About

Professor Samuel Isaacson is a member of the Applied Mathematics research group at Boston University. He is a faculty member in the Department of Mathematics & Statistics, with office hours on Tuesdays from 12:15 to 1:15 pm and Wednesdays from 4 to 5 pm. For more information about his research, he has a personal webpage. His work focuses on applied mathematics, contributing to the department's research and academic activities.

Research topics

• Computer Science
• Cell biology
• Biology
• Thermodynamics
• Biochemistry
• Statistics
• Pure mathematics
• Applied mathematics
• Mathematical analysis
• Physics
• Genetics
• Biophysics
• Mathematics
• Statistical physics

Selected publications

• A Macroscopically Consistent Reactive Langevin Dynamics Model

  SIAM Journal on Applied Mathematics · 2026-01-20

  article1st authorCorresponding
  PublisherDOI

• Mean field limits of particle-based stochastic reaction-drift-diffusion models^*

  Nonlinearity · 2025-01-07

  articleOpen accessCorresponding

  Abstract 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 of the particles are formulated as measure-valued stochastic processes (MVSPs), which describe the evolution of the singular, stochastic concentration fields of each chemical species. The mean field large population limit of such models is derived and proven, giving coarse-grained deterministic partial integro-differential equations (PIDEs) for the limiting deterministic concentration fields’ dynamics. We generalize previous studies on the mean field limit of models involving only diffusive motion, with care to formulating the MVSP representation to ensure detailed balance of reversible reactions in the presence of potentials. Our work illustrates the more general set of PIDEs that arise in the mean field limit, demonstrating that the limiting macroscopic reactive interaction terms for reversible reactions obtain additional nonlinear concentration-dependent coefficients compared to the purely diffusive case. Numerical studies are presented which illustrate that two-body repulsive potential interactions can have a significant impact on the reaction dynamics, and also demonstrate the empirical numerical convergence of solutions to the PBSRDD model to the derived mean field PIDEs as the population size increases.

  PublisherOA PDFDOI

• Publisher Correction: The molecular reach of antibodies crucially underpins their viral neutralisation capacity

  Nature Communications · 2025-03-20

  erratumOpen access
  PublisherOA PDFDOI

• The molecular reach of antibodies crucially underpins their viral neutralisation capacity

  Nature Communications · 2025-01-02 · 14 citations

  articleOpen access

  Key functions of antibodies, such as viral neutralisation, depend on high-affinity binding. However, viral neutralisation poorly correlates with antigen affinity for reasons that have been unclear. Here, we use a new mechanistic model of bivalent binding to study >45 patient-isolated IgG1 antibodies interacting with SARS-CoV-2 RBD surfaces. The model provides the standard monovalent affinity/kinetics and new bivalent parameters, including the molecular reach: the maximum antigen separation enabling bivalent binding. We find large variations in these parameters across antibodies, including reach variations (22-46 nm) that exceed the physical antibody size (~15 nm). By using antigens of different physical sizes, we show that these large molecular reaches are the result of both the antibody and antigen sizes. Although viral neutralisation correlates poorly with affinity, a striking correlation is observed with molecular reach. Indeed, the molecular reach explains differences in neutralisation for antibodies binding with the same affinity to the same RBD-epitope. Thus, antibodies within an isotype class binding the same antigen can display differences in molecular reach, substantially modulating their binding and functional properties.

  PublisherOA PDFDOI

• Correction: Catalyst: Fast and flexible modeling of reaction networks

  PLoS Computational Biology · 2025-06-12

  erratumOpen accessSenior author

  [This corrects the article DOI: 10.1371/journal.pcbi.1011530.].

  PublisherOA PDFDOI

• An Unstructured Mesh Reaction-Drift-Diffusion Master Equation with Reversible Reactions

  Bulletin of Mathematical Biology · 2024-12-09

  article1st author
  PublisherDOI

• Extending JumpProcesses.jl for fast point process simulation with time-varying intensities

  JuliaCon Proceedings · 2024-04-04 · 2 citations

  articleOpen access

  Zagatti et al., (2024). Extending JumpProcesses.jl for fast point process simulation with time-varying intensities. The Proceedings of the JuliaCon Conferences, 6(58), 133, https://doi.org/10.21105/jcon.00133

  PublisherOA PDFDOI

• An Unstructured Mesh Reaction-Drift-Diffusion Master Equation with Reversible Reactions

  arXiv (Cornell University) · 2024-05-01

  preprintOpen access1st authorCorresponding

  We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The generalized CRDDME is obtained through two steps. We first derive an unstructured grid jump process approximation for reversible diffusions, enabling the simulation of drift-diffusion processes where the drift arises due to a conservative field that biases particle motion. Leveraging the Edge-Averaged Finite Element method, our approach preserves detailed balance of drift-diffusion fluxes at equilibrium, and preserves an equilibrium Gibbs-Boltzmann distribution for particles undergoing drift-diffusion on the unstructured mesh. We next formulate a spatially-continuous volume reactivity particle-based reaction-drift-diffusion model for reversible reactions of the form $\textrm{A} + \textrm{B} \leftrightarrow \textrm{C}$. A finite volume discretization is used to generate jump process approximations to reaction terms in this model. The discretization is developed to ensure the combined reaction-drift-diffusion jump process approximation is consistent with detailed balance of reaction fluxes holding at equilibrium, along with supporting a discrete version of the continuous equilibrium state. The new CRDDME model represents a continuous-time discrete-space jump process approximation to the underlying volume reactivity model. We demonstrate the convergence and accuracy of the new CRDDME through a number of numerical examples, and illustrate its use on an idealized model for membrane protein receptor dynamics in T cell signaling.

  PublisherOA PDFDOI

• Fluctuation analysis for particle-based stochastic reaction–diffusion models

  Stochastic Processes and their Applications · 2023-10-17 · 3 citations

  article
  PublisherDOI

• Analysis of emergent bivalent antibody binding identifies the molecular reach as a critical determinant of SARS-CoV-2 neutralisation potency

  bioRxiv (Cold Spring Harbor Laboratory) · 2023-09-07 · 2 citations

  preprintOpen accessCorresponding

  Key functions of antibodies, such as viral neutralisation, depend on bivalent binding but the factors that influence it remain poorly characterised. Here, we develop and employ a new bivalent model to mechanistically analyse binding between >45 patient-isolated IgG1 antibodies interacting with SARS-CoV-2 RBD surfaces. Our method reproduces the monovalent on/off-rates and enables measurements of the bivalent on-rate and the molecular reach: the maximum antigen separation that supports bivalent binding. We find large variations in these parameters across antibodies, including variations in reach (22-46 nm) that exceed the physical antibody size (~15 nm) due to the antigen size. The bivalent model integrates all parameters, including reach and antigen density, to predict an emergent binding potency for each antibody that matches their neutralisation potency. Indeed, antibodies with similar monovalent affinities to the same RBD-epitope but with different reaches display differences in emergent bivalent binding that match differences in their neutralisation potency. Together, our work highlights that antibodies within an isotype class binding the same antigen can display differences in molecular reach that can substantially modulate their emergent binding and functional properties.

  PublisherOA PDFDOI

Recent grants

• CAREER: Numerical Methods for Stochastic Reaction Diffusion Equations

  NSF · $434k · 2013–2019

• Multiscale Modeling of Subcellular Structure and its Effects on Gene Expression and Regulation

  NSF · $273k · 2009–2013

• Collaborative Research: Computational Methods for Understanding the Influence of Cellular Geometry and Substructure on Signaling

  NSF · $700k · 2019–2025

Frequent coauthors

• Charles S. Peskin

  13 shared

• Jesse Goyette

  EMBL Australia

  12 shared

• Omer Dushek

  University of Oxford

  9 shared

• Carolyn A. Larabell

  University of California, San Francisco

  8 shared

• Jun Allard

  University of California, Irvine

  8 shared

• Mark A. Le Gros

  Lawrence Berkeley National Laboratory

  8 shared

• Konstantinos Spiliopoulos

  7 shared

• Ying Zhang

  Boston University

  7 shared

Education

• Postdoctoral Fellow of the Biomathematics Research Group, Mathematics

  University of Utah

  2008

• Ph.D., Mathematics

  Courant Institute of Mathematical Sciences

  2005

• Sc.B., Applied Mathematics and Computer Science

  Brown University

  2000