Department of Mathematics
University of Utah
155 South 1400 East
Salt Lake City
Tel.: 801 585 1633
Fax.: 801 581 4148
Department of Mathematics
Tel.: 801 585 1633
A major goal of this research is to understand the fundamental biophysical mechanisms underlying cellular function in health and disease. This includes both single cells and multicellular systems. Our work draws upon a wide variety of methods in applied mathematics and theoretical physics including stochastic processes, statistical physics, nonlinear PDEs, and dynamical systems theory. Applications range from molecular and cellular neuroscience to gene networks to bacterial cell polarization and quorum sensing. We are also developing new mathematical and numerical methods for analyzing complex and stochastic nonlinear systems. Current research topics include the following:
Biological processes in switching environments: diffusion in domains with randomly switching boundaries; diffusion-limited reactions; stochastic gap junctions; genetic switches; bacterial persistence in switching environments
Intracellular transport: molecular motors; synaptic democracy and axonal transport; exclusion processes; aggregation models of intracellular transport; random intermittent search;
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
Stochastic hybrid systems: stochastic ion channels; large deviations and path-integrals; switching master equations
Quorum sensing: coupled PDE-ODE systems; stochastic models and moment closure
Our research in this area focuses on the spatio-temporal dynamics of continuum neural fields. Neural fields model the large-scale dynamics of spatially structured biological neural networks in terms of nonlinear integro-differential equations, whose associated integral kernels represent the spatial distribution of neuronal synaptic connections. They provide an important example of spatially extended excitable systems with nonlocal interactions, and exhibit a wide range of spatially coherent dynamics, including traveling waves, oscillations and Turing-like patterns. Current research topics include the following:
Neural field models of visual cortex: traveling waves; pattern formation and visual hallucinations; symmetric bifurcations; laminar neural fields.
Stochastic neural fields: stochastic hybrid models of neural networks; large deviation theory and bistability; stochastic traveling waves
Neural field models of binocular rivalry waves
Paul C. Bressloff Stochastic Processes in Cell Biology Interdisciplinary Applied Mathematics (Springer) August (2014)
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)
P. C. Bressloff and S. D. Lawley. Dynamically active compartments coupled by a stochastically-gated gap junction. Submitted (2016)
P. C. Bressloff. Stochastic switching in biology: from genotype to phenotype (Review) Submitted (2016)
P. C. Bressloff. Stochastic Fokker-Planck equation in random environments. Submitted (2016).
P. C. Bressloff. Stochastic Liouville equation for particles driven by dichotomous environmental noise. Submitted (2016).
E. Levien and P. C. Bressloff. Coupling sample paths to the partial thermodynamic limit in stochastic chemical reaction networks. Submitted (2016).
E. Levien and P. C. Bressloff. A stochastic hybrid framework for obtaining statistics of many random walkers in a switching environment. Multiscale Methods. Simul. In press (2016).
P. C. Bressloff. Ultrasensitivity and noise amplification in a model of V. harveyi quorum sensing. Phys. Rev. E 93 062418 (2016).
P. C. Bressloff. Diffusion in cells with stochastically-gated gap junctions. SIAM J. Appl. Math. 76 1658-1682 (2016).
P. C. Bressloff and S. D. Lawley. Diffusion on a tree with stochastically-gated nodes. J. Phys. A 49 245601 (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).
H. A. Brooks and P. C. Bressloff. A mechanism for Turing pattern formation with active and passive transport. SIAM J. Appl. Dyn. Syst. 15 1823-1843 (2016).
Bin Xu and P. C. Bressloff. A PDE-DDE model for cell polarization in fission yeast SIAM J. Appl. Math 76 1844-1870 (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).
B. Karamched and P. C. Bressloff. Effects of geometry on reversible vesicular transport. Submitted (2016).
P. C. Bressloff and B. Karamched. Model of reversible vesicular transport with exclusion J. Phys. A 49 345602 (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. Propagation of CaMKII translocation waves in heterogeneous spiny dendrites. J. Math. Biol. 66 1499-1525 (2013).
P. C. Bressloff and J. M. Newby. Stochastic models of intracellular transport (Review) Rev. Mod. Phys. 85 135-196 (2013)
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 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).
S. Carroll and P. C. Bressloff. Symmetric Bifurcations in a Neural Field Model for encoding the direction of spatial contrast gradients. Submitted (2016).
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).
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).
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).
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. Spatiotemporal Dynamics of Continuum Neural Fields (Review) J. Phys. A 45 (2012) 033001
P. C. Bressloff and M. A. Webber. Neural field model of binocular rivalry waves. J. Comput. Neurosci. 32 233-252 (2012).
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).
Bridget Fan (Utah) T. B. A. (2nd year)
Patrick Murphy (Utah) T. B. A. (2nd year)
Ethan Levien (Utah) Biological processes in switching environments (3rd year)
Sam Carroll (Utah) Neural field theory (4th year)
Bhargav Karamched (Utah) Axonal transport (5th year)
Bin Xu (Utah) Cell polarization (5th year)
Heather Brooks (Utah) Intracellular pattern formation (5th 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)
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
I have a strong interest in philosophy, particularly philosophy of mind, ethics, and philosophy of science.
Dead Horse Point
Colorado River nr. Moab
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