A fundamental question in modern cell biology is how cellular and subcellular structures are formed and maintained given their particular molecular components. How are the different shapes, sizes, and functions of cellular organelles determined, and why are specific structures formed at particular locations and stages of the life cycle of a cell? In order to address these questions, it is necessary to consider the theory of self-organizing non-equilibrium systems. We are particularly interested in identifying and analyzing novel mechanisms for pattern formation that go beyond the standard Turing mechanism and diffusion-based mechanisms of protein gradient formation.
P. C. Bressloff. Directional search-and-capture model of cytoneme-based morphogenesis. SIAM J. Appl. Math 81 919-938 (2021)
P. C. Bressloff and H. Kim. A search-and-capture model of cytoneme-mediated morphogen gradient formation Phys. Rev. E 99 052401 (2019).
H. Kim and P. C. Bressloff. Impulsive signaling model of cytoneme-based morphogen gradient formation Phys. Biol. 16 056005 (2019).
H. Kim and P. C. Bressloff. Direct vs. synaptic contacts in a mathematical model of cytoneme-based morphogen gradient formation SIAM J. Appl. Math 78 2323-2347 (2018).
P. C. Bressloff and H. Kim. Bidirectional transport model of morphogen gradient formation via cytonemes Phys. Biol. 15 026010 (2018).
P. C. Bressloff. Two-dimensional Ostwald ripening in a concentration gradient. J. Phys. A 53 365002 (2020)
P. C. Bressloff. Active suppression of Ostwald ripening: Beyond mean field theory. Phys. Rev. E 101 042804 (2020)
P. C. Bressloff. Multi-spike solutions of a hybrid reaction-transport model. Proc Roy. Soc. A 477 20200829 (2021)
H. Kim and P. C. Bressloff. Stochastic Turing pattern formation in a model with active and passive transport. Bull. Math. Biol. 82 144 (2020)
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).
G. Fan, G. Russo and P. C. Bressloff. Node to node and node to medium synchronization in quorum sensing networks affected by state dependent noise. SIAM J. Appl. Dyn. Sys. 18 1934-1953 (2019).
G. Fan and P. C. Bressloff. Modeling the role of feedback in the adaptive response of bacterial quorum sensing Bull. Math. Biol. 81 1479-1505 (2019)
G. Fan and P. C. Bressloff. Population model of quorum sensing with multiple parallel pathways Bull. Math. Biol. 79 2599-2626 (2017)
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 theory of synchrony for active compartments with delays coupled through bulk diffusion Physica D 341 45-59 (2017).
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 78 719-741 (2018).
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. A stochastic model of intraflagellar transport. Phys. Rev. E 73 061916 (2006).
P. C. Bressloff. Propagation of CaMKII translocation waves in heterogeneous spiny dendrites. J. Math. Biol. 66 1499-1525 (2013).
B. A. Earnshaw and P. C. Bressloff. Diffusion-activation model for CaMKII translocation waves in dendrites. J. Comp. Neurosci. 28 77-89 (2010).
S. Coombes and P. C. Bressloff. Saltatory waves in the spike-diffuse-spike model of active dendritic spines. Phys. Rev. Lett. 91 028102 (2003).
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. Spatially periodic modulation of cortical patterns by long-range horizontal connections. Physica D 185 131-157 (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 and P. J. Thomas. Scalar and pseudoscalar bifurcations: pattern formation on the visual cortex. Nonlinearity 14 739-775 (2001).
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. Lond. B 356 299-330 (2001).