455 research outputs found
Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study
The last decade has seen an explosion in models that describe phenomena in
systems medicine. Such models are especially useful for studying signaling
pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to
showcase current mathematical and statistical techniques that enable modelers
to gain insight into (models of) gene regulation, and generate testable
predictions. We introduce a range of modeling frameworks, but focus on ordinary
differential equation (ODE) models since they remain the most widely used
approach in systems biology and medicine and continue to offer great potential.
We present methods for the analysis of a single model, comprising applications
of standard dynamical systems approaches such as nondimensionalization, steady
state, asymptotic and sensitivity analysis, and more recent statistical and
algebraic approaches to compare models with data. We present parameter
estimation and model comparison techniques, focusing on Bayesian analysis and
coplanarity via algebraic geometry. Our intention is that this (non exhaustive)
review may serve as a useful starting point for the analysis of models in
systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte
Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly
Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as Alzheimerâs disease. Amyloid brils also have potential applications in nano-engineering of biomaterials. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration as seen in bulk experiments and experiments that mimic the small volumes of cells. Here, to investigate the origins and the properties of the observed variability in the lag phase of amyloid assembly currently not accounted for by deterministic nucleation dependent mechanisms, we formulate a new stochastic minimal model that is capable of describing the characteristics of amyloid growth curves despite its simplicity. We then solve the stochastic di erential equations of our model and give mathematical proof of a central limit theorem for the sample growth trajectories of the nucleated aggregation process. These results give an asymptotic description for our simple model, from which closed form analytical results capable of describing and predicting the variability of nucleated amyloid assembly were derived. We also demonstrate the application of our results to inform experiments in a conceptually friendly and clear fashion. Our model o ers a new perspective and paves the way for a new and e cient approach on extracting vital information regarding the key initial events of amyloid formation
Intrinsic noise of microRNA-regulated genes and the ceRNA hypothesis
MicroRNAs are small noncoding RNAs that regulate genes post-transciptionally
by binding and degrading target eukaryotic mRNAs. We use a quantitative model
to study gene regulation by inhibitory microRNAs and compare it to gene
regulation by prokaryotic small non-coding RNAs (sRNAs). Our model uses a
combination of analytic techniques as well as computational simulations to
calculate the mean-expression and noise profiles of genes regulated by both
microRNAs and sRNAs. We find that despite very different molecular machinery
and modes of action (catalytic vs stoichiometric), the mean expression levels
and noise profiles of microRNA-regulated genes are almost identical to genes
regulated by prokaryotic sRNAs. This behavior is extremely robust and persists
across a wide range of biologically relevant parameters. We extend our model to
study crosstalk between multiple mRNAs that are regulated by a single microRNA
and show that noise is a sensitive measure of microRNA-mediated interaction
between mRNAs. We conclude by discussing possible experimental strategies for
uncovering the microRNA-mRNA interactions and testing the competing endogenous
RNA (ceRNA) hypothesis.Comment: 32 pages, 11 figure
Analysis of Large Unreliable Stochastic Networks
In this paper a stochastic model of a large distributed system where users'
files are duplicated on unreliable data servers is investigated. Due to a
server breakdown, a copy of a file can be lost, it can be retrieved if another
copy of the same file is stored on other servers. In the case where no other
copy of a given file is present in the network, it is definitively lost. In
order to have multiple copies of a given file, it is assumed that each server
can devote a fraction of its processing capacity to duplicate files on other
servers to enhance the durability of the system.
A simplified stochastic model of this network is analyzed. It is assumed that
a copy of a given file is lost at some fixed rate and that the initial state is
optimal: each file has the maximum number of copies located on the servers
of the network. Due to random losses, the state of the network is transient and
all files will be eventually lost. As a consequence, a transient
-dimensional Markov process with a unique absorbing state describes
the evolution this network. By taking a scaling parameter related to the
number of nodes of the network. a scaling analysis of this process is
developed. The asymptotic behavior of is analyzed on time scales of
the type for . The paper derives asymptotic
results on the decay of the network: Under a stability assumption, the main
results state that the critical time scale for the decay of the system is given
by . When the stability condition is not satisfied, it is
shown that the state of the network converges to an interesting local
equilibrium which is investigated. As a consequence it sheds some light on the
role of the key parameters , the duplication rate and , the maximal
number of copies, in the design of these systems
Probing microscopic origins of confined subdiffusion by first-passage observables
Subdiffusive motion of tracer particles in complex crowded environments, such
as biological cells, has been shown to be widepsread. This deviation from
brownian motion is usually characterized by a sublinear time dependence of the
mean square displacement (MSD). However, subdiffusive behavior can stem from
different microscopic scenarios, which can not be identified solely by the MSD
data. In this paper we present a theoretical framework which permits to
calculate analytically first-passage observables (mean first-passage times,
splitting probabilities and occupation times distributions) in disordered media
in any dimensions. This analysis is applied to two representative microscopic
models of subdiffusion: continuous-time random walks with heavy tailed waiting
times, and diffusion on fractals. Our results show that first-passage
observables provide tools to unambiguously discriminate between the two
possible microscopic scenarios of subdiffusion. Moreover we suggest experiments
based on first-passage observables which could help in determining the origin
of subdiffusion in complex media such as living cells, and discuss the
implications of anomalous transport to reaction kinetics in cells.Comment: 21 pages, 3 figures. Submitted versio
Stochastic Delay Accelerates Signaling in Gene Networks
The creation of protein from DNA is a dynamic process consisting of numerous reactions, such as transcription, translation and protein folding. Each of these reactions is further comprised of hundreds or thousands of sub-steps that must be completed before a protein is fully mature. Consequently, the time it takes to create a single protein depends on the number of steps in the reaction chain and the nature of each step. One way to account for these reactions in models of gene regulatory networks is to incorporate dynamical delay. However, the stochastic nature of the reactions necessary to produce protein leads to a waiting time that is randomly distributed. Here, we use queueing theory to examine the effects of such distributed delay on the propagation of information through transcriptionally regulated genetic networks. In an analytically tractable model we find that increasing the randomness in protein production delay can increase signaling speed in transcriptional networks. The effect is confirmed in stochastic simulations, and we demonstrate its impact in several common transcriptional motifs. In particular, we show that in feedforward loops signaling time and magnitude are significantly affected by distributed delay. In addition, delay has previously been shown to cause stable oscillations in circuits with negative feedback. We show that the period and the amplitude of the oscillations monotonically decrease as the variability of the delay time increases
Collective Effects in Models for Interacting Molecular Motors and Motor-Microtubule Mixtures
Three problems in the statistical mechanics of models for an assembly of
molecular motors interacting with cytoskeletal filaments are reviewed. First, a
description of the hydrodynamical behaviour of density-density correlations in
fluctuating ratchet models for interacting molecular motors is outlined.
Numerical evidence indicates that the scaling properties of dynamical behavior
in such models belong to the KPZ universality class. Second, the generalization
of such models to include boundary injection and removal of motors is provided.
In common with known results for the asymmetric exclusion processes,
simulations indicate that such models exhibit sharp boundary driven phase
transitions in the thermodynamic limit. In the third part of this paper, recent
progress towards a continuum description of pattern formation in mixtures of
motors and microtubules is described, and a non-equilibrium ``phase-diagram''
for such systems discussed.Comment: Proc. Int. Workshop on "Common Trends in Traffic Systems", Kanpur,
India, Feb 2006; to be published in Physica
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