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


Mathematical Neuroscience and Cell Biology

I am a Professor of Mathematics in the Department of Mathematics at the University of Utah, where I am a faculty member of the Mathematical Biology Group and the Brain Institute. I am also a Visiting Professor at the Mathematical Institute, University of Oxford and INRIA, Sophia-Antipolis.

My main research interests lie in the areas of mathematical neuroscience and cell biology, with a particular focus on stochastic processes. My work draws upon a wide range of techniques in applied mathematics and theoretical physics such as non-equilibrium statistical physics, partial differential equations, pattern formation and nonlinear wave theory, dynamical systems theory, and the theory of self-organizing systems. Current research topics include the following:

Continuum neural field models of binocular rivalry waves

Stochastic neural field theory

Large deviations and metastability in stochastic hybrid systems, with applications to ion channels, chemical reaction networks, and neuronal population dynamics

Stochastic active transport models of cell polarization

Molecular motor models of axonal length control and polarization

Stochastic models of vesicular transport and delivery


NEW! 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 Modelling 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)

  • Notes and corrections
  • 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-)

    Stochastic hybrid systems and metastability

    P. C. Bressloff and O. Faugeras. On the Hamiltonian structure of large deviations in stochastic hybrid systems. Submitted (2015).

    P. C. Bressloff and S. D. Lawley. Escape from a potential well with a switching boundary Submitted (2015).

    H. A. Brooks and P. C. Bressloff. Quasicycles in the stochastic hybrid Morris-Lecar neural model Submitted (2015).

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

    P. C. Bressloff and S. D. Lawley. Moment equations for a piecewise deterministic PDE J. Phys. A 48 105001 (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. Keeener. 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 models of intracellular transport

    P. C. Bressloff and E. Levien. Synaptic democracy and active intracellular transport in axons. Submitted (2015).

    B. Karamched and P. C. Bressloff. A delayed feedback model of axonal length sensing. Submitted (2015).

    P. C. Bressloff and B. Xu. Stochastic active-transport model of cell polarization. SIAM J. Appl. Appl. Math. In press (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 Two-pool model of cooperative vesicular transport Phys. Rev. E 86 031911 (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. Directed intermittent search for a hidden target on a dendritic tree. Phys. Rev. E 80 021913 (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. Modeling the role of lateral membrane diffusion on AMPA receptor trafficking along a spiny dendrite. J. Comput. Neurosci. 25 366-389 (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 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. In press (2015).

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

    M. A. Webber and P. C. Bressloff. The effects of noise on binocular rivalry waves: a stochastic neural field model. J. Stat. Mech. (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 and Y-M Lai. Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. J. Math. Neurosci. 1 2 (2011).

    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

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

    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).

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

    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).

    P. C. Bressloff and A. M. Oster. A theory for the alignment of cortical feature maps during development. Phys. Rev. E 82 021920 (2010).

    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).

    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).

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

    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).

    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).

    P. C. Bressloff and J. D. Cowan, The visual cortex as a crystal. Physica D 173 :226-258 (2002).

    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).

    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).

    Editorial Boards

    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) TBA (1st year)

    Sam Carroll (Utah) Neural field theory (2nd year)

    Bhargav Karamched (Utah) Axonal transport (3rd year)

    Bin Xu (Utah) Cell polarization (3rd year)

    Heather Brooks (Utah) Stochastic hybrid systems (3rd 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 (2014-2017)

    Jay Newby (2010-2012)

    Berton Earnshaw (2007-2009)

    Lars Schwabe (2005-2006)

    Steve Coombes (1996-1998)

    Conferences and Workshops

    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



    Dead Horse Point

    Colorado River nr. Moab

    Powder in Solitude