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

My research draws upon a wide range of methods in applied mathematics and theoretical physics (nonlinear PDEs, stochastic processes, statistical physics, dynamical systems theory) to explore biological processes at a mechanistic level. After many years working in mathematical neuroscience and neural field theory, I have recently refocused my research efforts to stochastic processes in cell biology (eg. intracellular transport, randomly switching environments, cellular self-organization, intracellular patterns and waves). Current research topics include the following:

  1. Vesicular transport
  2. Synaptic democracy with reversible targets

    Reversible vesicular transport with exclusion

    Aggregation models of vesicular transport

  3. Cell polarization
  4. Active transport in budding yeast

    MT regulation and growth cone polarization

    Diffusion-based mechanism of NETO in fission yeast

  5. Intracellular pattern formation
  6. Turing mechanism based on active transport

    Synaptogenesis in C elegans

    Pattern formation on 2D MT networks

  7. Cellular length control
  8. Delayed feedback model of axonal length sensing

    Stochastic models of intraflagellar transport

    Biosynthesis and cell size control

  1. Diffusion in domains with switching boundaries
  2. Moment equations

    Escape from potential wells

    Diffusion-limited reaction rates

    Stochastic gap junctions

    Diffusion on trees with switching nodes

    Dynamical compartments coupled by gated diffusion

  3. Stochastic hybrid systems
  4. Stochastic ion channels


    Switching master equations

    Flashing ratchets

  5. Neural field theory
  6. Binocular rivalry waves

    Product neural fields

    Waves in stochastic neural fields

    Laminar neural fields


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)

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-)

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. Submitted (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. 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 In press (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