38,790 research outputs found
Dynamic sensitivity analysis of biological systems
BACKGROUND: A mathematical model to understand, predict, control, or even design a real biological system is a central theme in systems biology. A dynamic biological system is always modeled as a nonlinear ordinary differential equation (ODE) system. How to simulate the dynamic behavior and dynamic parameter sensitivities of systems described by ODEs efficiently and accurately is a critical job. In many practical applications, e.g., the fed-batch fermentation systems, the system admissible input (corresponding to independent variables of the system) can be time-dependent. The main difficulty for investigating the dynamic log gains of these systems is the infinite dimension due to the time-dependent input. The classical dynamic sensitivity analysis does not take into account this case for the dynamic log gains. RESULTS: We present an algorithm with an adaptive step size control that can be used for computing the solution and dynamic sensitivities of an autonomous ODE system simultaneously. Although our algorithm is one of the decouple direct methods in computing dynamic sensitivities of an ODE system, the step size determined by model equations can be used on the computations of the time profile and dynamic sensitivities with moderate accuracy even when sensitivity equations are more stiff than model equations. To show this algorithm can perform the dynamic sensitivity analysis on very stiff ODE systems with moderate accuracy, it is implemented and applied to two sets of chemical reactions: pyrolysis of ethane and oxidation of formaldehyde. The accuracy of this algorithm is demonstrated by comparing the dynamic parameter sensitivities obtained from this new algorithm and from the direct method with Rosenbrock stiff integrator based on the indirect method. The same dynamic sensitivity analysis was performed on an ethanol fed-batch fermentation system with a time-varying feed rate to evaluate the applicability of the algorithm to realistic models with time-dependent admissible input. CONCLUSION: By combining the accuracy we show with the efficiency of being a decouple direct method, our algorithm is an excellent method for computing dynamic parameter sensitivities in stiff problems. We extend the scope of classical dynamic sensitivity analysis to the investigation of dynamic log gains of models with time-dependent admissible input
Likelihood based observability analysis and confidence intervals for predictions of dynamic models
Mechanistic dynamic models of biochemical networks such as Ordinary
Differential Equations (ODEs) contain unknown parameters like the reaction rate
constants and the initial concentrations of the compounds. The large number of
parameters as well as their nonlinear impact on the model responses hamper the
determination of confidence regions for parameter estimates. At the same time,
classical approaches translating the uncertainty of the parameters into
confidence intervals for model predictions are hardly feasible.
In this article it is shown that a so-called prediction profile likelihood
yields reliable confidence intervals for model predictions, despite arbitrarily
complex and high-dimensional shapes of the confidence regions for the estimated
parameters. Prediction confidence intervals of the dynamic states allow a
data-based observability analysis. The approach renders the issue of sampling a
high-dimensional parameter space into evaluating one-dimensional prediction
spaces. The method is also applicable if there are non-identifiable parameters
yielding to some insufficiently specified model predictions that can be
interpreted as non-observability. Moreover, a validation profile likelihood is
introduced that should be applied when noisy validation experiments are to be
interpreted.
The properties and applicability of the prediction and validation profile
likelihood approaches are demonstrated by two examples, a small and instructive
ODE model describing two consecutive reactions, and a realistic ODE model for
the MAP kinase signal transduction pathway. The presented general approach
constitutes a concept for observability analysis and for generating reliable
confidence intervals of model predictions, not only, but especially suitable
for mathematical models of biological systems
Instantaneous modelling and reverse engineering of data-consistent prime models in seconds!
A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time series data in seconds. This has resulted in the formulation and formalisation of new reverse engineering and dynamic methods for automated systems modelling of complex systems, including complex biological, financial, control, and artificial neural network systems. The systems/model theory behind the invention has been formalised as a new, effective and robust system identification strategy complementary to process-based modelling. The proposed dynamic modelling and network inference solutions often involve tackling extremely difficult parameter estimation challenges, inferring unknown underlying network structures, and unsupervised formulation and construction of smart and intelligent ODE models of complex systems. In underdetermined conditions, i.e., cases of dealing with how best to instantaneously and rapidly construct data-consistent prime models of unknown (or well-studied) complex system from small-sized time series data, inference of unknown underlying network of interaction is more challenging. This article reports a robust step-by-step mathematical and computational analysis of the entire prime model construction process that determines a model from data in less than a minute
Model Checking Tap Withdrawal in C. Elegans
We present what we believe to be the first formal verification of a
biologically realistic (nonlinear ODE) model of a neural circuit in a
multicellular organism: Tap Withdrawal (TW) in \emph{C. Elegans}, the common
roundworm. TW is a reflexive behavior exhibited by \emph{C. Elegans} in
response to vibrating the surface on which it is moving; the neural circuit
underlying this response is the subject of this investigation. Specifically, we
perform reachability analysis on the TW circuit model of Wicks et al. (1996),
which enables us to estimate key circuit parameters. Underlying our approach is
the use of Fan and Mitra's recently developed technique for automatically
computing local discrepancy (convergence and divergence rates) of general
nonlinear systems. We show that the results we obtain are in agreement with the
experimental results of Wicks et al. (1995). As opposed to the fixed parameters
found in most biological models, which can only produce the predominant
behavior, our techniques characterize ranges of parameters that produce (and do
not produce) all three observed behaviors: reversal of movement, acceleration,
and lack of response
Grid-enabled SIMAP utility: Motivation, integration technology and performance results
A biological system comprises large numbers of functionally diverse and frequently multifunctional sets of elements that interact selectively and nonlinearly to produce coherent behaviours. Such a system can be anything from an intracellular biological process (such as a biochemical reaction cycle, gene regulatory network or signal transduction pathway) to a cell, tissue, entire organism, or even an ecological web. Biochemical systems are
responsible for processing environmental signals, inducing the appropriate cellular responses and sequence of
internal events. However, such systems are not fully or even poorly understood. Systems biology is a scientific field that is concerned with the systematic study of biological and biochemical systems in terms of complex interactions rather than their individual molecular components. At the core of systems biology is computational
modelling (also called mathematical modelling), which is the process of constructing and simulating an abstract
model of a biological system for subsequent analysis. This methodology can be used to test hypotheses via insilico experiments, providing predictions that can be tested by in-vitro and in-vivo studies. For example, the ERbB1-4 receptor tyrosine kinases (RTKs) and the signalling pathways they activate, govern most core cellular processes such as cell division, motility and survival (Citri and Yarden, 2006) and are strongly linked to cancer when they malfunction due to mutations etc. An ODE (ordinary differential equation)-based mass action ErbB model has been constructed and analysed by Chen et al. (2009) in order to depict what roles of each protein plays and ascertain to how sets of proteins coordinate with each other to perform distinct physiological functions. The
model comprises 499 species (molecules), 201 parameters and 828 reactions. These in silico experiments can often be computationally very expensive, e.g. when multiple biochemical factors are being considered or a variety of complex networks are being simulated simultaneously. Due to the size and complexity of the models
and the requirement to perform comprehensive experiments it is often necessary to use high-performance computing (HPC) to keep the experimental time within tractable bounds. Based on this as part of an EC funded
cancer research project, we have developed the SIMAP Utility that allows the SImulation modeling of the MAP kinase pathway (http://www.simap-project.org). In this paper we present experiences with Grid-enabling SIMAP using Condor
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
Recommended from our members
Differential Equations arising from Organising Principles in Biology
This workshop brought together experts in modeling and analysis of organising principles of multiscale biological systems such as cell assemblies, tissues and populations. We focused on questions arising in systems biology and medicine which are related to emergence, function and control of spatial and inter-individual heterogeneity in population dynamics. There were three main areas represented of differential equation models in mathematical biology. The first area involved the mathematical description of structured populations. The second area concerned invasion, pattern formation and collective dynamics. The third area treated the evolution and adaptation of populations, following the Darwinian paradigm. These problems led to differential equations, which frequently are non-trivial extensions of classical problems. The examples included but were not limited to transport-type equations with nonlocal boundary conditions, mixed ODE-reaction-diffusion models, nonlocal diffusion and cross-diffusion problems or kinetic equations
Language-based Abstractions for Dynamical Systems
Ordinary differential equations (ODEs) are the primary means to modelling
dynamical systems in many natural and engineering sciences. The number of
equations required to describe a system with high heterogeneity limits our
capability of effectively performing analyses. This has motivated a large body
of research, across many disciplines, into abstraction techniques that provide
smaller ODE systems while preserving the original dynamics in some appropriate
sense. In this paper we give an overview of a recently proposed
computer-science perspective to this problem, where ODE reduction is recast to
finding an appropriate equivalence relation over ODE variables, akin to
classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366
- …