97 citations · 250 across the 15 of their papers we have counts for
15 papers
A Convergent Reaction-Drift-Diffusion Master Equation with Interaction Potentials
Max Heldman, Samuel A. Isaacson
We extend the convergent reaction-diffusion master equation (CRDME) framework on unstructured grids to include two-body interaction potentials between particles. Such interactions…
A Macroscopically Consistent Reactive Langevin Dynamics Model
Samuel A. Isaacson, Qianhan Liu, Konstantinos Spiliopoulos +1
Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for capturing stochasticity in reaction and transport processes across biological systems. In som…
Mean field limits of particle-based stochastic reaction-drift-diffusion models
Max Heldman, Samuel A. Isaacson, Qianhan Liu +1
We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics…
Fluctuation analysis for particle-based stochastic reaction-diffusion models
Max Heldman, Samuel Isaacson, Jingwei Ma +1
Recent works have derived and proven the large-population mean-field limit for several classes of particle-based stochastic reaction-diffusion (PBSRD) models. These limits correspo…
Detailed Balance for Particle Models of Reversible Reactions in Bounded Domains
Ying Zhang, Samuel A. Isaacson
In particle-based stochastic reaction-diffusion models, reaction rate and placement kernels are used to decide the probability per time a reaction can occur between reactant partic…
How reaction-diffusion PDEs approximate the large-population limit of stochastic particle models
Samuel A Isaacson, Jingwei Ma, Konstantinos Spiliopoulos
Reaction-diffusion PDEs and particle-based stochastic reaction-diffusion (PBSRD) models are commonly-used approaches for modeling the spatial dynamics of chemical and biological sy…
How Retroactivity Affects the Behavior of Incoherent Feed-Forward Loops
Junmin Wang, Calin Belta, Samuel A. Isaacson
An incoherent feed-forward loop (IFFL) is a network motif known for its ability to accelerate responses and generate pulses. Though functions of IFFLs are well studied, most previo…
Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models
Samuel A. Isaacson, Jingwei Ma, Konstantinos Spiliopoulos
Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for studying biological systems involving both noise in the reaction process and diffusive transp…
An Unstructured Mesh Convergent Reaction-Diffusion Master Equation for Reversible Reactions
Samuel A. Isaacson, Ying Zhang
The convergent reaction-diffusion master equation (CRDME) was recently developed to provide a lattice particle-based stochastic reaction-diffusion model that is a convergent approx…
Uniform asymptotic approximation of diffusion to a small target: generalized reaction models
Sam Isaacson, Ava Mauro, Jay Newby
The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction-radius at which the reactant and target may interact is often a small pa…
The Influence of Spatial Variation in Chromatin Density Determined by X-ray Tomograms on the Time to Find DNA Binding Sites
Samuel A. Isaacson, Carolyn A. Larabell, Mark A. Le Gros +2
In this work we examine how volume exclusion caused by regions of high chromatin density might influence the time required for proteins to find specific DNA binding sites. The spat…
Uniform asymptotic approximation of diffusion to a small target
Samuel A. Isaacson, Jay Newby
The problem of the time required for a diffusing molecule, within a large bounded domain, to first locate a small target is prevalent in biological modeling. Here we study this pro…
A First-Passage Kinetic Monte Carlo Method for Reaction-Drift-Diffusion Processes
Ava J. Mauro, Jon Karl Sigurdsson, Justin Shrake +2
Stochastic reaction-diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction proce…
A Comparison of Bimolecular Reaction Models for Stochastic Reaction Diffusion Systems
Ikemefuna C. Agbanusi, Samuel A. Isaacson
Stochastic reaction-diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the…
A Convergent Reaction-Diffusion Master Equation
Samuel A Isaacson
The reaction-diffusion master equation (RDME) is a lattice stochastic reaction-diffusion model that has been used to study spatially distributed cellular processes. The RDME is oft…