Samuel Isaacson

Department of Mathematics and Statistics
Boston University
Office: CDS 442

Mailing address:
Samuel Isaacson
Boston University
Department of Mathematics and Statistics
665 Commonwealth Ave.
Boston, MA 02215


CV: [pdf]

Fall 2023 Teaching

  • MA861, Numerical PDEs, see Blackboard for course information.


  • M. Heldman, S. A. Isaacson, Q. Liu, and K. Spiliopoulos, Mean field limits of particle-based stochastic reaction-drift-diffusion models Preprint (2023) [arXiv preprint]
  • A Huhn,..., S. A. Isaacson, O. Dushek, The molecular reach of antibodies determines their SARS- CoV-2 neutralisation potency, Submitted (2023). [bioRxiv preprint]
  • G. A. Zagati, S. A. Isaacson, et. al, Extending JumpProcess.jl for fast point process simulation with time-varying intensities Submitted (2023). [arXiv preprint]
  • M. Heldman, S. A. Isaacson, J. Ma, and K. Spiliopoulos Fluctuation analysis for particle-based stochastic reaction-diffusion models, Accepted, Stochastic Process. Appl. (2023). [arXiv preprint],
  • T. Loman, Y. Ma, V. Ilin, S. Gowda, N. Korsbo, N. Yewale, C. V. Rackauckas, and S. A. Isaacson, Catalyst: Fast and flexible modeling of reaction networks, PLOS Computational Biology 19(10): e1011530 (2023). [Open Access journal version], [bioRxiv preprint],
  • Y. Zhang and S. A. Isaacson, Detailed Balance for Particle Models of Reversible Reactions in Bounded Domains, J. Chem. Phys., 156, 204105 (2022). [journal version], [arXiv preprint],
  • J. Goyette, D. Depoil, Z. Yang, S. A. Isaacson, J. Allard, P. Anton van der Merwe, K. Gaus, M. L. Dustin, and O. Dushek, Dephosphorylation accelerates the dissociation of ZAP70 from the T cell receptor, PNAS, 119(9), e2116815119 (2022). [open access journal version]
  • S. A. Isaacson, J. Ma, K. Spiliopoulos, Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models, SIAM J. Math. Analysis 54(1), 453-511 (2022). [journal version], [arXiv preprint],
  • S. A. Isaacson, J. Ma and K. Spiliopoulos, How reaction-diffusion PDEs approximate the large-population limit of stochastic particle models, SIAM J. Applied Math, 81(6), 2622-2657 (2021). [journal version], [arXiv version]
  • J. Wang, C. Belta and S. A. Isaacson, How Retroactivity Affects the Behavior of Incoherent Feed-Forward Loops, iScience, Vol. 23, No. 12, 101779 (16pp) (2020). [Open Access Journal Version]
  • J. Ma, M. Do, M. A. Le Gros, C. S. Peskin, C. A. Larabell, Y. Mori, and S A. Isaacson, Strong Intracellular Signal Inactivation Produces Sharper and more Robust Signaling from Cell Membrane to Nucleus, PLOS Comp. Bio., Vol. 16, No. 11, pp 1-19 (2020). [Open Access Journal Version]
  • Y. Zhang, L. Clemens, J. Goyette, J. Allard, O. Dushek and S. A. Isaacson, The Influence of Molecular Reach and Diffusivity on the Efficacy of Membrane-Confined Reactions, Biophysical Journal, Vol. 117, No. 7, pp 1189-1201 (2019). [Open Access Journal Version]
  • J. Wang, S. A. Isaacson and C. Belta, Modeling Genetic Circuit Behavior in Transiently Transfected Mammalian Cells, ACS Synthetic Biology, Vol. 8, No. 4, pp 697-707 (2019). [journal link] [accepted version preprint pdf]
  • J. Wang, S. A. Isaacson and C. Belta, Predictions of Genetic Circuit Behavior Based on Modular Composition in Transiently Transfected Mammalian Cells, Proceedings of the IEEE Life Sciences Conference, Montreal, Canada, 10.1109/LSC.2018.8572174 (4 pp) (2018). [published article link]
  • S. T. Johnston, C. N. Angstmann, S. N.V. Arjunan, C. H. L. Beentjes, A. Coulier, S. A. Isaacson, A. A. Khan, K. L Lipkow, and S. S. Andrews, Accurate particle-based reaction algorithms for fixed timestep simulators, 2018 MATRIX Annals (16 pp) (2018). [published article link]
  • S. A. Isaacson and Y. Zhang, An Unstructured Mesh Convergent Reaction-Diffusion Master Equation for Reversible Reactions, J. Comp. Phys., Vol. 374, pp. 954-983 (2018). [journal link] [arXiv version of accepted manuscript]
  • J. Goyette, C. S. Salas, N. C. Gordon, M. Bridge, S. A. Isaacson, J. Allard and O. Dushek, Biophysical assay for tethered signaling reactions reveals tether-controlled activity for the phosphatase SHP-1, Science Advances, Vol. 3, No. 3, e1601692 (14 pp) (2017). [journal link] [pdf]
  • S. A. Isaacson, A. J. Mauro and J. Newby, Uniform Asymptotic Approximation of Diffusion to a Small Target: Generalized Reaction Models, Phys. Rev. E, Vol 94, No. 4, 042414 (17 pp) (2016). [journal version] [arXiv version]
  • S. J. Chapman, R. Erban and S. A. Isaacson, Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics, SIAM Journal on Applied Mathematics, Vol. 76, No. 1, pp 368-390 (2016). [journal version]
  • M. Do, S. A. Isaacson, G. McDermott, M. A. Le Gros, and C. A. Larabell, Imaging and Characterizing Cells using Tomography, Arch. Biochem. and Biophys., Vol. 581, pp 111-121 (2015). [journal version]
  • I. C. Agbanusi and S. A. Isaacson, A Comparison of Bimolecular Reaction Models for Stochastic Reaction Diffusion Systems, Bulletin of Mathematical Biology, Vol 76, No. 4, pp 922-946 (2014). [preprint pdf] [journal version]
  • A. J. Mauro, JK Sigurdsson, J. Shrake, P. J. Atzberger and S. A. Isaacson, A First-Passage Kinetic Monte Carlo Method for Reaction-Drift-Diffusion Processes, J. Computational Physics, Vol. 259, pp 536-567 (2014). [preprint pdf] [journal version]
  • S. A. Isaacson, C. A. Larabell, M. A. Le Gros, D. M. McQueen and C. S. Peskin, The Influence of Spatial Variation in Chromatin Density Determined by X-ray Tomograms on the Time to Find DNA Binding Sites, Bulletin of Mathematical Biology, Vol. 75, No. 11, pp 2093-2117 (2013). [preprint pdf] [journal version] []
  • S. A. Isaacson, A Convergent Reaction-Diffusion Master Equation, J. Chem. Phys, Vol. 139, No. 5, 054101 (12 pp) (2013). [pdf]
  • S. A. Isaacson and J. Newby, Uniform Asymptotic Approximation of Diffusion to a Small Target, J. Newby. Phys. Rev. E, Vol. 88, No. 1, 012820 (13 pp) (2013). [pdf]
  • S. A. Isaacson and R. M. Kirby, Numerical Solution of Linear Volterra Integral Equations of the Second Kind with Sharp Gradients, J. Comput. Appl. Math, Vol. 235, No. 14, pp 4283-4301 (2011). [preprint pdf] [journal version]
  • S. A. Isaacson, D. M. McQueen and C. S. Peskin, The Influence of Volume Exclusion by Chromatin on the Time Required to Find Specific DNA Binding Sites by Diffusion, Proceedings of the National Academy of Sciences, Vol. 108, No. 9, pp 3815-3820 (2011). [pdf] [journal link] [supplementary material - journal link]
  • S. A. Isaacson and D. Isaacson, The Reaction-Diffusion Master Equation, Diffusion Limited Reactions, and Singular Potentials, Phys. Rev. E, Vol. 80, No. 6, pg 066106 (9pp) (2009). [pdf]
  • S. A. Isaacson, The Reaction-Diffusion Master Equation as an Asymptotic Approximation of Diffusion to a Small Target, SIAM J. Appl. Math., Vol. 70, No. 1, pp 77-111 (2009). [pdf]
  • P. J. Atzberger, S. A. Isaacson and C. S. Peskin, A Microfluidic Pumping Mechanism Driven by Non-Equilibrium Osmotic Effects, Physica D, Vol. 238, No. 14, pp 1168-1179 (2009). [pdf]
  • S. A. Isaacson, Relationship Between the Reaction-Diffusion Master Equation and Particle Tracking Models, J. Phys. A: Math. Theor., Vol. 41, No. 6, 065003 (15 pp) (2008). [pdf]
  • S. A. Isaacson and C. S. Peskin, Incorporating Diffusion in Complex Geometries into Stochastic Chemical Kinetics Simulations, SIAM Journal on Scientific Computing, Vol. 28, No. 1, pp 47-74 (2006). [pdf]
  • S. A. Isaacson, Stochastic Reaction-Diffusion Methods for Modeling Gene Expression and Spatially Distributed Chemical Kinetics, Ph. D. thesis (September 2005). [pdf]


  • A Stochastic Reaction-Diffusion Active Transport Method for Studying the Control of Gene Expression in Eukaryotic Cells, [pdf]
    • With C. S. Peskin. Presented at "Workshop on Applications of Methods of Stochastic Systems and Statistical Physics in Biology", Notre Dame, 2005.
  • A Stochastic Reaction-Diffusion Method for Studying the Control of Gene Expression in Eukaryotic Cells, [pdf]
    • With C. S. Peskin. Presented at "Symposium on Computational Cell Biology", Lenox, MA 2005.

Online Talks

  • Workshop on Mathematical and Computational Methods in Biology, Mathematical Biosciences Institute, Ohio State University (2020)
    • Strong intracellular signal inactivation produces sharper and more robust signaling from cell membrane to nucleus, [here].
  • BIRS Workshop on Particle-Based Stochastic Reaction-Diffusion Models in Biology 2014
    • Lattice Approximation of Spatially-Continuous Particle-Based Stochastic Reaction-Diffusion Models, [here].
  • SIAM Conference on the Life Sciences 2012
    • Minitutorial on Stochastic Simulation of Spatially-Distributed Models Arising in the Life Sciences,
    • Keynote (with movies): [here], pdf (no movies): [here].
  • Workshop on Stochastic Modeling of Stochastic Reaction-Diffusion Processes in Biology 2012
    • Talk on Influence of Nuclear Substructure on Gene Regulation and Expression,
    • Keynote (with movies): [here]. Pdf (no movies): [here].
  • National Centers for Systems Biology Annual Meeting 2009: [here].
    • The talk is about 24 minutes into the video stream for day 2.

Research and Educational Software (all on my Github: [here], or within the SciML Github: [here])

  • I contribute to DiffEqJump - SSAs for simulating stochastic chemical kinetics models and general jump processes in Julia.
  • I contribute to Catalyst - a domain specific language (DSL) for specifying chemical reaction networks in Julia, enabling the easy construction of ODE, SDE or jump process models from a reaction network.
  • I contribute to ModelingToolkit - an intermediate language (IR) for specifying symbolic models in Julia, with support for transforming and analyzing models, along with generating optimized solvers from model specifications.
  • I contribute to DiffEqTutorials - tutorials for SciML packages, including the three proceeding libraries.
  • ibmethod2d, A 2D Periodic, Cartesian Grid Immersed Boundary Navier-Stokes Solver: [here].