The National Institute of Diabetes & Digestive & Kidney Diseases

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.

Recently we have begun to combine the relatively fast (10's of seconds) ionic, electrical oscillations with slower (minutes) metabolic oscillations, resulting from oscillations in glycolysis. One goal is to expose how each aspect contributes to the total insulin secretion process. Another is to use the longer time scales of the glycolytic oscillations to begin to relate the secretory events to the dynamics of insulin action, which also operates on a slower time scale (minutes).

Models are developed in collaboration with experimentalists and are used to interpret data and to design new experimental tests of hypotheses. Our primary tool for the analysis of models 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.

G. de Vries and A. Sherman Beyond Synchronization: Modulatory and Emergent Effects of Coupling in Square-Wave Bursting. In: Bursting: The Genesis of Rhythm in the Nervous System. S. Coombes and P. Bressloff, editors. World Scientific, London, 2005. pp.243-272

Nunemaker CS, Zhang M, Wasserman DH, McGuinness OP, Powers AC, Bertram R, Sherman A, Satin LS 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, 2005. [Full Text/Abstract]

A. Sherman and R. Bertram Integrative Modeling of the Pancreatic beta-Cell Wiley Interscience Encyclopedia of Genetics, Genomics, Proteomics, and Bioinformatics, Part 3 Proteomics(DOI: 10.1002/047001153X.g308213), 2005. [Full Text/Abstract]

Pedersen MG, Bertram R, Sherman A Intra- and inter-islet synchronization of metabolically driven insulin secretion. Biophys J (89): 107-19, 2005. [Full Text/Abstract]

R. Bertram and A. Sherman Negative Calcium Feedback: The Road from Chay-Keizer. In: Bursting: The Genesis of Rhythm in the Nervous System. S. Coombes and P. Bressloff, editors. World Scientific, London, 2005. pp.19-48

Bertram R Sherman A A calcium-based phantom bursting model for pancreatic islets. Bull Math Biol (66): 1313-44, 2004. [Full Text/Abstract]

Bertram R, Satin L, Zhang M, Smolen P, Sherman A Calcium and glycolysis mediate multiple bursting modes in pancreatic islets. Biophys J (87): 3074-87, 2004. [Full Text/Abstract]

Matveev V Zucker RS Sherman A Facilitation through buffer saturation: constraints on endogenous buffering properties. Biophys J (86): 2691-709, 2004. [Full Text/Abstract]

Bertram R, Sherman A Filtering of calcium transients by the endoplasmic reticulum in pancreatic beta-cells. Biophys J (87): 3775-85, 2004. [Full Text/Abstract]

Zimliki CL Mears D Sherman A Three roads to islet bursting: emergent oscillations in coupled phantom bursters. Biophys J (87): 193-206, 2004. [Full Text/Abstract]

Zhang M Goforth P Bertram R Sherman A Satin L The Ca2+ dynamics of isolated mouse beta-cells and islets: implications for mathematical models. Biophys J (84): 2852-70, 2003. [Full Text/Abstract]

Sedaghat AR Sherman A Quon MJ A mathematical model of metabolic insulin signaling pathways. Am J Physiol Endocrinol Metab (283): E1084-101, 2002. [Full Text/Abstract]

Goforth PB Bertram R Khan FA Zhang M Sherman A Satin LS Calcium-activated K+ channels of mouse beta-cells are controlled by both store and cytoplasmic Ca2+: experimental and theoretical studies. J Gen Physiol (120): 307-22, 2002. [Full Text/Abstract]

Matveev V Sherman A Zucker RS New and corrected simulations of synaptic facilitation. Biophys J (83): 1368-73, 2002. [Full Text/Abstract]

de Vries G Sherman A From spikers to bursters via coupling: help from heterogeneity. Bull Math Biol (63): 371-91, 2001. [Full Text/Abstract]

Van Goor F LeBeau AP Krsmanovic LZ Sherman A Catt KJ Stojilkovic SS Amplitude-dependent spike-broadening and enhanced Ca(2+) signaling in GnRH-secreting neurons. Biophys J (79): 1310-23, 2000. [Full Text/Abstract]

De Vries G Sherman A Channel sharing in pancreatic beta -cells revisited: enhancement of emergent bursting by noise. J Theor Biol (207): 513-30, 2000. [Full Text/Abstract]

Bertram R Sherman A Dynamical complexity and temporal plasticity in pancreatic beta-cells. J Biosci (25): 197-209, 2000. [Full Text/Abstract]

LeBeau AP Van Goor F Stojilkovic SS Sherman A Modeling of membrane excitability in gonadotropin-releasing hormone-secreting hypothalamic neurons regulated by Ca2+-mobilizing and adenylyl cyclase-coupled receptors. J Neurosci (20): 9290-7, 2000. [Full Text/Abstract]

Bertram R Previte J Sherman A Kinard TA Satin LS The phantom burster model for pancreatic beta-cells. Biophys J (79): 2880-92, 2000. [Full Text/Abstract]

Bertram R Smith GD Sherman A Modeling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release. Biophys J (76): 735-50, 1999. [Full Text/Abstract]

Kinard TA de Vries G Sherman A Satin LS Modulation of the bursting properties of single mouse pancreatic beta-cells by artificial conductances. Biophys J (76): 1423-35, 1999. [Full Text/Abstract]

Sherman A Smolen P Computer modeling of heterogeneous beta-cell populations. Adv Exp Med Biol (426): 275-84, 1997. [Full Text/Abstract]

Mears D Sheppard NF Jr Atwater I Rojas E Bertram R Sherman A Evidence that calcium release-activated current mediates the biphasic electrical activity of mouse pancreatic beta-cells. J Membr Biol (155): 47-59, 1997. [Full Text/Abstract]

Sherman A Contributions of modeling to understanding stimulus-secretion coupling in pancreatic beta-cells. Am J Physiol (271): E362-72, 1996. [Full Text/Abstract]

Bertram R Sherman A Stanley EF Single-domain/bound calcium hypothesis of transmitter release and facilitation. J Neurophysiol (75): 1919-31, 1996. [Full Text/Abstract]

Bertram R Smolen P Sherman A Mears D Atwater I Martin F Soria B A role for calcium release-activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells. Biophys J (68): 2323-32, 1995. [Full Text/Abstract]

Sherman A Xu L Stokes CL Estimating and eliminating junctional current in coupled cell populations by leak subtraction. A computational study. J Membr Biol (143): 79-87, 1995. [Full Text/Abstract]

Bertram R Butte MJ Kiemel T Sherman A Topological and phenomenological classification of bursting oscillations. Bull Math Biol (57): 413-39, 1995. [Full Text/Abstract]

Sherman A Anti-phase, asymmetric and aperiodic oscillations in excitable cells--I. Coupled bursters. Bull Math Biol (56): 811-35, 1994. [Full Text/Abstract]

Smolen P Sherman A Phase independent resetting in relaxation and bursting oscillators. J Theor Biol (169): 339-48, 1994. [Full Text/Abstract]

Smolen P Rinzel J Sherman A Why pancreatic islets burst but single beta cells do not. The heterogeneity hypothesis. Biophys J (64): 1668-80, 1993. [Full Text/Abstract]

Sherman A Rinzel J Rhythmogenic effects of weak electrotonic coupling in neuronal models. Proc Natl Acad Sci U S A (89): 2471-4, 1992. [Full Text/Abstract]

Sherman A Rinzel J Model for synchronization of pancreatic beta-cells by gap junction coupling. Biophys J (59): 547-59, 1991. [Full Text/Abstract]

Sherman A Keizer J Rinzel J Domain model for Ca2(+)-inactivation of Ca2+ channels at low channel density. Biophys J (58): 985-95, 1990. [Full Text/Abstract]

Sherman A Rinzel J Keizer J Emergence of organized bursting in clusters of pancreatic beta-cells by channel sharing. Biophys J (54): 411-25, 1988. [Full Text/Abstract]