We use mathematical models to study the mechanisms of oscillatory electrical activity arising from ion channels in cell membranes and modulated by intracellular chemical processes. We are interested in both the behavior of single cells and the ways in which cells communicate and modify each other's behavior. Our main application has been to the biophysical basis of insulin secretion in pancreatic beta-cells. We have examined bursting oscillations in membrane potential and the role of electrical coupling between cells in the islet of Langerhans. Long term goals are to understand how the membrane dynamics interact with intracellular events to regulate secretion and to generalize to other secretory cells and neurons. Our primary tool is the numerical solution of ordinary and partial differential equations. We use analytical, geometrical, graphical, and numerical techniques from the mathematical theory of dynamical systems to help construct and interpret the models. Perturbation techniques are used to get analytical results in special cases. We study both detailed biophysical models and simplified models which are more amenable to analysis. Such an approach aids the isolation of the essential or minimal mechanisms underlying phenomena, the search for general principles, and the application of concepts and analogies from other fields. We see a role for our group as intermediaries between the mathematical and biological disciplines. This includes disseminating the insights of mathematical work to biologists in accessible language and alerting mathematicians and other theoreticians to new and challenging problems arising from biological issues.

Project Start
Project End
Budget Start
Budget End
Support Year
6
Fiscal Year
1995
Total Cost
Indirect Cost
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Country
United States
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Matveev, Victor; Bertram, Richard; Sherman, Arthur (2006) Residual bound Ca2+ can account for the effects of Ca2+ buffers on synaptic facilitation. J Neurophysiol 96:3389-97
Bertram, Richard; Gram Pedersen, Morten; Luciani, Dan S et al. (2006) A simplified model for mitochondrial ATP production. J Theor Biol 243:575-86
Tsaneva-Atanasova, Krasimira; Zimliki, Charles L; Bertram, Richard et al. (2006) Diffusion of calcium and metabolites in pancreatic islets: killing oscillations with a pitchfork. Biophys J 90:3434-46
Nunemaker, Craig S; Bertram, Richard; Sherman, Arthur et al. (2006) Glucose modulates [Ca2+]i oscillations in pancreatic islets via ionic and glycolytic mechanisms. Biophys J 91:2082-96
Nunemaker, Craig S; Zhang, Min; Wasserman, David H et al. (2005) Individual mice can be distinguished by the period of their islet calcium oscillations: is there an intrinsic islet period that is imprinted in vivo? Diabetes 54:3517-22
Pedersen, Morten Gram; Bertram, Richard; Sherman, Arthur (2005) Intra- and inter-islet synchronization of metabolically driven insulin secretion. Biophys J 89:107-19
Zimliki, Charles L; Mears, David; Sherman, Arthur (2004) Three roads to islet bursting: emergent oscillations in coupled phantom bursters. Biophys J 87:193-206
Bertram, Richard; Sherman, Arthur (2004) Filtering of calcium transients by the endoplasmic reticulum in pancreatic beta-cells. Biophys J 87:3775-85
Matveev, Victor; Zucker, Robert S; Sherman, Arthur (2004) Facilitation through buffer saturation: constraints on endogenous buffering properties. Biophys J 86:2691-709
Bertram, Richard; Sherman, Arthur (2004) A calcium-based phantom bursting model for pancreatic islets. Bull Math Biol 66:1313-44

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