4,820 research outputs found
Estimation of kinetic rates of MAP kinase activation from experimental data
Mathematical model is an important tool in systems biology to study the dynamics of biological systems inside the cell. One of the significant challenges in systems biology is the lack of kinetic rates that should be measured in experiments or estimated from experimental data. This work addresses this issue by using a genetic algorithm to estimate reaction rates related to the phosphorylation and dephosphorylation of MAP kinase (ERK) in the mitogen-activated protein (MAP) kinase pathway from biological measurements. In addition, we discuss the robustness of the mathematical model with regards to the variation of kinetic rates together with external noise due to environmental fluctuations. This has been proposed as an additional criterion to choose the estimate from the candidate parameter sets that are obtained from different implementations of the genetic algorithm
Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics.
A stochastic reaction network model of Ca(2+) dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, 'graph-constrained correlation dynamics', requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice
The Goldbeter-Koshland switch in the first-order region and its response to dynamic disorder
In their classical work (Proc. Natl. Acad. Sci. USA, 1981, 78:6840-6844),
Goldbeter and Koshland mathematically analyzed a reversible covalent
modification system which is highly sensitive to the concentration of
effectors. Its signal-response curve appears sigmoidal, constituting a
biochemical switch. However, the switch behavior only emerges in the
"zero-order region", i.e. when the signal molecule concentration is much lower
than that of the substrate it modifies. In this work we showed that the
switching behavior can also occur under comparable concentrations of signals
and substrates, provided that the signal molecules catalyze the modification
reaction in cooperation. We also studied the effect of dynamic disorders on the
proposed biochemical switch, in which the enzymatic reaction rates, instead of
constant, appear as stochastic functions of time. We showed that the system is
robust to dynamic disorder at bulk concentration. But if the dynamic disorder
is quasi-static, large fluctuations of the switch response behavior may be
observed at low concentrations. Such fluctuation is relevant to many biological
functions. It can be reduced by either increasing the conformation
interconversion rate of the protein, or correlating the enzymatic reaction
rates in the network.Comment: 23 pages, 4 figures, accepted by PLOS ON
The Energetic Costs of Cellular Computation
Cells often perform computations in response to environmental cues. A simple
example is the classic problem, first considered by Berg and Purcell, of
determining the concentration of a chemical ligand in the surrounding media. On
general theoretical grounds (Landuer's Principle), it is expected that such
computations require cells to consume energy. Here, we explicitly calculate the
energetic costs of computing ligand concentration for a simple two-component
cellular network that implements a noisy version of the Berg-Purcell strategy.
We show that learning about external concentrations necessitates the breaking
of detailed balance and consumption of energy, with greater learning requiring
more energy. Our calculations suggest that the energetic costs of cellular
computation may be an important constraint on networks designed to function in
resource poor environments such as the spore germination networks of bacteria.Comment: 9 Pages (including Appendix); 4 Figures; v3 corrects even more typo
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An introduction to Biomodel engineering, illustrated for signal transduction pathways
BioModel Engineering is the science of designing, constructing
and analyzing computational models of biological systems. It is inspired
by concepts from software engineering and computing science.
This paper illustrates a major theme in BioModel Engineering, namely
that identifying a quantitative model of a dynamic system means building
the structure, finding an initial state, and parameter fitting. In our
approach, the structure is obtained by piecewise construction of models
from modular parts, the initial state is obtained by analysis of the structure
and parameter fitting comprises determining the rate parameters of
the kinetic equations. We illustrate this with an example in the area of
intracellular signalling pathways
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