Professor Paul C Bressloff

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
Email: bressloff@math.utah.edu


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 selforganization, intracellular patterns and waves). Current research topics include the following:
 Vesicular transport
Synaptic democracy with reversible targets
Reversible vesicular transport with exclusion
Aggregation models of vesicular transport
 Cell polarization
Active transport in budding yeast
MT regulation and growth cone polarization
Diffusionbased mechanism of NETO in fission yeast
 Intracellular pattern formation
Turing mechanism based on active transport
Synaptogenesis in C elegans
Pattern formation on 2D MT networks
 Cellular length control
Delayed feedback model of axonal length sensing
Stochastic models of intraflagellar transport
Biosynthesis and cell size control


 Diffusion in domains with switching boundaries
Moment equations
Escape from potential wells
Diffusionlimited reaction rates
Stochastic gap junctions
Diffusion on trees with switching nodes
Dynamical compartments coupled by gated diffusion
 Stochastic hybrid systems
Stochastic ion channels
Pathintegrals
Switching master equations
Flashing ratchets
 Neural field theory
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 135196 (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 293398 (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 11:23432393 (1997).
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 stochasticallygated gap junctions. Submitted (2016).
P. C. Bressloff and S. D. Lawley. Diffusion on a tree with stochasticallygated nodes. Submitted (2016).
P. C. Bressloff and S. D. Lawley. Stochasticallygated diffusionlimited 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 14201445 (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).
Selforganization 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 22032214 (2015).
P. C. Bressloff and B. Xu. Stochastic activetransport model of cell polarization. SIAM J. Appl. Appl. Math. 75 652678 (2015).
P. C. Bressloff and B. Karamched. A frequencydependent 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 24082419 (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. Aggregationfragmentation model of vesicular transport in neurons. J. Phys. A In press (2016).
E. Levien and P. C. Bressloff. Quasisteadystate 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. Quasisteady state analysis of motordriven transport on a twodimensional microtubular network. Phys. Rev. E 83 061139 (2011).
J. Newby and P. C. Bressloff. Local synaptic signalling enhances the stochastic transport of motordriven cargo in neurons. Phys. Biol. 7 036004 (2010).
J. Newby and P. C. Bressloff. Random intermittent search and the tugofwar model of motordriven transport. J. Stat. Mech. P04014 (2010).
J. Newby and P. C. Bressloff. Quasisteady state reduction of molecularbased models of directed intermittent search. Bull. Math. Biol. 72 18401866 (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 17891802 (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 12231246 (2008).
B. A. Earnshaw and P. C. Bressloff. A biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD. J. Neurosci. 26 1236212373 (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 Pathintegral 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. Pathintegrals 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 13941435 (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 305334 (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 708740 (2012).
P. C. Bressloff. Metastable states and quasicycles in a stochastic WilsonCowan model of neural population dynamics. Phys. Rev. E 82 051903 (2010).
P. C. Bressloff. Stochastic neural field theory and the systemsize expansion. SIAM J. Appl. Math 70 14881521 (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 285 817 (2014).
P. C. Bressloff and S. M. Carroll. Spatiotemporal dynamics of neural fields on product spaces. SIAM J. Appl. Dyns. Syst. 13 16201653 (2014).
P. C. Bressloff. Propagation of CaMKII translocation waves in heterogeneous spiny dendrites. J. Math. Biol. 66 14991525 (2013).
P. C. Bressloff and M. A. Webber. Neural field model of binocular rivalry waves. J. Comput. Neurosci. 32 233252 (2012).
Z. P. Kilpatrick and P. C. Bressloff. Binocular rivalry in a competitive neural network with synaptic depression. SIAM J. Appl. Dyn. Syst. 9 13031347 (2010).
Z. P. Kilpatrick and P. C. Bressloff. Stability of bumps in piecewise smooth neural fields with nonlinear adaptation. Physica D 239 10481060 (2010).
Z. P. Kilpatrick and P. C. Bressloff. Spatially structured oscillations in a 2D excitatory neuronal network with synaptic depression. J. Comput. Neurosci. 239 10481060 (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 161185 (2008).
S. E. Folias and P. C. Bressloff, Breathers in twodimensional excitable neural media. Phys. Rev. Lett. 95: 208107(2005).
S. E. Folias and P. C. Bressloff, Stimuluslocked waves and breathers in an excitatory neural network. SIAM J. Appl. Math 65:20672092 (2005).
S. E. Folias and P. C. Bressloff, Breathing pulses in an excitatory neural network. SIAM J. Appl. Dyn. Syst. 3,: 378407(2004).
P. C. Bressloff and S. E. Folias, Front bifurcations in an excitatory neural network. SIAM J. Appl. Math. 65: 131151 (2004).
S. Coombes and P. C. Bressloff. Saltatory waves in the spikediffusespike 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 :83100 (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 6083 (2016).
M. Galtier, O. Faugeras and P. C. Bressloff. Hebbian learning of recurrent connections: a geometrical perspective. Neural Comput. 24 23462383 (2012).
A. M. Oster and P. C. Bressloff, A developmental model of ocular dominance formation on a growing cortex Bull. Math. Biol. 68 7398 (2006).
P. C. Bressloff, Spontaneous symmetry breaking in selforganizing neural fields. Biol. Cybern. 93: 256274 (2005).
P. C. Bressloff, Euclidean shifttwist symmetry in population models of selfaligning objects. SIAM J. Appl. Math. 64:16681690 (2004).
P. C. Bressloff, Spatially periodic modulation of cortical patterns by longrange horizontal connections. Physica D 185:131157 (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 358:16431667 (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 :299330
(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 orientationtuning of surround modulation in primate V1. J. Neurosci. 32 308321 (2012).
J. Icheda, L. Schwabe, P. C. Bressloff and A. Angelucci. Response
facilitation from the ``suppressive'' surround of V1 neurons. J. Neurophysiol. 98 21682181 (2007).
A. Angelucci and P. C. Bressloff. The contribution of feedforward, lateral and feedback
connections to the classical receptive field center and extraclassical receptive field surround
of primate V1 neurons Prog. Brain Res. 154 93121 (2006).
L. Schwabe, K. Obermayer, A. Angelucci and P. C. Bressloff. The
role of feedback in shaping the extraclassical receptive field of
cortical neurons: a recurrent network model J. Neurosci. 26 91179129 (2006).
J. S. Lund, A. Angelucci and P. C. Bressloff, Anatomical
substrates for the functional column in macaque primary visual cortex. Cerebral Cortex 12:1524 (2003).
P. C. Bressloff and J. D. Cowan, An amplitude equation approach to contextual effects in primary visual cortex. Neural Comput. 14 :493525 (2002).
Stochastic population oscillators and noiseinduced synchronization
P. C. Bressloff and Yi Ming Lai. Dispersal and noise: Various modes of synchrony in ecological oscillators. J. Math. Biol.
67 16691690 (2013).
YM 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 YM Lai. Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. J. Math. Neurosci. 1 2 (2011).
Dynamics of integrateandfire networks
P. C. Bressloff, Traveling waves and pulses in a onedimensional
network of integrateandfire neurons. J. Math. Biol. 40 :169183
(2000).
P. C. Bressloff and S. Coombes, Dynamical theory of spike train
dynamics in networks of integrateandfire oscillators. SIAM J. Appl. Math. 60:828841 (2000).
S. Coombes and P. C. Bressloff, Solitary waves in a model of dendritic
cable with active spines. SIAM J. Appl. Math. 61:432453 (2000).
P. C. Bressloff and S. Coombes, Dynamics of strongly coupled spiking
neurons. Neural Comput. 12 :91129 (2000).
P. C. Bressloff, Synaptically generated wave propagation in excitable
neural media. Phys. Rev. Lett. 82:29792982 (1999).
P. C. Bressloff and S. Coombes, Symmetry and phaselocking in a ring of
pulsecoupled oscillators with distributed delays. Physica D 126 :99122
(1999).
P. C. Bressloff and S. Coombes, Travelling waves in a chain of pulsecoupled
integrateandfire oscillators with distributed delays.
Physica D 130:232254 (1999).
P. C. Bressloff and S. Coombes, Travelling waves in chain of pulsecoupled
oscillators. Phys. Rev. Lett. 80:48154818 (1998).
P. C. Bressloff and S. Coombes, Desynchronization, modelocking and
bursting in stronglycoupled integrateandfire oscillators. Phys. Rev. Lett. 81:21682171 (1998).
P. C. Bressloff and S. Coombes, Spike train dynamics underlying pattern
formation in an integrateandfire oscillator network. Phys. Rev. Lett. 81:23842387 (1998).
P. C. Bressloff and S. Coombes, Synchrony in an array of integrateandfire
neurons with dendritic structure. Phys. Rev. Lett. 78:46654668 (1997).
P. C. Bressloff, S. Coombes and B. De Souza, Dynamics of a ring of
pulsecoupled oscillators: Group theoretic approach. Phys. Rev. Lett. 79:27912794 (1997).
Miscellaneous
P. C. Bressloff and G. Rowlands, Exact travelling wave solutions of an
"integrable" discrete reactiondiffusion equation. Physica D 106:255269
(1997).
P. C. Bressloff, A selforganizing network in the weak coupling limit.
Physica D 110:195208 (1997).
P. C. Bressloff, A new Green's function method for solving linear PDE's
in two variables. J. Math. Anal. Appl. 210:390415 (1997).
P. C. Bressloff, V. M. Dwyer and M. J. Kearney, Classical diffusion and
percolation in random environments on trees. Phys. Rev. E 55:67656775
(1997).
P. C. Bressloff, C. V. Wood and P. A. Howarth, Nonlinear shunting model
of the pupil light reflex. Proc. Roy. Soc. B 263:953960 (1996).
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 motorbased 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)
Stimulusinduced 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 Noiseinduced effects in neural systems (Ph. D 1998)
Postdocs
Sean Lawley (20142016)
Jay Newby (20102012)
Berton Earnshaw (20072009)
Lars Schwabe (20052006)
Steve Coombes (19961998)
Spatially Distributed Stochastic Dynamical Systems in Biology Isaac Newton Institute, Cambridge, UK, June 2024, 2016
The First International Conference on Mathematical NeuroScience (ICMNS), Antibes, JuanLesPins, France, June 810, 2015
Axonal Transport and Neuronal Mechanics, Mathematical Biosciences Institute, Ohio State, November 37, 2014
SIAM Conference on Nonlinear Waves and Coherent Structures, University of Cambridge, August 1114, 2014
Stochastic Network Models of Neocortex (a Festschrift for Jack Cowan), Banff International research station, July 1318, 2014
Nonlinear dynamics and stochastic methods: from neuroscience to other biological applications (Bard Ermentrout’s 60th) University of Pittsburgh, March 1012, 2014
Oxford Conference on Challenges in Applied Mathematics University of Oxford, July 15, 2013
Stochastic Modeling of Biological Processes, IMA, University of Minnesota, May 1317, 2013
Random models in neuroscience Université Pierre et Marie Curie, July 26, 2012
Stochastic Modelling in Biological Systems, University of Oxford, March 1823, 2012
SpatioTemporal Evolution Equations and Neural Fields, CIRM, Marseilles, October 2428, 2011
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