3,753 research outputs found
Elasticity sampling links thermodynamics to metabolic control
Metabolic networks can be turned into kinetic models in a predefined steady
state by sampling the reaction elasticities in this state. Elasticities for
many reversible rate laws can be computed from the reaction Gibbs free
energies, which are determined by the state, and from physically unconstrained
saturation values. Starting from a network structure with allosteric regulation
and consistent metabolic fluxes and concentrations, one can sample the
elasticities, compute the control coefficients, and reconstruct a kinetic model
with consistent reversible rate laws. Some of the model variables are manually
chosen, fitted to data, or optimised, while the others are computed from them.
The resulting model ensemble allows for probabilistic predictions, for
instance, about possible dynamic behaviour. By adding more data or tighter
constraints, the predictions can be made more precise. Model variants differing
in network structure, flux distributions, thermodynamic forces, regulation, or
rate laws can be realised by different model ensembles and compared by
significance tests. The thermodynamic forces have specific effects on flux
control, on the synergisms between enzymes, and on the emergence and
propagation of metabolite fluctuations. Large kinetic models could help to
simulate global metabolic dynamics and to predict the effects of enzyme
inhibition, differential expression, genetic modifications, and their
combinations on metabolic fluxes. MATLAB code for elasticity sampling is freely
available
Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise
It is well known that the kinetics of an intracellular biochemical network is
stochastic. This is due to intrinsic noise arising from the random timing of
biochemical reactions in the network as well as due to extrinsic noise stemming
from the interaction of unknown molecular components with the network and from
the cell's changing environment. While there are many methods to study the
effect of intrinsic noise on the system dynamics, few exist to study the
influence of both types of noise. Here we show how one can extend the
conventional linear-noise approximation to allow for the rapid evaluation of
the molecule numbers statistics of a biochemical network influenced by
intrinsic noise and by slow lognormally distributed extrinsic noise. The theory
is applied to simple models of gene regulatory networks and its validity
confirmed by comparison with exact stochastic simulations. In particular we
show how extrinsic noise modifies the dependence of the variance of the
molecule number fluctuations on the rate constants, the mutual information
between input and output signalling molecules and the robustness of
feed-forward loop motifs.Comment: 43 pages, 4 figure
Forward Flux Sampling for rare event simulations
Rare events are ubiquitous in many different fields, yet they are notoriously
difficult to simulate because few, if any, events are observed in a conventiona
l simulation run. Over the past several decades, specialised simulation methods
have been developed to overcome this problem. We review one recently-developed
class of such methods, known as Forward Flux Sampling. Forward Flux Sampling
uses a series of interfaces between the initial and final states to calculate
rate constants and generate transition paths, for rare events in equilibrium or
nonequilibrium systems with stochastic dynamics. This review draws together a
number of recent advances, summarizes several applications of the method and
highlights challenges that remain to be overcome.Comment: minor typos in the manuscript. J.Phys.:Condensed Matter (accepted for
publication
Asymptotic analysis of noisy fitness maximization, applied to metabolism and growth
We consider a population dynamics model coupling cell growth to a diffusion
in the space of metabolic phenotypes as it can be obtained from realistic
constraints-based modelling. In the asymptotic regime of slow diffusion, that
coincides with the relevant experimental range, the resulting non-linear
Fokker-Planck equation is solved for the steady state in the WKB approximation
that maps it into the ground state of a quantum particle in an Airy potential
plus a centrifugal term. We retrieve scaling laws for growth rate fluctuations
and time response with respect to the distance from the maximum growth rate
suggesting that suboptimal populations can have a faster response to
perturbations.Comment: 24 pages, 6 figure
Learning and Designing Stochastic Processes from Logical Constraints
Stochastic processes offer a flexible mathematical formalism to model and
reason about systems. Most analysis tools, however, start from the premises
that models are fully specified, so that any parameters controlling the
system's dynamics must be known exactly. As this is seldom the case, many
methods have been devised over the last decade to infer (learn) such parameters
from observations of the state of the system. In this paper, we depart from
this approach by assuming that our observations are {\it qualitative}
properties encoded as satisfaction of linear temporal logic formulae, as
opposed to quantitative observations of the state of the system. An important
feature of this approach is that it unifies naturally the system identification
and the system design problems, where the properties, instead of observations,
represent requirements to be satisfied. We develop a principled statistical
estimation procedure based on maximising the likelihood of the system's
parameters, using recent ideas from statistical machine learning. We
demonstrate the efficacy and broad applicability of our method on a range of
simple but non-trivial examples, including rumour spreading in social networks
and hybrid models of gene regulation
Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes
Multiple biological processes are driven by oscillatory gene expression at
different time scales. Pulsatile dynamics are thought to be widespread, and
single-cell live imaging of gene expression has lead to a surge of dynamic,
possibly oscillatory, data for different gene networks. However, the regulation
of gene expression at the level of an individual cell involves reactions
between finite numbers of molecules, and this can result in inherent randomness
in expression dynamics, which blurs the boundaries between aperiodic
fluctuations and noisy oscillators. Thus, there is an acute need for an
objective statistical method for classifying whether an experimentally derived
noisy time series is periodic. Here we present a new data analysis method that
combines mechanistic stochastic modelling with the powerful methods of
non-parametric regression with Gaussian processes. Our method can distinguish
oscillatory gene expression from random fluctuations of non-oscillatory
expression in single-cell time series, despite peak-to-peak variability in
period and amplitude of single-cell oscillations. We show that our method
outperforms the Lomb-Scargle periodogram in successfully classifying cells as
oscillatory or non-oscillatory in data simulated from a simple genetic
oscillator model and in experimental data. Analysis of bioluminescent live cell
imaging shows a significantly greater number of oscillatory cells when
luciferase is driven by a {\it Hes1} promoter (10/19), which has previously
been reported to oscillate, than the constitutive MoMuLV 5' LTR (MMLV) promoter
(0/25). The method can be applied to data from any gene network to both
quantify the proportion of oscillating cells within a population and to measure
the period and quality of oscillations. It is publicly available as a MATLAB
package.Comment: 36 pages, 17 figure
Towards Understanding the Origin of Genetic Languages
Molecular biology is a nanotechnology that works--it has worked for billions
of years and in an amazing variety of circumstances. At its core is a system
for acquiring, processing and communicating information that is universal, from
viruses and bacteria to human beings. Advances in genetics and experience in
designing computers have taken us to a stage where we can understand the
optimisation principles at the root of this system, from the availability of
basic building blocks to the execution of tasks. The languages of DNA and
proteins are argued to be the optimal solutions to the information processing
tasks they carry out. The analysis also suggests simpler predecessors to these
languages, and provides fascinating clues about their origin. Obviously, a
comprehensive unraveling of the puzzle of life would have a lot to say about
what we may design or convert ourselves into.Comment: (v1) 33 pages, contributed chapter to "Quantum Aspects of Life",
edited by D. Abbott, P. Davies and A. Pati, (v2) published version with some
editin
Information theoretic framework for stochastic sensitivity and specificity analysis in biochemical networks
Biochemical reaction networks involve many chemical species and are inherently stochastic and complex in nature. Reliable and organised functioning of such systems in varied environments requires that their behaviour is robust with respect to certain parameters while sensitive to other variations, and that they exhibit specific responses to various stimuli. There is a continuous need for improved models and methodologies to unravel the complex behaviour of the dynamics of such systems. In this thesis, we apply ideas from information theory to develop novel methods to study properties of biochemical networks.
In the first part of the thesis, a framework for the study of parametric sensitivity in stochastic models of biochemical networks using entropies and mutual information is developed. The concept of noise entropy is introduced and its interplay with parametric sensitivity is studied as the system becomes more stochastic. Using the methodology for gene expression models, it is shown that noise can change the sensitivities of the system at var- ious orders of parameter interaction. An approximate and computationally more efficient way of calculating the sensitivities is also developed using unscented transform. Finally, the methodology is applied to a circadian clock model, illustrating the applicability of the approach to more complex systems.
In the second part of the thesis, a novel method for specificity quantification in a receptor-ligand binding system is proposed in terms of mutual information estimates be- tween appropriate stimulus and system response. The maximum specificity of 2 Ă 2 affinity matrices in a parametric setup is theoretically studied. Parameter optimisation methodology and specificity upper bounds are presented for maximum specificity estimates of a given affinity matrix. The quantification framework is then applied to experimental data from T-Cell signalling. Finally, generalisation of the scheme for stochastic systems is discussed.Open Acces
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