theory with free ends

Slender body theory is a commonly used approximation in computational models of thin fibers in viscous fluids, especially in simulating the motion of cilia or flagella in swimming microorganisms. In [23], we developed a PDE framework for analyzing the error introduced by the slender body approximation for closed-loop fibers with constant radius $ε$, and showed that the difference between our closed-loop PDE solution and the slender body approximation is bounded by an expression proportional to $ε|\logε|$. Here we extend the slender body PDE framework to the free endpoint setting, which is more physically relevant from a modeling standpoint but more technically demanding than the closed loop analysis. The main new difficulties arising in the free endpoint setting are defining the endpoint geometry, identifying the extent of the 1D slender body force density, and determining how the well-posedness constants depend on the non-constant fiber radius. Given a slender fiber satisfying certain geometric constraints at the filament endpoints and a one-dimensional force density satisfying an endpoint decay condition, we show a bound for the difference between the solution to the slender body PDE and the slender body approximation in the free endpoint setting. The bound is a sum of the same $ε|\logε|$ term appearing in the closed loop setting and an endpoint term proportional to $ε$, where $ε$ is now the maximum fiber radius.

math.AP↗

arXiv2018

From Electrodiffusion Theory to the Electrohydrodynamics of Leaky Dielectrics through the Weak Electrolyte Limit

The Taylor-Melcher (TM) model is the standard model for describing the dynamics of poorly conducting leaky dielectric fluids under an electric field. The TM model treats the fluids as Ohmic conductors, without modeling the underlying ion dynamics. On the other hand, electrodiffusion models, which have been successful in describing electrokinetic phenomena, incorporate ionic concentration dynamics. Mathematical reconciliation of the electrodiffusion picture and the TM model has been a major issue for electrohydrodynamic theory. Here, we derive the TM model from an electrodiffusion model in which we explicitly model the electrochemistry of ion dissociation. We introduce salt dissociation reaction terms in the bulk electrodiffusion equations and take the limit in which the salt dissociation is weak; the assumption of weak dissociation corresponds to the fact that the TM model describes poor conductors. Together with the assumption that the Debye length is small, we derive the TM model with or without the surface charge convection term depending upon the scaling of relevant dimensionless parameters. An important quantity that emerges is the Galvani potential (GP), the jump in voltage across the liquid-liquid interface between the two leaky dielectric media; the GP arises as a natural consequence of the interfacial boundary conditions for the ionic concentrations, and is absent under certain parametric conditions. When the GP is absent, we recover the TM model. Our analysis also reveals the structure of the Debye layer at the liquid-liquid interface, which suggests how interfacial singularities may arise under strong imposed electric fields. In the presence of a non-zero GP, our model predicts that the liquid droplet will drift under an imposed electric field, the velocity of which is computed explicitly to leading order.

physics.flu-dyn↗

arXiv2018

Well-posedness and global behavior of the Peskin problem of an immersed elastic filament in Stokes flow

We consider the problem of a one dimensional elastic filament immersed in a two dimensional steady Stokes fluid. Immersed boundary problems in which a thin elastic structure interacts with a surrounding fluid are prevalent in science and engineering, a class of problems for which Peskin has made pioneering contributions. Using boundary integrals, we first reduce the fluid equations to an evolution equation solely for the immersed filament configuration. We then establish local well-posedness for this equation with initial data in low-regularity Hölder spaces. This is accomplished by first extracting the principal linear evolution by a small scale decomposition and then establishing precise smoothing estimates on the nonlinear remainder. Higher regularity of these solutions is established via commutator estimates with error terms generated by an explicit class of integral kernels. Furthermore, we show that the set of equilibria consists of uniformly parametrized circles and prove nonlinear stability of these equilibria with explicit exponential decay estimates, the optimality of which we verify numerically. Finally, we identify a quantity which respects the symmetries of the problem and controls global-in-time behavior of the system.

math.AP↗

arXiv2016

Rhythmomimetic drug delivery: modeling, analysis and numerical simulation

We develop, analyse and numerically simulate a model of a prototype, glucose-driven, rhythmic drug delivery device, aimed at hormone therapies, and based on chemomechanical interaction in a polyelectrolyte gel membrane. The pH-driven interactions trigger volume phase transitions between the swollen and collapsed states of the gel.For a robust set of material parameters, we find a class of solutions of the governing system that oscillate between such states, and cause the membrane to rhythmically swell, allowing for transport of the drug, fuel and reaction products across it, and collapse, hampering all transport across it. The frequency of the oscillations can be adjusted so that it matches the natural frequency of the hormone to be released. The work is linked to extensive laboratory experimental studies of the device built by Siegel's team. The thinness of the membrane and its clamped boundary, together with the homogeneously held conditions in the experimental apparatus, justify neglecting spatial dependence on the fields of the problem. Upon identifying the forces and energy relevant to the system, and taking into account its dissipative properties, we apply Rayleigh's variational principle to obtain the governing equations. The material assumptions guarantee the monotonicity of the system and lead to the existence of a three dimensional limit cycle. By scaling and asymptotic analysis, this limit cycle is found to be related to a two-dimensional one that encodes the volume phase transitions of the model. The identification of the relevant parameter set of the model is aided by a Hopf bifurcation study of steady state solutions.

physics.chem-ph↗

arXiv2014

A Multidomain Model for Ionic Electrodiffusion and Osmosis with an Application to Cortical Spreading Depression

Ionic electrodiffusion and osmotic water flow are central processes in many physiological systems. We formulate a system of partial differential equations that governs ion movement and water flow in biological tissue. A salient feature of this model is that it satisfies a free energy identity, ensuring the thermodynamic consistency of the model. A numerical scheme is developed for the model in one spatial dimension and is applied to a model of cortical spreading depression, a propagating breakdown of ionic and cell volume homeostasis in the brain.

q-bio.TO↗

arXiv2011

Mathematical Properties of Pump-Leak Models of Cell Volume Control and Electrolyte Balance

Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.

q-bio.CB↗