Preprints

2025

A Macroscopically Consistent Reactive Langevin Dynamics Model

Samuel A Isaacson, Qianhan Liu, Konstantinos Spiliopoulos, and Chen Yao

arXiv preprint, 2025

Abs arXiv Bib

Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for capturing stochasticity in reaction and transport processes across biological systems. In some contexts, the overdamped approximation inherent in such models may be inappropriate, necessitating the use of more microscopic Langevin Dynamics models for spatial transport. In this work we develop a novel particle-based Reactive Langevin Dynamics (RLD) model, with a focus on deriving reactive interaction kernels that are consistent with the physical constraint of detailed balance of reactive fluxes at equilibrium. We demonstrate that, to leading order, the overdamped limit of the resulting RLD model corresponds to the volume reactivity PBSRD model, of which the well-known Doi model is a particular instance. Our work provides a step towards systematically deriving PBSRD models from more microscopic reaction models, and suggests possible constraints on the latter to ensure consistency between the two physical scales.
@article{isaacson2025macroscopically, title = {A Macroscopically Consistent Reactive Langevin Dynamics Model}, author = {Isaacson, Samuel A and Liu, Qianhan and Spiliopoulos, Konstantinos and Yao, Chen}, journal = {arXiv preprint}, year = {2025}, }

Published Articles

2025

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

Samuel A Isaacson and Ying Zhang

Bulletin of mathematical biology, 2025

Abs Journal Link arXiv Bib

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 A + B <–> 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.
@article{isaacson2025unstructured, title = {An Unstructured Mesh Reaction-Drift-Diffusion Master Equation with Reversible Reactions}, author = {Isaacson, Samuel A and Zhang, Ying}, journal = {Bulletin of mathematical biology}, volume = {87}, number = {1}, pages = {1--41}, year = {2025}, publisher = {Springer US}, url = {https://doi.org/10.1007/s11538-024-01392-z}, doi = {10.1007/s11538-024-01392-z} }
Mean field limits of particle-based stochastic reaction-drift-diffusion models

Max Heldman, Samuel A Isaacson, Qianhan Liu, and Konstantinos Spiliopoulos

Nonlinearity, 2025

Abs Journal Link arXiv Bib

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.
@article{heldman2025mean, title = {Mean field limits of particle-based stochastic reaction-drift-diffusion models}, author = {Heldman, Max and Isaacson, Samuel A and Liu, Qianhan and Spiliopoulos, Konstantinos}, journal = {Nonlinearity}, volume = {38}, number = {2}, pages = {025004}, year = {2025}, publisher = {IOP Publishing}, url = {https://dx.doi.org/10.1088/1361-6544/ad8fea}, doi = {10.1088/1361-6544/ad8fea} }
The molecular reach of antibodies crucially underpins their viral neutralisation capacity

Anna Huhn, Daniel Nissley, Daniel B Wilson, Mikhail A Kutuzov, Robert Donat, Tiong Kit Tan, Ying Zhang, Michael I Barton, Chang Liu, Wanwisa Dejnirattisai, Piyada Supasa, Juthathip Mongkolsapaya, Alain Townsend, William James, Gavin Screaton, P Anton Merwe, Charlotte M Deane, Samuel A Isaacson, and Omer Dushek

Nature Communications, 2025

Abs Journal Link Bib PDF

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.
@article{huhn2025molecular, title = {The molecular reach of antibodies crucially underpins their viral neutralisation capacity}, author = {Huhn, Anna and Nissley, Daniel and Wilson, Daniel B and Kutuzov, Mikhail A and Donat, Robert and Tan, Tiong Kit and Zhang, Ying and Barton, Michael I and Liu, Chang and Dejnirattisai, Wanwisa and Supasa, Piyada and Mongkolsapaya, Juthathip and Townsend, Alain and James, William and Screaton, Gavin and van der Merwe, P Anton and Deane, Charlotte M and Isaacson, Samuel A and Dushek, Omer}, journal = {Nature Communications}, volume = {16}, number = {1}, pages = {338}, year = {2025}, publisher = {Nature Publishing Group UK London}, url = {https://doi.org/10.1038/s41467-024-54916-5}, doi = {10.1038/s41467-024-54916-5} }

2024

Fluctuation analysis for particle-based stochastic reaction–diffusion models

Max Heldman, SA Isaacson, Jingwei Ma, and Konstantinos Spiliopoulos

Stochastic Processes and their Applications, 2024

Journal Link arXiv Bib

@article{heldman2024fluctuation,
  title = {Fluctuation analysis for particle-based stochastic reaction--diffusion models},
  author = {Heldman, Max and Isaacson, SA and Ma, Jingwei and Spiliopoulos, Konstantinos},
  journal = {Stochastic Processes and their Applications},
  volume = {167},
  pages = {104234},
  year = {2024},
  publisher = {North-Holland},
  url = {https://doi.org/10.1016/j.spa.2023.104234},
  doi = {10.1016/j.spa.2023.104234}
}

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

Guilherme Augusto Zagatti, Samuel A Isaacson, Christopher Rackauckas, Vasily Ilin, See-Kiong Ng, and Stéphane Bressan

In The Proceedings of the JuliaCon Conferences, 2024

Journal Link arXiv Bib

@inproceedings{zagatti2024extending,
  title = {Extending JumpProcess. jl for fast point process simulation with time-varying intensities},
  author = {Zagatti, Guilherme Augusto and Isaacson, Samuel A and Rackauckas, Christopher and Ilin, Vasily and Ng, See-Kiong and Bressan, St{\'e}phane},
  booktitle = {The Proceedings of the JuliaCon Conferences},
  volume = {6},
  number = {58},
  pages = {13--pp},
  year = {2024},
  url = {https://doi.org/10.21105/jcon.00133},
  doi = {10.21105/jcon.00133}
}

2023

Catalyst: Fast and flexible modeling of reaction networks

Torkel E Loman, Yingbo Ma, Vasily Ilin, Shashi Gowda, Niklas Korsbo, Nikhil Yewale, Chris Rackauckas, and Samuel A Isaacson

PLOS Computational Biology, 2023

Journal Link Bib PDF

@article{loman2023catalyst,
  title = {Catalyst: Fast and flexible modeling of reaction networks},
  author = {Loman, Torkel E and Ma, Yingbo and Ilin, Vasily and Gowda, Shashi and Korsbo, Niklas and Yewale, Nikhil and Rackauckas, Chris and Isaacson, Samuel A},
  journal = {PLOS Computational Biology},
  volume = {19},
  number = {10},
  pages = {e1011530},
  year = {2023},
  publisher = {Public Library of Science},
  url = {https://doi.org/10.1371/journal.pcbi.1011530},
  doi = {10.1371/journal.pcbi.1011530}
}

2022

Mean field limits of particle-based stochastic reaction-diffusion models

Samuel A Isaacson, Jingwei Ma, and Konstantinos Spiliopoulos

SIAM Journal on Mathematical Analysis, 2022

Journal Link arXiv Bib

@article{isaacson2022mean,
  title = {Mean field limits of particle-based stochastic reaction-diffusion models},
  author = {Isaacson, Samuel A and Ma, Jingwei and Spiliopoulos, Konstantinos},
  journal = {SIAM Journal on Mathematical Analysis},
  volume = {54},
  number = {1},
  pages = {453--511},
  year = {2022},
  publisher = {Society for Industrial and Applied Mathematics},
  url = {https://doi.org/10.1137/20M1365600},
  doi = {10.1137/20M1365600}
}

Dephosphorylation accelerates the dissociation of ZAP70 from the T cell receptor

Jesse Goyette, David Depoil, Zhengmin Yang, Samuel A Isaacson, Jun Allard, P Anton Merwe, Katharina Gaus, Michael L Dustin, and Omer Dushek

Proceedings of the National Academy of Sciences, 2022

Journal Link Bib

@article{goyette2022dephosphorylation,
  title = {Dephosphorylation accelerates the dissociation of ZAP70 from the T cell receptor},
  author = {Goyette, Jesse and Depoil, David and Yang, Zhengmin and Isaacson, Samuel A and Allard, Jun and van der Merwe, P Anton and Gaus, Katharina and Dustin, Michael L and Dushek, Omer},
  journal = {Proceedings of the National Academy of Sciences},
  volume = {119},
  number = {9},
  pages = {e2116815119},
  year = {2022},
  publisher = {National Academy of Sciences},
  url = {https://doi.org/10.1073/pnas.2116815119},
  doi = {10.1073/pnas.2116815119}
}

Detailed balance for particle models of reversible reactions in bounded domains

Ying Zhang and Samuel A Isaacson

The Journal of Chemical Physics, 2022

Journal Link arXiv Bib

@article{zhang2022detailed,
  title = {Detailed balance for particle models of reversible reactions in bounded domains},
  author = {Zhang, Ying and Isaacson, Samuel A},
  journal = {The Journal of Chemical Physics},
  volume = {156},
  number = {20},
  year = {2022},
  publisher = {AIP Publishing},
  url = {https://doi.org/10.1063/5.0085296},
  doi = {10.1063/5.0085296}
}

2021

How reaction-diffusion PDEs approximate the large-population limit of stochastic particle models

Samuel A Isaacson, Jingwei Ma, and Konstantinos Spiliopoulos

SIAM Journal on Applied Mathematics, 2021

Journal Link arXiv Bib

@article{isaacson2021reaction,
  title = {How reaction-diffusion PDEs approximate the large-population limit of stochastic particle models},
  author = {Isaacson, Samuel A and Ma, Jingwei and Spiliopoulos, Konstantinos},
  journal = {SIAM Journal on Applied Mathematics},
  volume = {81},
  number = {6},
  pages = {2622--2657},
  year = {2021},
  publisher = {Society for Industrial and Applied Mathematics},
  url = {https://doi.org/10.1137/20M1365429},
  doi = {10.1137/20M1365429}
}

2020

Accurate particle-based reaction algorithms for fixed timestep simulators

Stuart T Johnston, Christopher N Angstmann, Satya NV Arjunan, Casper HL Beentjes, Adrien Coulier, Samuel A Isaacson, Ash A Khan, Karen Lipkow, and Steven S Andrews

2018 MATRIX Annals, 2020

Journal Link Bib PDF

@article{johnston2020accurate,
  title = {Accurate particle-based reaction algorithms for fixed timestep simulators},
  author = {Johnston, Stuart T and Angstmann, Christopher N and Arjunan, Satya NV and Beentjes, Casper HL and Coulier, Adrien and Isaacson, Samuel A and Khan, Ash A and Lipkow, Karen and Andrews, Steven S},
  journal = {2018 MATRIX Annals},
  pages = {149--164},
  year = {2020},
  publisher = {Springer International Publishing},
  url = {https://doi.org/10.1007/978-3-030-38230-8_11},
  doi = {10.1007/978-3-030-38230-8_11}
}

Strong intracellular signal inactivation produces sharper and more robust signaling from cell membrane to nucleus

Jingwei Ma, Myan Do, Mark A Le Gros, Charles S Peskin, Carolyn A Larabell, Yoichiro Mori, and Samuel A Isaacson

PLoS computational biology, 2020

Journal Link Bib

@article{ma2020strong,
  title = {Strong intracellular signal inactivation produces sharper and more robust signaling from cell membrane to nucleus},
  author = {Ma, Jingwei and Do, Myan and Le Gros, Mark A and Peskin, Charles S and Larabell, Carolyn A and Mori, Yoichiro and Isaacson, Samuel A},
  journal = {PLoS computational biology},
  volume = {16},
  number = {11},
  pages = {e1008356},
  year = {2020},
  publisher = {Public Library of Science},
  url = {https://doi.org/10.1371/journal.pcbi.1008356},
  doi = {10.1371/journal.pcbi.1008356}
}

How retroactivity affects the behavior of incoherent feedforward loops

Junmin Wang, Calin Belta, and Samuel A Isaacson

Iscience, 2020

Journal Link arXiv Bib

@article{wang2020retroactivity,
  title = {How retroactivity affects the behavior of incoherent feedforward loops},
  author = {Wang, Junmin and Belta, Calin and Isaacson, Samuel A},
  journal = {Iscience},
  volume = {23},
  number = {12},
  year = {2020},
  publisher = {Elsevier},
  url = {https://doi.org/10.1016/j.isci.2020.101779},
  doi = {10.1016/j.isci.2020.101779}
}

2019

Modeling genetic circuit behavior in transiently transfected mammalian cells

Junmin Wang, Samuel A Isaacson, and Calin Belta

ACS synthetic biology, 2019

Journal Link Bib PDF

@article{wang2019modeling,
  title = {Modeling genetic circuit behavior in transiently transfected mammalian cells},
  author = {Wang, Junmin and Isaacson, Samuel A and Belta, Calin},
  journal = {ACS synthetic biology},
  volume = {8},
  number = {4},
  pages = {697--707},
  year = {2019},
  publisher = {American Chemical Society},
  url = {https://doi.org/10.1021/acssynbio.8b00166},
  doi = {10.1021/acssynbio.8b00166}
}

The influence of molecular reach and diffusivity on the efficacy of membrane-confined reactions

Ying Zhang, Lara Clemens, Jesse Goyette, Jun Allard, Omer Dushek, and Samuel A Isaacson

Biophysical Journal, 2019

Journal Link Bib

@article{zhang2019influence,
  title = {The influence of molecular reach and diffusivity on the efficacy of membrane-confined reactions},
  author = {Zhang, Ying and Clemens, Lara and Goyette, Jesse and Allard, Jun and Dushek, Omer and Isaacson, Samuel A},
  journal = {Biophysical Journal},
  volume = {117},
  number = {7},
  pages = {1189--1201},
  year = {2019},
  publisher = {Elsevier},
  url = {https://doi.org/10.1016/j.bpj.2019.08.023},
  doi = {10.1016/j.bpj.2019.08.023}
}

2018

An unstructured mesh convergent reaction–diffusion master equation for reversible reactions

Samuel A Isaacson and Ying Zhang

Journal of Computational Physics, 2018

Journal Link arXiv Bib

@article{isaacson2018unstructured,
  title = {An unstructured mesh convergent reaction--diffusion master equation for reversible reactions},
  author = {Isaacson, Samuel A and Zhang, Ying},
  journal = {Journal of Computational Physics},
  volume = {374},
  pages = {954--983},
  year = {2018},
  publisher = {Academic Press},
  url = {https://doi.org/10.1016/j.jcp.2018.07.036},
  doi = {10.1016/j.jcp.2018.07.036}
}

Predictions of genetic circuit behaviors based on modular composition in transiently transfected mammalian cells

Junmin Wang, Samuel A Isaacson, and Calin Belta

In 2018 IEEE Life Sciences Conference (LSC), 2018

Journal Link Bib

@inproceedings{wang2018predictions,
  title = {Predictions of genetic circuit behaviors based on modular composition in transiently transfected mammalian cells},
  author = {Wang, Junmin and Isaacson, Samuel A and Belta, Calin},
  booktitle = {2018 IEEE Life Sciences Conference (LSC)},
  pages = {85--88},
  year = {2018},
  organization = {IEEE},
  url = {https://doi.org/10.1109/LSC.2018.8572174},
  doi = {10.1109/LSC.2018.8572174}
}

2017

Biophysical assay for tethered signaling reactions reveals tether-controlled activity for the phosphatase SHP-1

Jesse Goyette, Citlali Solis Salas, Nicola Coker-Gordon, Marcus Bridge, Samuel A Isaacson, Jun Allard, and Omer Dushek

Science advances, 2017

Journal Link Bib PDF

@article{goyette2017biophysical,
  title = {Biophysical assay for tethered signaling reactions reveals tether-controlled activity for the phosphatase SHP-1},
  author = {Goyette, Jesse and Salas, Citlali Solis and Coker-Gordon, Nicola and Bridge, Marcus and Isaacson, Samuel A and Allard, Jun and Dushek, Omer},
  journal = {Science advances},
  volume = {3},
  number = {3},
  pages = {e1601692},
  year = {2017},
  publisher = {American Association for the Advancement of Science},
  url = {http://doi.org/10.1126/sciadv.1601692},
  doi = {10.1126/sciadv.1601692}
}

2016

Reactive boundary conditions as limits of interaction potentials for Brownian and Langevin dynamics

S Jonathan Chapman, Radek Erban, and Samuel A Isaacson

SIAM Journal on Applied Mathematics, 2016

Journal Link arXiv Bib PDF

@article{chapman2016reactive,
  title = {Reactive boundary conditions as limits of interaction potentials for Brownian and Langevin dynamics},
  author = {Chapman, S Jonathan and Erban, Radek and Isaacson, Samuel A},
  journal = {SIAM Journal on Applied Mathematics},
  volume = {76},
  number = {1},
  pages = {368--390},
  year = {2016},
  publisher = {Society for Industrial and Applied Mathematics},
  url = {https://doi.org/10.1137/15M1030662},
  doi = {10.1137/15M1030662}
}

Uniform asymptotic approximation of diffusion to a small target: Generalized reaction models

Samuel A Isaacson, Ava J Mauro, and Jay Newby

Physical Review E, 2016

Journal Link arXiv Bib

@article{isaacson2016uniform,
  title = {Uniform asymptotic approximation of diffusion to a small target: Generalized reaction models},
  author = {Isaacson, Samuel A and Mauro, Ava J and Newby, Jay},
  journal = {Physical Review E},
  volume = {94},
  number = {4},
  pages = {042414},
  year = {2016},
  publisher = {American Physical Society},
  url = {https://doi.org/10.1103/PhysRevE.94.042414},
  doi = {10.1103/PhysRevE.94.042414}
}

2015

Imaging and characterizing cells using tomography

Myan Do, Samuel A Isaacson, Gerry McDermott, Mark A Le Gros, and Carolyn A Larabell

Archives of biochemistry and biophysics, 2015

Journal Link Bib

@article{do2015imaging,
  title = {Imaging and characterizing cells using tomography},
  author = {Do, Myan and Isaacson, Samuel A and McDermott, Gerry and Le Gros, Mark A and Larabell, Carolyn A},
  journal = {Archives of biochemistry and biophysics},
  volume = {581},
  pages = {111--121},
  year = {2015},
  publisher = {Academic Press},
  url = {https://doi.org/10.1016/j.abb.2015.01.011},
  doi = {10.1016/j.abb.2015.01.011}
}

2014

A first-passage kinetic Monte Carlo method for reaction–drift–diffusion processes

Ava J Mauro, Jon Karl Sigurdsson, Justin Shrake, Paul J Atzberger, and Samuel A Isaacson

Journal of Computational Physics, 2014

Journal Link arXiv Bib PDF

@article{mauro2014first,
  title = {A first-passage kinetic Monte Carlo method for reaction--drift--diffusion processes},
  author = {Mauro, Ava J and Sigurdsson, Jon Karl and Shrake, Justin and Atzberger, Paul J and Isaacson, Samuel A},
  journal = {Journal of Computational Physics},
  volume = {259},
  pages = {536--567},
  year = {2014},
  publisher = {Academic Press},
  url = {https://doi.org/10.1016/j.jcp.2013.12.023},
  doi = {10.1016/j.jcp.2013.12.023}
}

A comparison of bimolecular reaction models for stochastic reaction–diffusion systems

Ikemefuna C Agbanusi and Samuel A Isaacson

Bulletin of mathematical biology, 2014

Journal Link arXiv Bib PDF

@article{agbanusi2014comparison,
  title = {A comparison of bimolecular reaction models for stochastic reaction--diffusion systems},
  author = {Agbanusi, Ikemefuna C and Isaacson, Samuel A},
  journal = {Bulletin of mathematical biology},
  volume = {76},
  number = {4},
  pages = {922--946},
  year = {2014},
  publisher = {Springer US},
  url = {https://doi.org/10.1007/s11538-013-9833-6},
  doi = {10.1007/s11538-013-9833-6}
}

2013

Uniform asymptotic approximation of diffusion to a small target

Samuel A Isaacson and Jay Newby

Physical Review E, 2013

Journal Link arXiv Bib PDF

@article{isaacson2013uniform,
  title = {Uniform asymptotic approximation of diffusion to a small target},
  author = {Isaacson, Samuel A and Newby, Jay},
  journal = {Physical Review E},
  volume = {88},
  number = {1},
  pages = {012820--13pp},
  year = {2013},
  url = {https://doi.org/10.1103/PhysRevE.88.012820},
  doi = {10.1103/PhysRevE.88.012820}
}

A convergent reaction-diffusion master equation

Samuel A Isaacson

Journal of Chemical Physics, 2013

Journal Link arXiv Bib PDF

@article{isaacson2013convergent,
  title = {A convergent reaction-diffusion master equation},
  author = {Isaacson, Samuel A},
  journal = {Journal of Chemical Physics},
  volume = {139},
  number = {5},
  pages = {054101--12pp},
  year = {2013},
  url = {https://doi.org/10.1063/1.4816377},
  doi = {10.1063/1.4816377}
}

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, David M McQueen, and Charles S Peskin

Bulletin of mathematical biology, 2013

Journal Link arXiv Bib PDF

@article{isaacson2013influence,
  title = {The influence of spatial variation in chromatin density determined by X-ray tomograms on the time to find DNA binding sites},
  author = {Isaacson, Samuel A and Larabell, Carolyn A and Le Gros, Mark A and McQueen, David M and Peskin, Charles S},
  journal = {Bulletin of mathematical biology},
  volume = {75},
  pages = {2093--2117},
  year = {2013},
  publisher = {Springer US},
  url = {https://doi.org/10.1007/s11538-013-9883-9},
  doi = {10.1007/s11538-013-9883-9}
}

2011

The influence of volume exclusion by chromatin on the time required to find specific DNA binding sites by diffusion

SA Isaacson, DM McQueen, and Charles S Peskin

Proceedings of the National Academy of Sciences, 2011

Journal Link Bib PDF

@article{isaacson2011influence,
  title = {The influence of volume exclusion by chromatin on the time required to find specific DNA binding sites by diffusion},
  author = {Isaacson, SA and McQueen, DM and Peskin, Charles S},
  journal = {Proceedings of the National Academy of Sciences},
  volume = {108},
  number = {9},
  pages = {3815--3820},
  year = {2011},
  publisher = {National Academy of Sciences},
  doi = {10.1073/pnas.1018821108},
  url = {https://doi.org/10.1073/pnas.1018821108}
}

Numerical solution of linear Volterra integral equations of the second kind with sharp gradients

Samuel A Isaacson and Robert M Kirby

Journal of computational and applied mathematics, 2011

Journal Link Bib PDF

@article{isaacson2011numerical,
  title = {Numerical solution of linear Volterra integral equations of the second kind with sharp gradients},
  author = {Isaacson, Samuel A and Kirby, Robert M},
  journal = {Journal of computational and applied mathematics},
  volume = {235},
  number = {14},
  pages = {4283--4301},
  year = {2011},
  publisher = {North-Holland},
  url = {10.1016/j.cam.2011.03.029},
  doi = {https://doi.org/10.1016/j.cam.2011.03.029}
}

2009

A microfluidic pumping mechanism driven by non-equilibrium osmotic effects

Paul J Atzberger, Samuel Isaacson, and Charles S Peskin

Physica D: Nonlinear Phenomena, 2009

Journal Link Bib PDF

@article{atzberger2009microfluidic,
  title = {A microfluidic pumping mechanism driven by non-equilibrium osmotic effects},
  author = {Atzberger, Paul J and Isaacson, Samuel and Peskin, Charles S},
  journal = {Physica D: Nonlinear Phenomena},
  volume = {238},
  number = {14},
  pages = {1168--1179},
  year = {2009},
  publisher = {Elsevier},
  url = {https://doi.org/10.1016/j.physd.2009.03.018},
  doi = {10.1016/j.physd.2009.03.018}
}

The reaction-diffusion master equation as an asymptotic approximation of diffusion to a small target

Samuel A Isaacson

SIAM Journal on Applied Mathematics, 2009

Journal Link Bib PDF

@article{isaacson2009reaction,
  title = {The reaction-diffusion master equation as an asymptotic approximation of diffusion to a small target},
  author = {Isaacson, Samuel A},
  journal = {SIAM Journal on Applied Mathematics},
  volume = {70},
  number = {1},
  pages = {77--111},
  year = {2009},
  publisher = {Society for Industrial and Applied Mathematics},
  doi = {10.1137/070705039},
  url = {https://doi.org/10.1137/070705039}
}

Reaction-diffusion master equation, diffusion-limited reactions, and singular potentials

Samuel A Isaacson and David Isaacson

Physical Review E, 2009

Journal Link Bib PDF

@article{isaacson2009reactioo,
  title = {Reaction-diffusion master equation, diffusion-limited reactions, and singular potentials},
  author = {Isaacson, Samuel A and Isaacson, David},
  journal = {Physical Review E},
  volume = {80},
  number = {6},
  pages = {066106},
  year = {2009},
  publisher = {American Physical Society},
  url = {https://doi.org/10.1103/PhysRevE.80.066106},
  doi = {10.1103/PhysRevE.80.066106}
}

2008

Relationship between the reaction–diffusion master equation and particle tracking models

Samuel A Isaacson

Journal of Physics A: Mathematical and Theoretical, 2008

Journal Link Bib PDF

@article{isaacson2008relationship,
  title = {Relationship between the reaction--diffusion master equation and particle tracking models},
  author = {Isaacson, Samuel A},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {41},
  number = {6},
  pages = {065003},
  year = {2008},
  publisher = {IOP Publishing},
  url = {https://doi.org/10.1088/1751-8113/41/6/065003},
  doi = {10.1088/1751-8113/41/6/065003}
}

2006

Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations

Samuel A Isaacson and Charles S Peskin

SIAM Journal on Scientific Computing, 2006

Journal Link Bib PDF

@article{isaacson2006incorporating,
  title = {Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations},
  author = {Isaacson, Samuel A and Peskin, Charles S},
  journal = {SIAM Journal on Scientific Computing},
  volume = {28},
  number = {1},
  pages = {47--74},
  year = {2006},
  publisher = {Society for Industrial and Applied Mathematics},
  url = {https://doi.org/10.1137/040605060},
  doi = {10.1137/040605060}
}

2005

Stochastic reaction-diffusion methods for modeling gene expression and spatially distributed chemical kinetics

Samuel A Isaacson

New York University, 2005

Bib PDF

@phdthesis{isaacson2005stochastic,
  title = {Stochastic reaction-diffusion methods for modeling gene expression and spatially distributed chemical kinetics},
  author = {Isaacson, Samuel A},
  year = {2005},
  school = {New York University},
  url = {https://www.proquest.com/docview/305431598?pq-origsite=gscholar&fromopenview=true&sourcetype=Dissertations%20&%20Theses},
}