10,358 research outputs found
The interplay between discrete noise and nonlinear chemical kinetics in a signal amplification cascade
We used various analytical and numerical techniques to elucidate signal
propagation in a small enzymatic cascade which is subjected to external and
internal noise. The nonlinear character of catalytic reactions, which underlie
protein signal transduction cascades, renders stochastic signaling dynamics in
cytosol biochemical networks distinct from the usual description of stochastic
dynamics in gene regulatory networks. For a simple 2-step enzymatic cascade
which underlies many important protein signaling pathways, we demonstrated that
the commonly used techniques such as the linear noise approximation and the
Langevin equation become inadequate when the number of proteins becomes too
low. Consequently, we developed a new analytical approximation, based on mixing
the generating function and distribution function approaches, to the solution
of the master equation that describes nonlinear chemical signaling kinetics for
this important class of biochemical reactions. Our techniques work in a much
wider range of protein number fluctuations than the methods used previously. We
found that under certain conditions the burst-phase noise may be injected into
the downstream signaling network dynamics, resulting possibly in unusually
large macroscopic fluctuations. In addition to computing first and second
moments, which is the goal of commonly used analytical techniques, our new
approach provides the full time-dependent probability distributions of the
colored non-Gaussian processes in a nonlinear signal transduction cascade.Comment: 16 pages, 9 figure
A variational approach to the stochastic aspects of cellular signal transduction
Cellular signaling networks have evolved to cope with intrinsic fluctuations,
coming from the small numbers of constituents, and the environmental noise.
Stochastic chemical kinetics equations govern the way biochemical networks
process noisy signals. The essential difficulty associated with the master
equation approach to solving the stochastic chemical kinetics problem is the
enormous number of ordinary differential equations involved. In this work, we
show how to achieve tremendous reduction in the dimensionality of specific
reaction cascade dynamics by solving variationally an equivalent quantum field
theoretic formulation of stochastic chemical kinetics. The present formulation
avoids cumbersome commutator computations in the derivation of evolution
equations, making more transparent the physical significance of the variational
method. We propose novel time-dependent basis functions which work well over a
wide range of rate parameters. We apply the new basis functions to describe
stochastic signaling in several enzymatic cascades and compare the results so
obtained with those from alternative solution techniques. The variational
ansatz gives probability distributions that agree well with the exact ones,
even when fluctuations are large and discreteness and nonlinearity are
important. A numerical implementation of our technique is many orders of
magnitude more efficient computationally compared with the traditional Monte
Carlo simulation algorithms or the Langevin simulations.Comment: 15 pages, 11 figure
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
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Geometric principles of second messenger dynamics in dendritic spines.
Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity
Approximations and their consequences for dynamic modelling of signal transduction pathways
Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system and its approximations with respect to the transient and steady state behavior
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