arXiv subjects

Thomas G. Fai

Publications and source records attributed to Thomas G. Fai.

At least 19 recordsLinked to original sources

arXiv2026

Squirming motion near corrugated surfaces

Swimming microorganisms often operate in complex confinement, where an interplay of long-ranged hydrodynamic interactions and a short-ranged repulsive interaction can give rise to interesting dynamical behaviors. Here, we theoretically investigate the trajectories of microswimmers - modeled as squirmers - in the presence of periodic boundaries. The latter modify their swimming velocity, leading to behaviors that differ qualitatively from swimming near planar walls. Using a perturbative approach based on bispherical coordinates and the Lorentz reciprocal theorem, we characterize the interaction between a squirmer and a periodic surface in the limit of small surface amplitude and systematically explore its dependence on the boundary corrugation wavelength, squirmer type, orientation, and swimmer-surface distance. Most importantly, our results reveal that pullers become trapped in the valley of the surface corrugations, in contrast to their sliding motion near planar walls. Furthermore, the near-surface dynamics of pushers display oscillations, reflecting the periodicity of the surface structure. A tilt of the swimmer orientation with respect to the surface corrugations results in a wave-length dependent drift that sorts pushers from pullers. These findings highlight the impact of hydrodynamic interactions in shaping microswimmer transport near structured boundaries with potential implications for microbiological phenomena, such as biofilm formation, and technological applications.

cond-mat.soft↗

arXiv2026

Fast Solver for the Reynolds Equation on Piecewise Linear Geometries

The Reynolds equation is derived from the incompressible Navier Stokes equations under the lubrication assumptions of a long and thin domain geometry and a small scaled Reynolds number. The Reynolds equation is an elliptic differential equation and a dramatic simplification from the governing equations. When the fluid domain is piecewise linear, the Reynolds equation has an exact solution that we formulate by coupling the exact solutions of each piecewise component. We consider a formulation specifically for piecewise constant heights, and a more general formulation for piecewise linear heights; in both cases the linear system is inverted using the Schur complement. These methods can also be applied in the case of non-linear heights by approximating the height as piecewise constant or piecewise linear, in which case the methods achieve second-order accuracy. We assess the time complexity of the two methods, and determine that the method for piecewise linear heights is linear time for the number of piecewise components. As an application of these methods, we explore the limits of validity for lubrication theory by comparing the solutions of the Reynolds and the Stokes equations for a variety of linear and non-linear textured slider geometries.

math.NA↗

arXiv2026

Dynamics and stochastic resonance in a mathematical model of bistable phosphorylation and nuclear size control

Robust oscillations play crucial roles in a wide variety of biological processes and are often generated by deterministic mechanisms. However, stochastic fluctuations often generate complex perturbations of these deterministic oscillations, potentially strengthening or weakening their robustness. In this paper, we study bistable phosphorylation as a mechanism for robust oscillation. We present a simple nucleocytoplasmic transport and cell growth model where cargo proteins undergo bistable phosphorylation prior to nuclear import. We perform a detailed bifurcation analysis to examine the system's dynamical behavior. We then introduce additive noise into the model and study the stochastic resonance behavior and robustness of oscillations under noise. Our results show that, depending on the phosphorylation threshold, time-scale parameters, and nucleocytoplasmic transport rate, bistable phosphorylation may generate oscillations via Hopf bifurcations; moreover, stochastic resonance and Bautin bifurcations enhance the robustness of the oscillations.

math.DS↗

arXiv2026

Comparison of Lubrication Theory and Stokes Flow in Corner Geometries with Flow Separation

The Reynolds equation from lubrication theory and the Stokes equations for zero Reynolds number flows are distinct models for an incompressible fluid with negligible inertia. Here we investigate the sensitivity of the Reynolds equation to large surface gradients, and explore flow recirculation in corner geometries in comparison to the Stokes equation. We compare the solutions for the Reynolds and Stokes equations in the backward facing step (BFS), the regularized BFS, and the lid-driven triangular cavity. For the BFS variations listed above, we compute the error in terms of the average pressure drop through the channel and show how the error increases with increasing expansion ratio and with increasing magnitude of surface gradients. We further investigate the phenomenology of corner flow recirculation that arises in the Stokes solutions. In particular, we observe that occluding the corner separated region in the Stokes solution to the BFS does not disrupt the bulk flow characteristics.

physics.flu-dyn↗

arXiv2026

Comparison of Extended Lubrication Theories for Stokes Flow

Lubrication theory makes use of the assumptions of a long and thin fluid domain and a small scaled Reynolds number to formulate a linearized approximation to the Navier-Stokes equations. Extended lubrication theory aims to improve the model accuracy by relaxing these assumptions and including additional terms in the formulation. However, such models are sensitive to large surface gradients which lead the assumptions of the model to break down. In this paper, we present a formulation of extended lubrication theory, and compare our model with several existing models, along with the numerical solution to the Stokes equations. The error in pressure and velocity is characterized for a variety of fluid domain geometries. Our results indicate that the new solution is suitable for a wide range of geometries. The magnitude of surface variation and the length scale ratio are both important factors influencing the accuracy of the extended lubrication theory models.

physics.flu-dyn↗

arXiv2025

Vesicle Translocation into Closed Constrictions as a Function of Molecular Motor Parameters

We study the dynamics of molecular motor-driven transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We further develop a stochastic model of vesicle transport in [Park, Singh, and Fai, SIAM J. Appl. Math. 82.3 (2022), pp. 793--820] by showing that second-order moments may be neglected. We exploit this property to significantly simplify the model and confirm through numerical simulations that the simplification retains key behaviors of the original agent-based myosin model of vesicle transport. We use the simplified model to explore the vesicle translocation time and probability through dendritic spines as a function of molecular motor parameters, which was previously not practically possible. Relevance to Life Sciences: We find that thinner dendritic spine geometry can greatly reduce the probability of vesicle translocation to the post-synaptic density. The cell may alter molecular motor parameters to compensate, but only to a point. These findings are consistent with the biological literature, where brain disorders are often associated with an excess of long, thin dendritic spines. Mathematical Content: We use a moment-generating function to deduce that second-order moments in motor attachment times may be neglected, and therefore the first-order moment is a sufficient approximation. Using only the mean attachment times and neglecting the variance yields a tractable master equation from which vesicle mean first passage times may be computed directly as a function of geometry and molecular motor parameters.

q-bio.SC↗

arXiv2025

Mathematical model of Nucleocytoplasmic Transport and Nuclear-to-Cell Ratio in a growing cell

It has been observed that the growth of the nucleus and the cytoplasm is coordinated during cell growth, resulting in a nearly constant nuclear-to-cell volume ratio (N/C) throughout the cell cycle. Previous studies have shown that the N/C ratio is determined by the ratio between the number of proteins in the nucleus and the total number of proteins in the cell. These observations suggest the importance of the nucleocytoplasmic transport process in nuclear size by regulating protein concentrations in the nucleus and cytoplasm. This paper combines a biophysical model of Ran-mediated nucleocytoplasmic transport and a simple cell growth model to provide insights into several key aspects of the N/C ratio homeostasis in growing cells. Our model shows that the permeability of the nuclear envelope needs to grow in line with the cell to maintain a nearly constant N/C ratio, that several parameters involved in the nucleocytoplasmic transport mechanism and gene translation significantly affect the N/C ratio, and that Ran may potentially compensate for the lack of NTF2 in the nucleocytoplasmic transport mechanism to maintain a viable N/C ratio. However, this compensation is possible only if RanGDP is allowed to translocate through the nuclear envelope independently of NTF2.

q-bio.CB↗

arXiv2025

Emergence of Anti-chemotactic Flocking in Active Biomimetic Colloids

Competition for resources is a fundamental constraint that guides the self-organization of natural, biological, and human systems, ranging from urban planning and ecosystem development to intracellular pattern formation. Here, we reveal that competition for resources is at the origin of the collective dynamics that emerge in a population of colloids propelled by actin treadmilling, an out-of-equilibrium process where filaments grow from one end while shrinking from the other. Using a combination of experiments and theory, we show that symmetry-breaking, self-propulsion, and flocking emerge from the local competition for actin monomers. We demonstrate that beads propelled by actin treadmilling are anti-chemotactic and spontaneously generate asymmetric actin gradients that trigger and sustain directed motility. Flocking emerges from the combined effects of anti-chemotaxis and local competition for monomers. The flocking transition depends on the actin polymerization rate, actin monomer diffusivity, and the bead's motility, whose interplay controls the emergence of short-range attractive interactions between the colloids. Our findings demonstrate that active stress generation coupled to reaction-diffusion is a generic mechanism that can lead to a multiscale cascade of behaviors when active agents remodel their environment. Actin treadmilling offers a platform to study how motile agents that interact through a field self-organize in novel dynamical phases, with potential applications in non-reciprocal and trainable active matter.

cond-mat.soft↗

arXiv2025

Stochastic Gene Expression Model of Nuclear-to-Cell Ratio Homeostasis

Cell size varies between different cell types, and between different growth and osmotic conditions. However, the nuclear-to-cell volume ratio (N/C ratio) remains nearly constant. In this paper, we build on existing deterministic models of N/C ratio homeostasis and develop a simplified gene translation model to study the effect of stochasticity on the N/C ratio homeostasis. We solve the corresponding chemical master equation and obtain the mean and variance of the N/C ratio. We also use a Taylor expansion approximation to study the effects of the system size on the fluctuations of the N/C ratio. We then combine the translation model with a cell division model to study the effects of extrinsic noises from cell division on the N/C ratio. Our model demonstrates that the N/C ratio homeostasis is maintained when the stochasticity in cell growth is taken into account, that the N/C ratio is largely determined by the gene fraction of nuclear proteins, and that the fluctuations in the N/C ratio diminish as the system size increases.

q-bio.CB↗

arXiv2023

A confined rod: mean field theory for hard rod-like particles

In this paper, we model the configurations of a system of hard rods by viewing each rod in a cell formed by its neighbors. By minimizing the free energy in the model and performing molecular dynamics, where, in both cases, the shape of the cell is a free parameter, we obtain the equilibrium orientational order parameter, free energy and pressure of the system. Our model enables the calculation of anisotropic stresses exerted on the walls of the cell due to shape change of the rod in photoisomerization. These results are a key step towards understanding molecular shape change effects in photomechanical systems under illumination.

cond-mat.soft↗

arXiv2023

Fast solver for diffusive transport times on dynamic intracellular networks

The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular structures, it is crucial to understand how temporal changes in the network structure affect diffusive transport. In this work, we use network theory to characterize complex intracellular biological environments across scales. We develop an efficient computational method to compute the mean first passage times for simulating a particle diffusing along two-dimensional planar networks extracted from fluorescence microscopy imaging. We first benchmark this methodology in the context of synthetic networks, and subsequently apply it to live-cell data from endoplasmic reticulum tubular networks.

physics.bio-ph↗

arXiv2023

Influence of the vessel wall geometry on the wall-induced migration of red blood cells

The geometry of the blood vessel wall plays a regulatory role on the motion of red blood cells (RBCs). The overall topography of the vessel wall depends on many features, among which the endothelial lining of the endothelial surface layer (ESL) is an important one. The endothelial lining of vessel walls presents a large surface area for exchanging materials between blood and tissues. The ESL plays a critical role in regulating vascular permeability, hindering leukocyte adhesion as well as inhibiting coagulation during inflammation. Changes in the ESL structure are believed to cause vascular hyperpermeability and entrap immune cells during sepsis, which could significantly alter the vessel wall geometry and disturb interactions between RBCs and the vessel wall, including the wall-induced migration of RBCs and the thickening of a cell-free layer. To investigate the influence of the vessel wall geometry particularly changed by the ESL under various pathological conditions, such as sepsis, on the motion of RBCs, we developed two models to represent the ESL using the immersed boundary method in two dimensions. In particular, we used simulations to study how the lift force and drag force on a RBC near the vessel wall vary with different wall thickness, spatial variation, and permeability associated with changes in the vessel wall geometry. We find that the spatial variation of the wall has a significant effect on the wall-induced migration of the RBC for a high permeability, and that the wall-induced migration is significantly inhibited as the vessel diameter is increased.

q-bio.QM↗

arXiv2023

Modeling the Transition between Localized and Extended Deposition in Flow Networks through Packings of Glass Beads

We use a theoretical model to explore how fluid dynamics, in particular, the pressure gradient and wall shear stress in a channel, affect the deposition of particles flowing in a microfluidic network. Experiments on transport of colloidal particles in pressure-driven systems of packed beads have shown that at lower pressure drop, particles deposit locally at the inlet, while at higher pressure drop, they deposit uniformly along the direction of flow. We develop a mathematical model and use agent-based simulations to capture these essential qualitative features observed in experiments. We explore the deposition profile over a two-dimensional phase diagram defined in terms of the pressure and shear stress threshold, and show that two distinct phases exist. We explain this apparent phase transition by drawing an analogy to simple one-dimensional models of aggregation in which the phase transition is calculated analytically.

cond-mat.soft↗

arXiv2022

Multiscale Model of Clogging in Microfluidic Devices with Grid-Like Geometries

We propose a coarse-grained theoretical model to capture the aging of microfluidic devices under different conditions including constant applied flow rate and constant applied pressure gradient. Microfluidic devices that sort cells by their deformability hold significant promise for medical applications. However, clogging in these microfluidic systems causes their properties to change over time and potentially limits their reliability. We compare the results of the coarse-grained model to those of stochastic simulations and to existing theoretical studies. Lastly, we apply the model to experimental data on the clogging of sickle red blood cells and discuss its wider applicability.

cond-mat.soft↗

arXiv2022

Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines

We study the dynamics of membrane vesicle motor transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We consider the stochastic analog of the vesicle transport model in [Park and Fai, The Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors. Bull. Math. Biol. 82, 141 (2020)]. The stochastic version, which may be considered as an agent-based model, relies mostly on the action of individual myosin motors to produce vesicle motion. To aid in our analysis, we coarse-grain this agent-based model using a master equation combined with a partial differential equation describing the probability of local motor positions. We confirm through convergence studies that the coarse-graining captures the essential features of bistability in velocity (observed in experiments) and waiting-time distributions to switch between steady-state velocities. Interestingly, these results allow us to reformulate the translocation problem in terms of the mean first passage time for a run-and-tumble particle moving on a finite domain with absorbing boundaries at the two ends. We conclude by presenting numerical and analytical calculations of vesicle translocation.

q-bio.SC↗

arXiv2022

Global asymptotic stability of the active disassembly model of flagellar length control

Organelle size control is a fundamental question in biology that demonstrates the fascinating ability of cells to maintain homeostasis within their highly variable environments. Theoretical models describing cellular dynamics have the potential to help elucidate the principles underlying size control. Here, we perform a detailed study of the active disassembly model proposed in [Fai et al, Length regulation of multiple flagella that self-assemble from a shared pool of components, eLife, 8, (2019): e42599]. We construct a hybrid system which is shown to be well-behaved throughout the domain. We rule out the possibility of oscillations arising in the model and prove global asymptotic stability in the case of two flagella by the construction of a suitable Lyapunov function. Finally, we generalize the model to the case of arbitrary flagellar number in order to study olfactory sensory neurons, which have up to twenty cilia per cell. We show that our theoretical results may be extended to this case and explore the implications of this universal mechanism of size control.

physics.bio-ph↗

arXiv2021

Cavity volume and free energy in many-body systems

Within this work we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable to systems across their entire range of density, as well as to particles within a general coordinate space. This provides a universal equation of state, and can thus relate the cavity volume to classical results, such as Mayer's cluster expansions. Through this we are able to provide some insight into the connections between cavity volume and free energy density, as well as their consequences. We use examples which permit explicit computations to further probe these results, reclaiming the exact results for a classical Tonks gas and providing a novel derivation of Onsager's free energy for a single species, isotropic system. Given the complexity of the problem we also provide a local lattice ansatz, exact in one dimension, with which we may approximate the cavity volume for hard sphere systems to provide an accurate equation of state in the cases of hard disks and spheres in both dilute regimes as well as beyond the freezing transition.

cond-mat.stat-mech↗

arXiv2021

Leaky Cell Model of Hard Spheres

We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e. the volume of space that a sphere can explore without touching another sphere. We compute these free volumes using a leaky cell model, in which the accessible space accounts for the possibility that spheres may escape from the local cage of lattice neighbors. We describe how elementary geometry may be used to calculate the free volume exactly for this leaky cell model in two- and three-dimensional lattice packings and compare the results to the well-known Carnahan-Starling and Percus-Yevick liquid models. We provide formulas for the free volumes of various lattices and use the common tangent construction to identify several phase transitions between them in the leaky cell regime, indicating the possibility of coexistence in crystalline materials.

cond-mat.soft↗