Contact details

Department of Mathematics
University of Utah
155 South 1400 East
Salt Lake City
Utah 84112

Tel.: 801 585 1633
Fax.: 801 581 4148



  • New! Elected a Fellow of the Society for Industrial and Applied Mathematics (2016)
  • Appointed Associate Editor of the SIAM Journal of Applied Mathematics (2015)
  • Plenary speaker: SIAM Conference on Nonlinear waves and Coherent Structures (2014)
  • Published two books for Springer (2014): Stochastic Processes in Cell Biology, Waves in Neural Media

  • Mathematical Cell Biology, Mathematical Neuroscience, Stochastic Processes, Statistical and Biological Physics

    My research interests can be divided into two broad areas: (i) stochastic processes in cell biology and (ii) mathematical neuroscience and neural field theory. My work draws upon a wide range of methods in applied mathematics and theoretical physics including nonlinear PDEs, stochastic processes, statistical physics, and dynamical systems theory. Current research areas include the following:

  • Vesicular transport: synaptic democracy, exclusion processes, aggregation models
  • Cell polarization: active transport in budding yeast; MT regulation in growth cones; symmetry unbreaking in fission yeast
  • Intracellular pattern formation: Turing mechanism and active transport; synaptogenesis in C elegans
  • Cellular length control: axonal length sensing, intraflagellar transport
  • Diffusion in switching environments: moment equations; diffusion-limited reactions; stochastic gap junctions; diffusion on tress with switching nodes; dynamical compartments coupled by gated diffusion
  • Stochastic hybrid systems: stochastic ion channels; large deviations and path-integrals; switching master equations; molecular motors
  • Quorum sensing: coupled PDE-ODE systems; stochastic models and moment closure
  • Neural field theory: binocular rivalry waves; symmetric bifurcations in product neural fields; waves in stochastic neural fields; laminar neural fields

  • Books

    Paul C. Bressloff Stochastic Processes in Cell Biology Interdisciplinary Applied Mathematics (Springer) August (2014)

    Supplementary material

    Paul C. Bressloff Waves in Neural Media: From Single Neurons to Neural Fields Lecture Notes on Mathematical Modeling in the Life Sciences (Springer) Published (2014)

    Stephen Coombes and Paul C. Bressloff(eds.) Bursting: the Genesis of Rhythm in the Nervous System World Scientific (2005)


    Paul C. Bressloff and J. Newby. Stochastic models of intracellular transport Rev. Mod. Phys. 85 135-196 (2013)

    Paul C. Bressloff. Spatiotemporal Dynamics of Continuum Neural Fields J. Phys. A 45 (2012) 033001

    P. C. Bressloff. Lectures in Mathematical Neuroscience In: Mathematical Biology, IAS/Park City Mathematical Series.(M. A. Lewis, M. A. J. Chaplain, J. P. Keener and P. K. Maini (eds) 14 293-398 (American Mathematical Society, 2009).

    P. C. Bressloff. Pattern formation in visual cortex. Les Houches Lectures in Neurophysics (2005).

    P. C. Bressloff and S. Coombes. Physics of the extended neuron. Int. J. Mod. Phys. B 11:2343-2393 (1997).

    Selected papers (2001-)

    Biological processes in switching environments

    E. Levien and P. C. Bressloff. A stochastic hybrid framework for obtaining statistics of many random walkers in a switching environment. Submitted (2016).

    P. C. Bressloff. Diffusion in cells with stochastically-gated gap junctions. Submitted (2016).

    P. C. Bressloff and S. D. Lawley. Diffusion on a tree with stochastically-gated nodes. J. Phys. A In press (2016).

    P. C. Bressloff and S. D. Lawley. Stochastically-gated diffusion-limited reactions for a small target in a bounded domain. Phys. Rev. E 92 062117 (2015).

    P. C. Bressloff and S. D. Lawley. Escape from subcellular domains with randomly switching boundaries. Multi-scale Model. Simul. 13 1420-1445 (2015).

    P. C. Bressloff and S. D. Lawley. Escape from a potential well with a switching boundary. J. Phys. A 48 225001 (2015).

    P. C. Bressloff and S. D. Lawley. Moment equations for a piecewise deterministic PDE. J. Phys. A 48 105001 (2015).

    Self-organization in biological cells

    H. A. Brooks and P. C. Bressloff. A mechanism for Turing pattern formation with active and passive transport. Submitted (2016).

    Bin Xu and P. C. Bressloff. A PDE-DDE model for cell polarization in fission yeast Submitted (2016).

    Bin Xu and P. C. Bressloff. Model of growth cone membrane polarization via microtubule length regulation. Biophys. J. 109 2203-2214 (2015).

    P. C. Bressloff and B. Xu. Stochastic active-transport model of cell polarization. SIAM J. Appl. Appl. Math. 75 652-678 (2015).

    P. C. Bressloff and B. Karamched. A frequency-dependent decoding mechanism for axonal length sensing. Front. Cellular Neurosci. 9 281 (2015).

    B. Karamched and P. C. Bressloff. A delayed feedback model of axonal length sensing. Biophys. J 108 2408-2419 (2015).

    V. M. Burlakov, N. Emptage, A. Goriely and P. C. Bressloff. Synaptic bistability due to nucleation and evaporation of receptor clusters. Phys. Rev. Lett. 108 028101 (2012).

    Stochastic models of intracellular transport

    P. C. Bressloff and B. Karamched. Model of reversible vesicular transport with exclusion Submitted (2016).

    P. C. Bressloff. Aggregation-fragmentation model of vesicular transport in neurons. J. Phys. A 49 145601 (2016).

    E. Levien and P. C. Bressloff. Quasi-steady-state analysis of flashing ratchets. Phys. Rev. E 92 042129 (2015).

    P. C. Bressloff and E. Levien. Synaptic democracy and active intracellular transport in axons. Phys. Rev. Lett. 114 168101 (2015).

    P. C. Bressloff and J. M. Newby. Filling of a Poisson trap by a population of random intermittent searchers. Phys. Rev. E 85 031909 (2012).

    P. C. Bressloff and J. Newby. Quasi-steady state analysis of motor-driven transport on a two-dimensional microtubular network. Phys. Rev. E 83 061139 (2011).

    J. Newby and P. C. Bressloff. Local synaptic signalling enhances the stochastic transport of motor-driven cargo in neurons. Phys. Biol. 7 036004 (2010).

    J. Newby and P. C. Bressloff. Random intermittent search and the tug-of-war model of motor-driven transport. J. Stat. Mech. P04014 (2010).

    J. Newby and P. C. Bressloff. Quasi-steady state reduction of molecular-based models of directed intermittent search. Bull. Math. Biol. 72 1840-1866 (2010).

    J. Newby and P. C. Bressloff. Directed intermittent search for a hidden target on a dendritic tree. Phys. Rev. E 80 021913 (2009).

    B. A. Earnshaw and P. C. Bressloff. A dynamical corral model of protein trafficking in spines. Biophys. J. 96 1789-1802 (2009).

    P. C. Bressloff, B. A. Earnshaw and M. J. Ward. Diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps. SIAM J. Appl. Math. 68 1223-1246 (2008).

    B. A. Earnshaw and P. C. Bressloff. A biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD. J. Neurosci. 26 12362-12373 (2006).

    P. C. Bressloff. A stochastic model of intraflagellar transport. Phys. Rev. E 73 061916 (2006).

    P. C. Bressloff, A stochastic model of protein receptor trafficking prior to synaptogenesis. Phys. Rev. E 74 031910 (2006).

    Stochastic hybrid systems, ion channels and large deviations

    P. C. Bressloff and O. Faugeras. On the Hamiltonian structure of large deviations in stochastic hybrid systems with applications to ion channels. Submitted (2016).

    P. C. Bressloff Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks. J. Math. Neurosci 5 33pp. (2015).

    P. C. Bressloff and J. M. Newby. Path-integrals and large deviations in stochastic hybrid systems. Phys. Rev. E 89 042701 (2014).

    P. C. Bressloff and J. M. Newby. Stochastic hybrid model of spontaneous dendritic NMDA spikes. Phys. Biol. 11 016006 (13pp) (2014).

    J. M. Newby, P. C. Bressloff and J. P. Keener. The effect of Potassium channels on spontaneous action potential initiation by stochastic ion channels. Phys. Rev. Lett. 111 128101 (2013).

    P. C. Bressloff and J. M. Newby. Metastability in a stochastic neural network modeled as a jump velocity Markov process. SIAM J. Appl. Dyn. Syst. 12 1394-1435 (2013).

    Stochastic neural fields

    P. C. Bressloff and Z. P. Kilpatrick. Nonlinear Langevin equations for the wandering of fronts in stochastic neural fields. SIAM J. Appl. Dyn. Syst. 14 305-334 (2015).

    M. A. Webber and P. C. Bressloff. The effects of noise on binocular rivalry waves: a stochastic neural field model. J. Stat. Mech. 3 P03001 (2013).

    P. C. Bressloff. From invasion to extinction in heterogeneous neural fields. J. Math. Neurosci. 2 6 (2012).

    P. C. Bressloff and M. A. Webber. Front Propagation in stochastic neural fields SIAM J. Appl. Dyn. Syst. 11 708-740 (2012).

    P. C. Bressloff. Metastable states and quasicycles in a stochastic Wilson-Cowan model of neural population dynamics. Phys. Rev. E 82 051903 (2010).

    P. C. Bressloff. Stochastic neural field theory and the system-size expansion. SIAM J. Appl. Math 70 1488-1521 (2009).

    Waves in neural media

    P. C. Bressloff and S. Carroll. Laminar neural field model of laterally propagating waves of orientation selectivity. PLoS Comput. Biol. 11 e1004545 (2015).

    S. Carroll and P. C. Bressloff. Binocular rivalry waves in directionally selective neural field models. Physica D 285 8-17 (2014).

    P. C. Bressloff and S. M. Carroll. Spatio-temporal dynamics of neural fields on product spaces. SIAM J. Appl. Dyns. Syst. 13 1620-1653 (2014).

    P. C. Bressloff. Propagation of CaMKII translocation waves in heterogeneous spiny dendrites. J. Math. Biol. 66 1499-1525 (2013).

    P. C. Bressloff and M. A. Webber. Neural field model of binocular rivalry waves. J. Comput. Neurosci. 32 233-252 (2012).

    Z. P. Kilpatrick and P. C. Bressloff. Binocular rivalry in a competitive neural network with synaptic depression. SIAM J. Appl. Dyn. Syst. 9 1303-1347 (2010).

    Z. P. Kilpatrick and P. C. Bressloff. Stability of bumps in piecewise smooth neural fields with nonlinear adaptation. Physica D 239 1048-1060 (2010).

    Z. P. Kilpatrick and P. C. Bressloff. Spatially structured oscillations in a 2D excitatory neuronal network with synaptic depression. J. Comput. Neurosci. 239 1048-1060 (2010).

    Z. P. Kilpatrick, S. E. Folias and P. C. Bressloff. Traveling pulses and wave propagation failure in an inhomogeneous neural network. SIAM J. Appl. Dyn. Syst. 7 161-185 (2008).

    S. E. Folias and P. C. Bressloff, Breathers in two-dimensional excitable neural media. Phys. Rev. Lett. 95: 208107(2005).

    S. E. Folias and P. C. Bressloff, Stimulus-locked waves and breathers in an excitatory neural network. SIAM J. Appl. Math 65:2067-2092 (2005).

    S. E. Folias and P. C. Bressloff, Breathing pulses in an excitatory neural network. SIAM J. Appl. Dyn. Syst. 3,: 378-407(2004).

    P. C. Bressloff and S. E. Folias, Front bifurcations in an excitatory neural network. SIAM J. Appl. Math. 65: 131-151 (2004).

    S. Coombes and P. C. Bressloff. Saltatory waves in the spike-diffuse-spike model of active dendrites. Phys. Rev. Lett. 91:028102 (2003).

    P. C. Bressloff, Traveling fronts and wave propagation failure in an inhomogeneous neural network. Physica D 155 :83-100 (2001).

    Neural pattern formation and models of primary visual cortex

    S. Carroll and P. C. Bressloff. Phase equation for patterns of orientation selectivity in a neural field model of visual cortex. SIAM J. Appl. Dan. Syst. 15 60-83 (2016).

    M. Galtier, O. Faugeras and P. C. Bressloff. Hebbian learning of recurrent connections: a geometrical perspective. Neural Comput. 24 2346-2383 (2012).

    A. M. Oster and P. C. Bressloff, A developmental model of ocular dominance formation on a growing cortex Bull. Math. Biol. 68 73-98 (2006).

    P. C. Bressloff, Spontaneous symmetry breaking in self-organizing neural fields. Biol. Cybern. 93: 256-274 (2005).

    P. C. Bressloff, Euclidean shift-twist symmetry in population models of self-aligning objects. SIAM J. Appl. Math. 64:1668-1690 (2004).

    P. C. Bressloff, Spatially periodic modulation of cortical patterns by long-range horizontal connections. Physica D 185:131-157 (2003).

    P. C. Bressloff and J. D. Cowan, Spherical model of orientation and spatial frequency tuning in a cortical hypercolumn. Phil. Trans. Roy. Soc. B 358:1643-1667 (2003).

    P. C. Bressloff, Bloch waves, periodic feature maps and cortical pattern formation. Phys. Rev. Lett. 89 : 088101 (2002).

    P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas and M. Wiener, Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex Phil. Trans. Roy. Soc. B 40 :299-330 (2001).

    Contextual effects in primary visual cortex

    Shushruth, P. Mangapathy, J. M. Ichida, P. C. Bressloff, L. Schwabe and A. Angelucci. Strong recurrent networks compute the orientation-tuning of surround modulation in primate V1. J. Neurosci. 32 308-321 (2012).

    J. Icheda, L. Schwabe, P. C. Bressloff and A. Angelucci. Response facilitation from the ``suppressive'' surround of V1 neurons. J. Neurophysiol. 98 2168-2181 (2007).

    A. Angelucci and P. C. Bressloff. The contribution of feedforward, lateral and feedback connections to the classical receptive field center and extra-classical receptive field surround of primate V1 neurons Prog. Brain Res. 154 93-121 (2006).

    L. Schwabe, K. Obermayer, A. Angelucci and P. C. Bressloff. The role of feedback in shaping the extra-classical receptive field of cortical neurons: a recurrent network model J. Neurosci. 26 9117-9129 (2006).

    J. S. Lund, A. Angelucci and P. C. Bressloff, Anatomical substrates for the functional column in macaque primary visual cortex. Cerebral Cortex 12:15-24 (2003).

    P. C. Bressloff and J. D. Cowan, An amplitude equation approach to contextual effects in primary visual cortex. Neural Comput. 14 :493-525 (2002).

    Stochastic population oscillators and noise-induced synchronization

    P. C. Bressloff and Yi Ming Lai. Dispersal and noise: Various modes of synchrony in ecological oscillators. J. Math. Biol. 67 1669-1690 (2013).

    Y-M Lai, J. Newby and P. C. Bressloff. Effects of demographic noise on the synchronization of metacommunities by a fluctuating environment. Phys. Rev. Lett 107 118102 (2011).

    P. C. Bressloff and Y-M Lai. Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. J. Math. Neurosci. 1 2 (2011).

    Selected papers (< 2001)

    Dynamics of integrate-and-fire networks

    P. C. Bressloff, Traveling waves and pulses in a one-dimensional network of integrate-and-fire neurons. J. Math. Biol. 40 :169-183 (2000).

    P. C. Bressloff and S. Coombes, Dynamical theory of spike train dynamics in networks of integrate-and-fire oscillators. SIAM J. Appl. Math. 60:828-841 (2000).

    S. Coombes and P. C. Bressloff, Solitary waves in a model of dendritic cable with active spines. SIAM J. Appl. Math. 61:432-453 (2000).

    P. C. Bressloff and S. Coombes, Dynamics of strongly coupled spiking neurons. Neural Comput. 12 :91-129 (2000).

    P. C. Bressloff, Synaptically generated wave propagation in excitable neural media. Phys. Rev. Lett. 82:2979-2982 (1999).

    P. C. Bressloff and S. Coombes, Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays. Physica D 126 :99-122 (1999).

    P. C. Bressloff and S. Coombes, Travelling waves in a chain of pulse-coupled integrate-and-fire oscillators with distributed delays. Physica D 130:232-254 (1999).

    P. C. Bressloff and S. Coombes, Travelling waves in chain of pulse-coupled oscillators. Phys. Rev. Lett. 80:4815-4818 (1998).

    P. C. Bressloff and S. Coombes, Desynchronization, mode-locking and bursting in strongly-coupled integrate-and-fire oscillators. Phys. Rev. Lett. 81:2168-2171 (1998).

    P. C. Bressloff and S. Coombes, Spike train dynamics underlying pattern formation in an integrate-and-fire oscillator network. Phys. Rev. Lett. 81:2384-2387 (1998).

    P. C. Bressloff and S. Coombes, Synchrony in an array of integrate-and-fire neurons with dendritic structure. Phys. Rev. Lett. 78:4665-4668 (1997).

    P. C. Bressloff, S. Coombes and B. De Souza, Dynamics of a ring of pulse-coupled oscillators: Group theoretic approach. Phys. Rev. Lett. 79:2791-2794 (1997).


    P. C. Bressloff and G. Rowlands, Exact travelling wave solutions of an "integrable" discrete reaction-diffusion equation. Physica D 106:255-269 (1997).

    P. C. Bressloff, A self-organizing network in the weak coupling limit. Physica D 110:195-208 (1997).

    P. C. Bressloff, A new Green's function method for solving linear PDE's in two variables. J. Math. Anal. Appl. 210:390-415 (1997).

    P. C. Bressloff, V. M. Dwyer and M. J. Kearney, Classical diffusion and percolation in random environments on trees. Phys. Rev. E 55:6765-6775 (1997).

    P. C. Bressloff, C. V. Wood and P. A. Howarth, Nonlinear shunting model of the pupil light reflex. Proc. Roy. Soc. B 263:953-960 (1996).

    Associate Editorships

    SIAM Journal of Applied Mathematics

    Physical Review E

    Journal of Mathematical Biology

    Journal of Mathematical Neuroscience

    European Journal of Applied Mathematics

    Biological Cybernetics

    Graduate students

    Ethan Levien (Utah) Biological processes in switching environments (2nd year)

    Sam Carroll (Utah) Neural field theory (3rd year)

    Jenna Noll (Utah) Cellular length control (4th year)

    Bhargav Karamched (Utah) Axonal transport (4th year)

    Bin Xu (Utah) Cell polarization (4th year)

    Heather Brooks (Utah) Intracellular pattern formation (4th year)

    Matthew Webber (Oxford) Stochastic neural field models of binocular rivalry waves (D. Phil. 2013)

    Yi Ming Lai (Oxford) Stochastic population oscillators in ecology and neuroscience (D. Phil. 2013)

    Jay Newby (Utah) Molecular motor-based models of random intermittent search in dendrites (Ph. D 2010)

    Zachary Kilpatrick (Utah) Spatially structured waves and oscillations in neuronal networks with synaptic depression and adaptation (Ph. D 2010)

    William Nesse (Utah) Random fluctuations in dynamical neural networks. (Ph. D 2008)

    Berton Earnshaw (Utah) Biophysical models of AMPA receptor trafficking and synaptic plasticity (Ph. D 2007)

    Andrew M. Oster (Utah) Models of cortical development (Ph. D 2006)

    Stefanos E. Folias (Utah) Stimulus-induced waves and breathers in excitable neural media (Ph. D 2005)

    Matthew James Oscillations and waves in IF networks (Ph. D 2002)

    Barry de Souza Dynamics of neuronal networks with dendritic interactions (Ph. D 2000)

    Peter Roper Noise-induced effects in neural systems (Ph. D 1998)


    Sean Lawley (2014-2016)

    Jay Newby (2010-2012)

    Berton Earnshaw (2007-2009)

    Lars Schwabe (2005-2006)

    Steve Coombes (1996-1998)

    Conferences and Workshops

    Spatially Distributed Stochastic Dynamical Systems in Biology Isaac Newton Institute, Cambridge, UK, June 20-24, 2016

    The First International Conference on Mathematical NeuroScience (ICMNS), Antibes, Juan-Les-Pins, France, June 8-10, 2015

    Axonal Transport and Neuronal Mechanics, Mathematical Biosciences Institute, Ohio State, November 3-7, 2014

    SIAM Conference on Nonlinear Waves and Coherent Structures, University of Cambridge, August 11-14, 2014

    Stochastic Network Models of Neocortex (a Festschrift for Jack Cowan), Banff International research station, July 13-18, 2014

    Nonlinear dynamics and stochastic methods: from neuroscience to other biological applications (Bard Ermentrout’s 60th) University of Pittsburgh, March 10-12, 2014

    Oxford Conference on Challenges in Applied Mathematics University of Oxford, July 1-5, 2013

    Stochastic Modeling of Biological Processes, IMA, University of Minnesota, May 13-17, 2013

    Random models in neuroscience Université Pierre et Marie Curie, July 2-6, 2012

    Stochastic Modelling in Biological Systems, University of Oxford, March 18-23, 2012

    Spatio-Temporal Evolution Equations and Neural Fields, CIRM, Marseilles, October 24-28, 2011

    Interesting Links and References

    I have a strong interest in philosophy, particularly philosophy of mind, ethics, and philosophy of science.

    Stanford Encyclopedia of Philosophy


    Why Evolution is True (Jerry Coyne)

    Sam Harris

    Everybody is wrong about God (James A. Lindsay)

    Theory in Biology: Figure 1 or Figure 7? (Rob Phillips)

    Morality for Humans (Mark Johnson)

    Essentialism (Greg Mckeown)

    Freedom Regained (Julian Baggini)

    Justice: What's the Right Thing to Do? (Michael J. Sandel)

    Sapiens: A Brief History of Humankind (Yuval Noah Harari)

    The Philosophy of Mind (Dale Jacquette)

    The Accidental Mind (David Linden)

    Beyond the Brain: How Body and Environment Shape Animal and Human Minds (Louise Barrett)

    Understanding Our Unseen Reality:Solving Quantum Riddles (Ruth E Kastner)

    The Beginning of Infinity (David Deutsch)

    Genius: The Life and Science of Richard Feynman (James Gleick)

    Brave Genius (Sean B. Carroll)

    The strangest Man: Paul Dirac (Graham Farmelo)



    Dead Horse Point

    Colorado River nr. Moab

    Powder in Solitude