My research involves the use of nonlinear dynamics
to study chemical and physical processes in chemistry and biology
which self-organize into temporal and/or spatial patterns. In previous
years, my group studied an enzyme-catalyzed oxidation known as the
peroxidase-oxidase reaction that occurs in plants and exhibits a
wide variety of interesting dynamical phenomena including bistability
and both periodic and chaotic oscillations. More recently we have
turned our attention to dynamical diseases which are based on the
same type of dynamical processes as those which occur in the peroxidase-oxidase
reaction. We are thus extending insights from nonlinear chemical
kinetics to nonlinear dynamics in more complex systems, namely the
human body.
Dynamical diseases are those which appear to be due to malfunctions
in timing mechanisms rather than to specific anatomical or biochemical
abnormalities. Examples of diseases that might be “dynamical”
in nature are heart arrhythmias and certain neurological disorders
including Parkinson’s disease and epilepsy. We are currently
working on developing computational models for the latter. The models
involve systems of differential equations that describe chemical
kinetic and transport processes involving key molecular components
such as glutamate (a neurotransmitter) and calcium ion (a signalling
molecule involved in neuronal communication). These processes, when
taken together, comprise a complex timing mechanism that may, when
malfunctioning, lead to seizures.
"R. Larter, "Oscillations and Spatial
Nonuniformities in Membranes," Chemical Reviews 90, 355-381
(1990)
T. Geest, C.G. Steinmetz, R. Larter and L.F. Olsen, "Period
doubling bifurcations and chaos in an enzyme reaction," Journal
of Physical Chemistry 96, 5678-5680 (1992)
P. Shen, J.T. Kim, R. Larter and K.B. Lipkowitz, "Chaos in
a Membrane Oscillator," Journal of Physical Chemistry 97,
1571 - 1575 (1993)
R. Larter, L.F. Olsen, C.G. Steinmetz and T. Geest, "Chaos
in Biochemical Systems; The Peroxidase Reaction as a Case Study,"
in Chaos in Chemical and Biochemical Systems, eds. R.J. Field
and L. Györgyi, World Scientific Press, Singapore (1993)
pp. 175-224.
T. Geest, C.G. Steinmetz, L.F. Olsen, R. Larter and W. Schaeffer,
"Nonlinear Analyses of the Peroxidase-Oxidase Reaction,"
Journal of Physical Chemistry 97, 8431-8441 (1993)
L.S. Cook, R. Larter, P. Shen and T. Geest, "Kinetics of
the Peroxidase-Oxidase Reaction with Immobilized Enzyme,"
Journal of Physical Chemistry 97, 9060-9063 (1993)
P. Shen and R. Larter, "Substrate Inhibition Kinetics in
Chemical Oscillations," Biophysical Journal 67, 1414-1428,
(1994)
P. Shen and R. Larter, "Chaos in intracellular Ca2+ oscillations
in a new model for non-excitable cells," Cell Calcium 17,
225-232, (1995)
D. Thompson and R. Larter, "Multiple time scale analysis
of two models of the peroxidase-oxidase reaction," Chaos
5, 448-457, (1995)
R. Larter and K. Showalter, "Computational Studies in Nonlinear
Dynamics," in Reviews in Computational Chemistry, K.B. Lipkowitz
and D. Boyd, Eds., VCH Press (1996), pp. 177-270.
R. Larter and S. Hemkin, "Further Refinements of the Peroxidase-Oxidase
Oscillator Mechanism: Mixed-Mode Oscillations and Chaos,"
Journal of Physical Chemistry 100, 18924-18930, (1996)
A. Scheeline, D. Olson, E. Williksen, G. Horras, M.L. Klein, and
R. Larter, "The Peroxidase-Oxidase Reaction and its Constituent
Chemistries," Chemical Reviews 97, 739-756 (1997)
B. Speelman, R. Larter and R. M. Worth, "A Coupled ODE Lattice
Model for the Simulation of Epileptic Seizures," Chaos 9,
795-804 (1999)
R. Larter, R.M. Worth and B. Speelman, “Nonlinear Dynamics
in Biochemical and Biophysical Systems: From Enzyme Kinetics to
Epilepsy”, in Self-organized Biological Dynamics and Nonlinear
Control by External Stimuli, J. Walleczek, Ed., Cambridge University
Press: Cambridge (2000), pp. 44-65.
R. Larter, "Life Lessons from the Newest Science: Bifurcation",
Noetic Science Review, No. 59, March 2002, pp. 22-27.
R. Larter, "Understanding Complexity in Biophysical Chemistry",
Journal of Physical Chemistry, Feature Article, in press (2002)
R. Larter, Life Lessons from the Newest Science, in preparation.
