67 research outputs found
Model of the Belousov-Zhabotinsky reaction
The article describes results of the modified model of the
Belousov-Zhabotinsky reaction, which resembles rather well the limit set
observed upon experimental performance of the reaction in the Petri dish. We
discuss the concept of the ignition of circular waves and show that only the
asymmetrical ignition leads to the formation of spiral structures. From the
qualitative assumptions on the behavior of dynamic systems, we conclude that
the Belousov-Zhabotinsky reaction likely forms a regular grid.Comment: 17 pages, 12 figure
State based model of long-term potentiation and synaptic tagging and capture
Recent data indicate that plasticity protocols have not only synapse-specific but also more widespread effects. In particular, in synaptic tagging and capture (STC), tagged synapses can capture plasticity-related proteins, synthesized in response to strong stimulation of other synapses. This leads to long-lasting modification of only weakly stimulated synapses. Here we present a biophysical model of synaptic plasticity in the hippocampus that incorporates several key results from experiments on STC. The model specifies a set of physical states in which a synapse can exist, together with transition rates that are affected by high- and low-frequency stimulation protocols. In contrast to most standard plasticity models, the model exhibits both early- and late-phase LTP/D, de-potentiation, and STC. As such, it provides a useful starting point for further theoretical work on the role of STC in learning and memory
A Mathematical model for Astrocytes mediated LTP at Single Hippocampal Synapses
Many contemporary studies have shown that astrocytes play a significant role
in modulating both short and long form of synaptic plasticity. There are very
few experimental models which elucidate the role of astrocyte over Long-term
Potentiation (LTP). Recently, Perea & Araque (2007) demonstrated a role of
astrocytes in induction of LTP at single hippocampal synapses. They suggested a
purely pre-synaptic basis for induction of this N-methyl-D- Aspartate (NMDA)
Receptor-independent LTP. Also, the mechanisms underlying this pre-synaptic
induction were not investigated. Here, in this article, we propose a
mathematical model for astrocyte modulated LTP which successfully emulates the
experimental findings of Perea & Araque (2007). Our study suggests the role of
retrograde messengers, possibly Nitric Oxide (NO), for this pre-synaptically
modulated LTP.Comment: 51 pages, 15 figures, Journal of Computational Neuroscience (to
appear
An Allosteric Mechanism for Switching between Parallel Tracks in Mammalian Sulfur Metabolism
Methionine (Met) is an essential amino acid that is needed for the synthesis of S-adenosylmethionine (AdoMet), the major biological methylating agent. Methionine used for AdoMet synthesis can be replenished via remethylation of homocysteine. Alternatively, homocysteine can be converted to cysteine via the transsulfuration pathway. Aberrations in methionine metabolism are associated with a number of complex diseases, including cancer, anemia, and neurodegenerative diseases. The concentration of methionine in blood and in organs is tightly regulated. Liver plays a key role in buffering blood methionine levels, and an interesting feature of its metabolism is that parallel tracks exist for the synthesis and utilization of AdoMet. To elucidate the molecular mechanism that controls metabolic fluxes in liver methionine metabolism, we have studied the dependencies of AdoMet concentration and methionine consumption rate on methionine concentration in native murine hepatocytes at physiologically relevant concentrations (40–400 µM). We find that both [AdoMet] and methionine consumption rates do not change gradually with an increase in [Met] but rise sharply (∼10-fold) in the narrow Met interval from 50 to 100 µM. Analysis of our experimental data using a mathematical model reveals that the sharp increase in [AdoMet] and the methionine consumption rate observed within the trigger zone are associated with metabolic switching from methionine conservation to disposal, regulated allosterically by switching between parallel pathways. This regulatory switch is triggered by [Met] and provides a mechanism for stabilization of methionine levels in blood over wide variations in dietary methionine intake
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