373,237 research outputs found
Logic Integer Programming Models for Signaling Networks
We propose a static and a dynamic approach to model biological signaling
networks, and show how each can be used to answer relevant biological
questions. For this we use the two different mathematical tools of
Propositional Logic and Integer Programming. The power of discrete mathematics
for handling qualitative as well as quantitative data has so far not been
exploited in Molecular Biology, which is mostly driven by experimental
research, relying on first-order or statistical models. The arising logic
statements and integer programs are analyzed and can be solved with standard
software. For a restricted class of problems the logic models reduce to a
polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic
model enables enumeration of possible time resolutions in poly-logarithmic
time. Computational experiments are included
Theory of Interface: Category Theory, Directed Networks and Evolution of Biological Networks
Biological networks have two modes. The first mode is static: a network is a
passage on which something flows. The second mode is dynamic: a network is a
pattern constructed by gluing functions of entities constituting the network.
In this paper, first we discuss that these two modes can be associated with the
category theoretic duality (adjunction) and derive a natural network structure
(a path notion) for each mode by appealing to the category theoretic
universality. The path notion corresponding to the static mode is just the
usual directed path. The path notion for the dynamic mode is called lateral
path which is the alternating path considered on the set of arcs. Their general
functionalities in a network are transport and coherence, respectively. Second,
we introduce a betweenness centrality of arcs for each mode and see how the two
modes are embedded in various real biological network data. We find that there
is a trade-off relationship between the two centralities: if the value of one
is large then the value of the other is small. This can be seen as a kind of
division of labor in a network into transport on the network and coherence of
the network. Finally, we propose an optimization model of networks based on a
quality function involving intensities of the two modes in order to see how
networks with the above trade-off relationship can emerge through evolution. We
show that the trade-off relationship can be observed in the evolved networks
only when the dynamic mode is dominant in the quality function by numerical
simulations. We also show that the evolved networks have features qualitatively
similar to real biological networks by standard complex network analysis.Comment: 59 pages, minor corrections from v
Network-Induced Oscillatory Behavior in Material Flow Networks
Network theory is rapidly changing our understanding of complex systems, but
the relevance of topological features for the dynamic behavior of metabolic
networks, food webs, production systems, information networks, or cascade
failures of power grids remains to be explored. Based on a simple model of
supply networks, we offer an interpretation of instabilities and oscillations
observed in biological, ecological, economic, and engineering systems. We find
that most supply networks display damped oscillations, even when their units -
and linear chains of these units - behave in a non-oscillatory way. Moreover,
networks of damped oscillators tend to produce growing oscillations. This
surprising behavior offers, for example, a new interpretation of business
cycles and of oscillating or pulsating processes. The network structure of
material flows itself turns out to be a source of instability, and cyclical
variations are an inherent feature of decentralized adjustments.Comment: For related work see http://www.helbing.or
Reducing complexity: An iterative strategy for parameter determination in biological networks
AbstractThe dynamics of biological networks are fundamental to a variety of processes in many areas of biology and medicine. Understanding of such networks on a systemic level is facilitated by mathematical models describing these networks. However, since mathematical models of signalling networks commonly aim to describe several highly connected biological quantities and many model parameters cannot be measured directly, quantitative dynamic models often present challenges with respect to model calibration. Here, we propose an iterative fitting routine to decompose the problem of fitting a system of coupled ordinary differential equations describing a signalling network into smaller subproblems. Parameters for each differential equation are estimated separately using a Differential Evolution algorithm while all other dynamic quantities in the model are treated as input to the system. The performance of this algorithm is evaluated on artificial networks with known structure and known model parameters and compared to a conventional optimisation procedure for the same problem. Our analysis indicates that the procedure results in a significantly higher quality of fit and more efficient reconstruction of the true parameters than the conventional algorithm
Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks
It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks
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