Casey Diekman uses a combination of mathematical modeling, numerical simulation, and dynamical systems analysis to gain insight into biological systems. He is currently focused on creating a mathematical framework to understand how dynamic changes in gene expression affect the electrical properties of neurons and ultimately animal behavior. Circadian (~24-hour) rhythms offer one of the clearest examples of the interplay between these different levels of organization, with rhythmic gene expression leading to daily rhythms in neural activity, physiology and behavior.
Diekman has developed mathematical models of the master circadian clock in the mammalian brain. These models and the mathematical theory associated with them led to counterintuitive predictions that have since been validated experimentally by Diekman’s collaborators.
The primary goal of Diekman’s research program in mathematical biology is to uncover mechanisms underlying biological timekeeping, neuronal rhythm generation, and the disruption of rhythmicity associated with certain pathological conditions including sleep disorders, Alzheimer´s disease, breathing problems, and ischemic stroke.
Prior to joining NJIT, Diekman was a postdoctoral fellow at the Mathematical Biosciences Institute (MBI). MBI, located at The Ohio State University, is a research institute funded by the National Science Foundation’s Division of Mathematical Sciences.
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Diekman CO and Golubitsky M (2014). Network symmetry and binocular rivalry experiments. Journal of Mathematical Neuroscience,4:12.
Diekman CO, Dasgupta K, Nair V, and Unnikrishnan K. (2014) Discovering functional neuronal connectivity from serial patterns in spike train data. Neural Computation, 26:1263-1297.
Terman D, Rubin J, and Diekman CO. (2013) Irregular activity arises as a natural consequence of synaptic inhibition. Chaos 23:046110.
Diekman CO, Belle M, Irwin R, Allen C, Piggins H, and Forger D. (2013) Causes and consequences of hyperexcitation in central clock neurons. PLOS Computational Biology 9(8):e1003196.
Diekman CO, Golubitsky M, and Wang Y. (2013) Derived patterns in binocular rivalry networks. Journal of Mathematical Neuroscience 3:6.
Diekman CO, Fall C, Lechleiter J, and Terman D. (2013) Modeling the neuroprotective role of enhancing astrocyte mitochondrial metabolism during stroke. Biophysical Journal 104:1752-1763.
Diekman CO, Golubitsky M, McMillen T, and Wang Y. (2012) Reduction and dynamics of a generalized rivalry network with two learned patterns. SIAM Journal of Applied Dynamical Systems 11:1270-1309.
Belle M, Diekman CO, Forger D, and Piggins H. (2009) Daily electrical silencing in the mammalian circadian clock. Science 326:281-284.
Diekman CO and Forger D. (2009) Clustering predicted by an electrophysiological model of the suprachiasmatic nucleus. Journal of Biological Rhythms 24:322-333.Diekman CO, Sastry P, and Unnikrishnan K. (2009) Statistical significance of sequential firing patterns in multi-neuronal spike trains. Journal of Neuroscience Methods 182:279-284.