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, with a particular emphasis on molecular and cellular neuroscience. 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. 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: intracellular diffusion in domains with stochastically gated boundaries; intercellular diffusion via stochastic gap junctions; diffusion-limited biochemical reactions in cells; bacterial persistence in switching environments
Stochastic models of axonal and dendritic transport: PDE models of motor-based vesicular transport; synaptic democracy and vesicular transport; exclusion processes; aggregation models of intracellular transport; random intermittent search processes.
Cell polarization: Microtubule regulation in growth cone steering; active transport in budding yeast; symmetry unbreaking in fission yeast.
Intracellular pattern formation: Synaptogenesis in C elegans; Turing mechanism and active transport; intracellular waves and chemical signaling.
Cellular length control: axonal length sensing; axonal regeneration; intraflagellar transport in bacteria
Stochastic hybrid systems: stochastic ion channels and voltage fluctuations; large deviations and path-integrals; stochastic neural oscillators; genetic switches and oscillators; stochastic neural networks.
Bacterial quorum sensing: parallel signaling pathways in Vibrio; contraction mappings and mean field theory; coupled PDE-ODE systems; stochastic models
Morphogenesis: cytoneme-mediated morphogen gradients; robustness
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 cortex: binocular rivalry waves; pattern formation, symmetric bifurcation theory and visual hallucinations; laminar neural fields.
Stochastic neural fields: stochastic traveling waves; variational methods and large deviations; homogenization of heterogeneous neural media
Recurrent network models of visual cortex: contextual image processing and the role of extrastriate feedback
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, B. M. Karamched, S. D. Lawley and E. Levien. Diffusive transport in the presence of stochastically gated absorption. Phys. Rev. E 96 022102 (2017).
P. C. Bressloff and S. D. Lawley. Hybrid colored noise process with space-dependent switching rates. Phys. Rev. E 96 012129 (2017).
P. C. Bressloff and S. D. Lawley. Temporal disorder as a mechanism for spatially heterogeneous diffusion. Phys. Rev. E 95 060101(R) (2017).
P. C. Bressloff and S. D. Lawley. Dynamically active compartments coupled by a stochastically-gated gap junction. J. Nonlin. Sci. 27 1487–1512 (2017)
P. C. Bressloff and S. D. Lawley. Residence times of a Brownian particle with temporal heterogeneity. J. Phys. A 50 195001 (2017).
P. C. Bressloff. Stochastically-gated local and occupation times of a Brownian particle. Phys. Rev. E 95 012130 (2017).
P. C. Bressloff. Stochastic Fokker-Planck equation in random environments. Phys. Rev. E 94 042129 (2016).
E. Levien and P. C. Bressloff. A stochastic hybrid framework for obtaining statistics of many random walkers in a switching environment. Multiscale Model. Simul. 14 1417-1433 (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. Multiscale 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).
P. C. Bressloff and J. M. Maclaurin. Stochastic hybrid systems in cellular neuroscience Submitted (2018)
P. C. Bressloff and J. Maclaurin. A variational method for analyzing limit cycle oscillations in stochastic hybrid systems.
P. C. Bressloff and J. Maclaurin. A variational method for analyzing stochastic limit cycle oscillators Submitted (2018).
E. Levien and P. C. Bressloff. Robustness of stochastic chemical reaction networks to extrinsic noise: the role of deficiency. Submitted (2018).
P. C. Bressloff. Stochastic switching in biology: from genotype to phenotype (Topical Review) J. Phys. A 50 133001 (2017)
P. C. Bressloff and S. D. Lawley. Mean first passage times for piecewise deterministic Markov processes and the effects of critical points. J. Stat. Mech. 063202 (2017).
P. C. Bressloff and O. Faugeras. On the Hamiltonian structure of large deviations in stochastic hybrid systems. J. Stat. Mech. 033206 (2017).
P. C. Bressloff. Feynman-Kac formula for stochastic hybrid systems. Phys. Rev. E 95 012138 (2017).
P. C. Bressloff. Stochastic Liouville equation for particles driven by dichotomous environmental noise. Phys. Rev. E 95 012124 (2017).
E. Levien and P. C. Bressloff. Reversibility and stationary distributions in hybrid chemical reaction networks. J. Phys. A 50 475004 (2017).
E. Levien and P. C. Bressloff. Coupling sample paths to the thermodynamic limit in Monte Carlo estimators with applications to gene expression. J. Comp. Phys. 346 1-13 (2017).
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).
P. C. Bressloff and H. Kim. Bidirectional transport model of morphogen gradient formation via cytonemes Submitted (2018).
G. Fan and P. C. Bressloff. Population model of quorum sensing with multiple parallel pathways Bull. Math. Biol. 79 2599-2626 (2017)
Bin Xu and P. C. Bressloff. A theory of synchrony for active compartments with delays coupled through bulk diffusion Physica D 341 45-59 (2017).
H. A. Brooks and P. C. Bressloff. Turing mechanism for homeostatic control of synaptic density in C. elegans. Phys. Rev. E 96 012413 (2017).
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).
P. C. Bressloff. Ultrasensitivity and noise amplification in a model of V. harveyi quorum sensing. Phys. Rev. E 93 062418 (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 doubly stochastic Poisson model of flagellar length control. SIAM J. Appl. Math In press (2018).
B. Karamched and P. C. Bressloff. Effects of geometry on reversible vesicular transport. J. Phys. A 50 055601 (2017).
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).
P. C. Bressloff and E. Levien. Synaptic democracy and active intracellular transport in axons. Phys. Rev. Lett. 114 168101 (2015).
E. Levien and P. C. Bressloff. Quasi-steady-state analysis of flashing ratchets. Phys. Rev. E 92 042129 (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).
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)
S. Carroll and P. C. Bressloff. Symmetric Bifurcations in a Neural Field Model for encoding the direction of spatial contrast gradients. SIAM J. Appl. Dyn. Syst. In press (2018).
A. Angelucci, M. Bijanzadeh, L. Nurminen, F. Federer, S. Merlin and P. C. Bressloff. Circuits and mechanisms for surround modulation in visual cortex. Ann. Rev. Neurosci. 40 425-451 (2017).
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).
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).
Hyunjoong Kim (Utah) Stochastic processes in cell biology (2nd year)
Bridget Fan (Utah) Quorum sensing (3rd year)
Patrick Murphy (Utah) Stochastic processes in cell biology (3rd year)
Ethan Levien (Utah) Biological processes in switching environments (4th year)
Sam Carroll (Utah) Neural field theory (5th year)
Heather Brooks (Utah) Intracellular pattern formation (5th year)
Bin Xu (Utah) Mathematical models of cell polarization (Ph. D 2017)
Bhargav Karamched (Utah) Mathematical models of motor-based intracellular transport (Ph. D 2017)
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)
James Maclaurin (2017-)
Sean Lawley (2014-2016)
Jay Newby (2010-2012)
Berton Earnshaw (2007-2009)
Lars Schwabe (2005-2006)
Steve Coombes (1996-1998)
The Third International Conference on Mathematical NeuroScience (ICMNS), University of Colorado Boulder, May 30-June 2, 2017
The Second International Conference on Mathematical NeuroScience (ICMNS), Antibes, Juan-Les-Pins, France, May 30 - June 1, 2016
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
Powder in Solitude