17,320 research outputs found
Modeling of negative autoregulated genetic networks in single cells
We discuss recent developments in the modeling of negative autoregulated
genetic networks. In particular, we consider the temporal evolution of the
population of mRNA and proteins in simple networks using rate equations. In the
limit of low copy numbers, fluctuation effects become significant and more
adequate modeling is then achieved using the master equation formalism. The
analogy between regulatory gene networks and chemical reaction networks on dust
grains in the interstellar medium is discussed. The analysis and simulation of
complex reaction networks are also considered.Comment: 15 pages, 4 figures. Published in Gen
Fractional diffusion emulates a human mobility network during a simulated disease outbreak
From footpaths to flight routes, human mobility networks facilitate the
spread of communicable diseases. Control and elimination efforts depend on
characterizing these networks in terms of connections and flux rates of
individuals between contact nodes. In some cases, transport can be
parameterized with gravity-type models or approximated by a diffusive random
walk. As a alternative, we have isolated intranational commercial air traffic
as a case study for the utility of non-diffusive, heavy-tailed transport
models. We implemented new stochastic simulations of a prototypical
influenza-like infection, focusing on the dense, highly-connected United States
air travel network. We show that mobility on this network can be described
mainly by a power law, in agreement with previous studies. Remarkably, we find
that the global evolution of an outbreak on this network is accurately
reproduced by a two-parameter space-fractional diffusion equation, such that
those parameters are determined by the air travel network.Comment: 26 pages, 4 figure
Detailed simulations of cell biology with Smoldyn 2.1.
Most cellular processes depend on intracellular locations and random collisions of individual protein molecules. To model these processes, we developed algorithms to simulate the diffusion, membrane interactions, and reactions of individual molecules, and implemented these in the Smoldyn program. Compared to the popular MCell and ChemCell simulators, we found that Smoldyn was in many cases more accurate, more computationally efficient, and easier to use. Using Smoldyn, we modeled pheromone response system signaling among yeast cells of opposite mating type. This model showed that secreted Bar1 protease might help a cell identify the fittest mating partner by sharpening the pheromone concentration gradient. This model involved about 200,000 protein molecules, about 7000 cubic microns of volume, and about 75 minutes of simulated time; it took about 10 hours to run. Over the next several years, as faster computers become available, Smoldyn will allow researchers to model and explore systems the size of entire bacterial and smaller eukaryotic cells
The validity of quasi steady-state approximations in discrete stochastic simulations
In biochemical networks, reactions often occur on disparate timescales and
can be characterized as either "fast" or "slow." The quasi-steady state
approximation (QSSA) utilizes timescale separation to project models of
biochemical networks onto lower-dimensional slow manifolds. As a result, fast
elementary reactions are not modeled explicitly, and their effect is captured
by non-elementary reaction rate functions (e.g. Hill functions). The accuracy
of the QSSA applied to deterministic systems depends on how well timescales are
separated. Recently, it has been proposed to use the non-elementary rate
functions obtained via the deterministic QSSA to define propensity functions in
stochastic simulations of biochemical networks. In this approach, termed the
stochastic QSSA, fast reactions that are part of non-elementary reactions are
not simulated, greatly reducing computation time. However, it is unclear when
the stochastic QSSA provides an accurate approximation of the original
stochastic simulation. We show that, unlike the deterministic QSSA, the
validity of the stochastic QSSA does not follow from timescale separation
alone, but also depends on the sensitivity of the non-elementary reaction rate
functions to changes in the slow species. The stochastic QSSA becomes more
accurate when this sensitivity is small. Different types of QSSAs result in
non-elementary functions with different sensitivities, and the total QSSA
results in less sensitive functions than the standard or the pre-factor QSSA.
We prove that, as a result, the stochastic QSSA becomes more accurate when
non-elementary reaction functions are obtained using the total QSSA. Our work
provides a novel condition for the validity of the QSSA in stochastic
simulations of biochemical reaction networks with disparate timescales.Comment: 21 pages, 4 figure
A flexible architecture for modeling and simulation of diffusional association
Up to now, it is not possible to obtain analytical solutions for complex
molecular association processes (e.g. Molecule recognition in Signaling or
catalysis). Instead Brownian Dynamics (BD) simulations are commonly used to
estimate the rate of diffusional association, e.g. to be later used in
mesoscopic simulations. Meanwhile a portfolio of diffusional association (DA)
methods have been developed that exploit BD.
However, DA methods do not clearly distinguish between modeling, simulation,
and experiment settings. This hampers to classify and compare the existing
methods with respect to, for instance model assumptions, simulation
approximations or specific optimization strategies for steering the computation
of trajectories.
To address this deficiency we propose FADA (Flexible Architecture for
Diffusional Association) - an architecture that allows the flexible definition
of the experiment comprising a formal description of the model in SpacePi,
different simulators, as well as validation and analysis methods. Based on the
NAM (Northrup-Allison-McCammon) method, which forms the basis of many existing
DA methods, we illustrate the structure and functioning of FADA. A discussion
of future validation experiments illuminates how the FADA can be exploited in
order to estimate reaction rates and how validation techniques may be applied
to validate additional features of the model
Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation
We present computer-assisted methods for analyzing stochastic models of gene
regulatory networks. The main idea that underlies this equation-free analysis
is the design and execution of appropriately-initialized short bursts of
stochastic simulations; the results of these are processed to estimate
coarse-grained quantities of interest, such as mesoscopic transport
coefficients. In particular, using a simple model of a genetic toggle switch,
we illustrate the computation of an effective free energy and of a
state-dependent effective diffusion coefficient that characterize an
unavailable effective Fokker-Planck equation. Additionally we illustrate the
linking of equation-free techniques with continuation methods for performing a
form of stochastic "bifurcation analysis"; estimation of mean switching times
in the case of a bistable switch is also implemented in this equation-free
context. The accuracy of our methods is tested by direct comparison with
long-time stochastic simulations. This type of equation-free analysis appears
to be a promising approach to computing features of the long-time,
coarse-grained behavior of certain classes of complex stochastic models of gene
regulatory networks, circumventing the need for long Monte Carlo simulations.Comment: 33 pages, submitted to The Journal of Chemical Physic
Modeling the emergence of polarity patterns for the intercellular transport of auxin in plants
The hormone auxin is actively transported throughout plants via protein
machineries including the dedicated transporter known as PIN. The associated
transport is ordered with nearby cells driving auxin flux in similar
directions. Here we provide a model of both the auxin transport and of the
dynamics of cellular polarisation based on flux sensing. Our main findings are:
(i) spontaneous intracellular PIN polarisation arises if PIN recycling dynamics
are sufficiently non-linear, (ii) there is no need for an auxin concentration
gradient, and (iii) ordered multi-cellular patterns of PIN polarisation are
favored by molecular noise.Comment: 17 pages and 9 figures (Main Text), 9 pages and 4 figures
(Supplementary Material), revised version with some rearrangement
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