16,354 research outputs found
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
The movement of many organisms can be described as a random walk at either or
both the individual and population level. The rules for this random walk are
based on complex biological processes and it may be difficult to develop a
tractable, quantitatively-accurate, individual-level model. However, important
problems in areas ranging from ecology to medicine involve large collections of
individuals, and a further intellectual challenge is to model population-level
behavior based on a detailed individual-level model. Because of the large
number of interacting individuals and because the individual-level model is
complex, classical direct Monte Carlo simulations can be very slow, and often
of little practical use. In this case, an equation-free approach may provide
effective methods for the analysis and simulation of individual-based models.
In this paper we analyze equation-free coarse projective integration. For
analytical purposes, we start with known partial differential equations
describing biological random walks and we study the projective integration of
these equations. In particular, we illustrate how to accelerate explicit
numerical methods for solving these equations. Then we present illustrative
kinetic Monte Carlo simulations of these random walks and show a decrease in
computational time by as much as a factor of a thousand can be obtained by
exploiting the ideas developed by analysis of the closed form PDEs. The
illustrative biological example here is chemotaxis, but it could be any random
walker which biases its movement in response to environmental cues.Comment: 30 pages, submitted to Physica
Chemotaxis When Bacteria Remember: Drift versus Diffusion
{\sl Escherichia coli} ({\sl E. coli}) bacteria govern their trajectories by
switching between running and tumbling modes as a function of the nutrient
concentration they experienced in the past. At short time one observes a drift
of the bacterial population, while at long time one observes accumulation in
high-nutrient regions. Recent work has viewed chemotaxis as a compromise
between drift toward favorable regions and accumulation in favorable regions. A
number of earlier studies assume that a bacterium resets its memory at tumbles
-- a fact not borne out by experiment -- and make use of approximate
coarse-grained descriptions. Here, we revisit the problem of chemotaxis without
resorting to any memory resets. We find that when bacteria respond to the
environment in a non-adaptive manner, chemotaxis is generally dominated by
diffusion, whereas when bacteria respond in an adaptive manner, chemotaxis is
dominated by a bias in the motion. In the adaptive case, favorable drift occurs
together with favorable accumulation. We derive our results from detailed
simulations and a variety of analytical arguments. In particular, we introduce
a new coarse-grained description of chemotaxis as biased diffusion, and we
discuss the way it departs from older coarse-grained descriptions.Comment: Revised version, journal reference adde
Modeling multi-cellular systems using sub-cellular elements
We introduce a model for describing the dynamics of large numbers of
interacting cells. The fundamental dynamical variables in the model are
sub-cellular elements, which interact with each other through phenomenological
intra- and inter-cellular potentials. Advantages of the model include i)
adaptive cell-shape dynamics, ii) flexible accommodation of additional
intra-cellular biology, and iii) the absence of an underlying grid. We present
here a detailed description of the model, and use successive mean-field
approximations to connect it to more coarse-grained approaches, such as
discrete cell-based algorithms and coupled partial differential equations. We
also discuss efficient algorithms for encoding the model, and give an example
of a simulation of an epithelial sheet. Given the biological flexibility of the
model, we propose that it can be used effectively for modeling a range of
multi-cellular processes, such as tumor dynamics and embryogenesis.Comment: 20 pages, 4 figure
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