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).