Gallery of Mathematical Models

The models are given as input files for xpp, but are human-readable ASCII files and can be easily adapted for use with other programs. The intent is for this site to maintain certified "gold standard" versions of published models. For information on software for simulating the models, including xpp, click here.

Pancreatic Beta-Cell Models
Neuron Models
Synaptic Models
Other Models

Beta-Cell Models

Original Chay-Keizer (K-Ca) (Chay and Keizer, Biophys. J. 42:181-190 1983)
Chay-Cook (K-Ca) (Modified from Chay and Cook, Math. Biosci. 90:139-153 1988)
Sherman-Rinzel-Keizer (Sherman et al, Biophys. J. 54:411-425 1988)
Sherman-Keizer-Rinzel (Ca-Ca) (Sherman et al, Biophys. J. 58:985-995 1990)
Keizer-Smolen (Keizer and Smolen, PNAS 88:3897-3901 1991)
Smolen-Keizer (Smolen and Keizer, J. Membr. Biol. 127:9-19 1992)
Generic Model (Sherman and Rinzel, Proc. Natl. Acad. Sci. USA. 89:2471-2474 1992)
CRAC Model I (Bertram et al., Biophys. J. 68:2323-2332 1995)
CRAC Model II (Mears et al., J. Membr. Biol. 155:47-59 1997)
Phase-independent resetting model (Smolen and Sherman, J. Theor. Biol. 169:339-348 1994)
Phantom Burster (Bertram et al., Biophys. J. 79:513-530 2000)
Calcium Subspace Model (Goforth et al., J. Gen. Physiol., 120:307-322 2002; Zhang et al. Biophys. J. 84:2852-2870 2003)
Calcium-based Phantom Model (Biophan) (Bertram and Sherman, Bull. Math. Biol., 66:1313-1344 2004)
Insulin-based Phantom Model (Biophan) (Bertram and Sherman, Phantom bursting in pancreatic islets: A potential role for insulin feedback, in "Recent Research Developments in Biophysics", S. G. Pandalai, ed., Transworld Research Network, Vol. 1, pp. 31--51.
Combined Glycolytic and Electrical Oscillator (Bertram et al, Biophys. J., 87:3074--3087 2004)
Calcium Filtering by the ER (Bertram and Sherman, Biophys. J., 87:3775-3785 2004)
Diffusion of Calcium and Metabolites (Tsaneva-Atanasova et al, Biophys. J., 90:3434--3446 2006)
Glucose Sensing with Combined Metabolic, Ionic Oscillation Model(Nunemaker et al, Biophys. J. 91:2082--2096.)

Neural Models

Integrate and Fire
Wilson-Cowan
FitzHugh-Nagumo
Morris-Lecar
Hindmarsh-Rose
Hodgkin-Huxley
Reduced (2D) Hodgkin-Huxley
Dopamine Neuron
Somatototroph (Tsaneva-Atanasova et al, J. Neurophysiol. 98(1):131-144, 2007)
Generic Pituitary (Stern et al, Bull. Math. Biol., in press)

Synaptic Release Models

Calcium Pulses (Bertram et al, J. Neurophysiol. 75:1919-1931 1996)
Voltage-Clamp Pulses (Bertram and Sherman, SIAM J. App. Math, 58:142-169 1998)
Mean Field Approximation (Bertram and Sherman, ibid.)
Two-Site Diffusion Model (Matveev et al, Biophys. J., 83:1368--73 2002)
Buffer Saturation Model (Matveev et al, Biophys. J., 86:2691-2709 2004)
Bound Calcium with Diffusion (Matveev et al, J. Neurophysiol., Biophys. J. 86:2691-2709 2006)

Other Models

Lotka-Volterra
Insulin Signaling (Sedaghat et al, Am. J. Physiol., 283:E1084-E1101 2002)
Goldbeter-Lefever model for glycolytic oscillations in yeast (Biophys. J. 12:1302-1315 1972)

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Last Updated 07/06/2005