arXiv subjects

Li-Tien Cheng

Publications and source records attributed to Li-Tien Cheng.

6 recordsLinked to original sources

arXiv2022

Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary: Rigorous Modeling and Robust Simulations

Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the cell movement. We study the cell polarity and movement based on a class of biophysical models that consist of reaction-diffusion equations for different proteins and the dynamics of moving cell boundary. Such a moving boundary is often simulated by a phase-filed model. We first apply the matched asymptotic analysis to give a rigorous derivation of the sharp-interface model of the cell boundary from a phase-field model. We then develop a robust numerical approach that combines the level-set method to track the sharp boundary of a moving cell and accurate discretization techniques for solving the reaction-diffusion equations on the moving cell region. Our extensive numerical simulations predict the cell polarization under various kinds of stimulus, and capture both the linear and circular trajectories of a moving cell for a long period of time. In particular, we have identified some key parameters controlling different cell trajectories that are less accurately predicted by reduced models. Our work has linked different models and also developed tools that can be adapted for the challenging three-dimensional simulations.

math.DS↗

arXiv2022

Explicit-Solute Implicit-Solvent Molecular Simulation with Binary Level-Set, Adaptive-Mobility, and GPU

Coarse-grained modeling and efficient computer simulations are critical to the study of complex molecular processes with many degrees of freedom and multiple spatiotemporal scales. Variational implicit-solvent model (VISM) for biomolecular solvation is such a modeling framework, and its initial success has been demonstrated consistently. In VISM, an effective free-energy functional of solute-solvent interfaces is minimized, and the surface energy is a key component of the free energy. In this work, we extend VISM to include the solute mechanical interactions, and develop fast algorithms and GPU implementation for the extended variational explicit-solute implicit-solvent (VESIS) molecular simulations to determine the underlying molecular equilibrium conformations. We employ a fast binary level-set method for minimizing the solvation free energy of solute-solvent interfaces and construct an adaptive-mobility gradient descent method for solute atomic optimization. We also implement our methods in GPU. Numerical tests and applications to several molecular systems verify the accuracy, stability, and efficiency of our methods and algorithms. It is found that our new methods and GPU implementation improve the efficiency of the molecular simulation significantly over the CPU implementation. Our fast computational techniques may enable us to simulate very large systems such as protein-protein interactions and membrane dynamics for which explicit-solvent all-atom molecular dynamics simulations can be very expensive.

physics.chem-ph↗

arXiv2021

Numerical Evidence of Exponential Mixing by Alternating Shear Flows

We performed a numerical study of the efficiency of mixing by alternating horizontal and vertical shear ``wedge'' flows on the two-dimensional torus. Our results suggest that except in cases where each individual flow is applied for only a short time, these flows produce exponentially fast mixing. The observed mixing rates are higher when the individual flow times are shorter (but not too short), and randomizing either the flow times or phase shifts of the flows does not appear to enhance mixing (again when the flow times are not too short). In fact, the latter surprisingly seems to inhibit it slightly.

math.AP↗

arXiv2021

Binary Level Set Method for Variational Implicit Solvation Model

In this article, we apply the binary level set method to the Variational Implicit Solvent Model (VISM), which is a theoretical and computational tool to study biomolecular systems with complex topology. Central in VISM is an effective free energy of all possible interfaces separating solutes (e.g., proteins) from solvent (e.g., water). Previously, such a functional is minimized numerically by the level set method to determine the stable equilibrium conformations and solvation free energies. We vastly improve the speed by applying the binary level set method, in which the interface is approximated by a binary level set function that only takes value $\pm 1$ on the solute/solvent region, leading to a discrete formulation of VISM energy. The surface area is approximated by convolution of an indicator function with a compactly supported kernel. The VISM energy can be minimized by iteratively "flipping" the binary level set function in a steepest descent fashion. Numerical experiments are performed to demonstrate the accuracy and performance of our method.

math.NA↗

arXiv2021

A Compact Coupling Interface Method with Accurate Gradient Approximation for Elliptic Interface Problems

We propose the Compact Coupling Interface Method (CCIM), a finite difference method capable of obtaining second-order accurate approximations of not only solution values but their gradients, for elliptic complex interface problems with interfacial jump conditions. Such elliptic interface boundary value problems with interfacial jump conditions are a critical part of numerous applications in fields such as heat conduction, fluid flow, materials science, and protein docking, to name a few. A typical example involves the construction of biomolecular shapes, where such elliptic interface problems are in the form of linearized Poisson-Boltzmann equations, involving discontinuous dielectric constants across the interface, that govern electrostatic contributions. Additionally, when interface dynamics are involved, the normal velocity of the interface might be comprised of the normal derivatives of solution, which can be approximated to second-order by our method, resulting in accurate interface dynamics. Our method, which can be formulated in arbitrary spatial dimensions, combines elements of the highly-regarded Coupling Interface Method, for such elliptic interface problems, and Smereka's second-order accurate discrete delta function. The result is a variation and hybrid with a more compact stencil than that found in the Coupling Interface Method, and with advantages, borne out in numerical experiments involving both geometric model problems and complex biomolecular surfaces, in more robust error profiles.

math.NA↗

arXiv2019

Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics

Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multi-method approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obtain the minimum energy paths and transition states between the various metastable ('dry' and 'wet') hydration states. The resulting dry-wet transition rates are then used in a spatially-dependent multi-state continuous-time Markov chain Brownian dynamics simulations, and the related Fokker-Planck equation calculations, of the ligand stochastic motion, providing the mean first-passage times for binding and unbinding. We find the hydration transitions to significantly slow down the binding process, in semi-quantitative agreement with existing explicit-water simulations, but significantly accelerate the unbinding process. Moreover, our methods allow the characterization of non-equilibrium hydration states of pocket and ligand during the ligand movement, for which we find substantial memory and hysteresis effects for binding versus unbinding. Our study thus provides a significant step forward towards efficient, physics-based interpretation and predictions of the complex kinetics in realistic ligand-receptor systems.

physics.bio-ph↗