64,002 research outputs found
Mechanism Deduction from Noisy Chemical Reaction Networks
We introduce KiNetX, a fully automated meta-algorithm for the kinetic
analysis of complex chemical reaction networks derived from semi-accurate but
efficient electronic structure calculations. It is designed to (i) accelerate
the automated exploration of such networks, and (ii) cope with model-inherent
errors in electronic structure calculations on elementary reaction steps. We
developed and implemented KiNetX to possess three features. First, KiNetX
evaluates the kinetic relevance of every species in a (yet incomplete) reaction
network to confine the search for new elementary reaction steps only to those
species that are considered possibly relevant. Second, KiNetX identifies and
eliminates all kinetically irrelevant species and elementary reactions to
reduce a complex network graph to a comprehensible mechanism. Third, KiNetX
estimates the sensitivity of species concentrations toward changes in
individual rate constants (derived from relative free energies), which allows
us to systematically select the most efficient electronic structure model for
each elementary reaction given a predefined accuracy. The novelty of KiNetX
consists in the rigorous propagation of correlated free-energy uncertainty
through all steps of our kinetic analyis. To examine the performance of KiNetX,
we developed AutoNetGen. It semirandomly generates chemistry-mimicking reaction
networks by encoding chemical logic into their underlying graph structure.
AutoNetGen allows us to consider a vast number of distinct chemistry-like
scenarios and, hence, to discuss assess the importance of rigorous uncertainty
propagation in a statistical context. Our results reveal that KiNetX reliably
supports the deduction of product ratios, dominant reaction pathways, and
possibly other network properties from semi-accurate electronic structure data.Comment: 36 pages, 4 figures, 2 table
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
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
Reduction of dynamical biochemical reaction networks in computational biology
Biochemical networks are used in computational biology, to model the static
and dynamical details of systems involved in cell signaling, metabolism, and
regulation of gene expression. Parametric and structural uncertainty, as well
as combinatorial explosion are strong obstacles against analyzing the dynamics
of large models of this type. Multi-scaleness is another property of these
networks, that can be used to get past some of these obstacles. Networks with
many well separated time scales, can be reduced to simpler networks, in a way
that depends only on the orders of magnitude and not on the exact values of the
kinetic parameters. The main idea used for such robust simplifications of
networks is the concept of dominance among model elements, allowing
hierarchical organization of these elements according to their effects on the
network dynamics. This concept finds a natural formulation in tropical
geometry. We revisit, in the light of these new ideas, the main approaches to
model reduction of reaction networks, such as quasi-steady state and
quasi-equilibrium approximations, and provide practical recipes for model
reduction of linear and nonlinear networks. We also discuss the application of
model reduction to backward pruning machine learning techniques
Energy-based Analysis of Biochemical Cycles using Bond Graphs
Thermodynamic aspects of chemical reactions have a long history in the
Physical Chemistry literature. In particular, biochemical cycles - the
building-blocks of biochemical systems - require a source of energy to
function. However, although fundamental, the role of chemical potential and
Gibb's free energy in the analysis of biochemical systems is often overlooked
leading to models which are physically impossible. The bond graph approach was
developed for modelling engineering systems where energy generation, storage
and transmission are fundamental. The method focuses on how power flows between
components and how energy is stored, transmitted or dissipated within
components. Based on early ideas of network thermodynamics, we have applied
this approach to biochemical systems to generate models which automatically
obey the laws of thermodynamics. We illustrate the method with examples of
biochemical cycles. We have found that thermodynamically compliant models of
simple biochemical cycles can easily be developed using this approach. In
particular, both stoichiometric information and simulation models can be
developed directly from the bond graph. Furthermore, model reduction and
approximation while retaining structural and thermodynamic properties is
facilitated. Because the bond graph approach is also modular and scaleable, we
believe that it provides a secure foundation for building thermodynamically
compliant models of large biochemical networks
A Molecular Implementation of the Least Mean Squares Estimator
In order to function reliably, synthetic molecular circuits require
mechanisms that allow them to adapt to environmental disturbances. Least mean
squares (LMS) schemes, such as commonly encountered in signal processing and
control, provide a powerful means to accomplish that goal. In this paper we
show how the traditional LMS algorithm can be implemented at the molecular
level using only a few elementary biomolecular reactions. We demonstrate our
approach using several simulation studies and discuss its relevance to
synthetic biology.Comment: Molecular circuits, synthetic biology, least mean squares estimator,
adaptive system
Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity
new type of instability in coupled reaction-diffusion-advection systems is analysed in a one-dimensional domain. This instability, arising due to the combined action of flow and diffusion, creates spatially periodic stationary waves termed flow and diffusion-distributed structures (FDS). Here we show, via linear stability analysis, that FDS are predicted in a considerably wider domain and are more robust (in the parameter domain) than the classical Turing instability patterns. FDS also represent a natural extension of the recently discovered flow-distributed oscillations (FDO). Nonlinear bifurcation analysis and numerical simulations in one-dimensional spatial domains show that FDS also have much richer solution behaviour than Turing structures. In the framework presented here Turing structures can be viewed as a particular instance of FDS. We conclude that FDS should be more easily obtainable in chemical systems than Turing (and FDO) structures and that they may play a potentially important role in biological pattern formation
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