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At least 253 records · Page 14Linked to original sources

arXiv2011

Finding weakly reversible realizations of chemical reaction networks using optimization

An algorithm is given in this paper for the computation of dynamically equivalent weakly reversible realizations with the maximal number of reactions, for chemical reaction networks (CRNs) with mass action kinetics. The original problem statement can be traced back at least 30 years ago. The algorithm uses standard linear and mixed integer linear programming, and it is based on elementary graph theory and important former results on the dense realizations of CRNs. The proposed method is also capable of determining if no dynamically equivalent weakly reversible structure exists for a given reaction network with a previously fixed complex set.

math.DS↗

arXiv2011

Role-similarity based comparison of directed networks

The widespread relevance of complex networks is a valuable tool in the analysis of a broad range of systems. There is a demand for tools which enable the extraction of meaningful information and allow the comparison between different systems. We present a novel measure of similarity between nodes in different networks as a generalization of the concept of self-similarity. A similarity matrix is assembled as the distance between feature vectors that contain the in and out paths of all lengths for each node. Hence, nodes operating in a similar flow environment are considered similar regardless of network membership. We demonstrate that this method has the potential to be influential in tasks such as assigning identity or function to uncharacterized nodes. In addition an innovative application of graph partitioning to the raw results extends the concept to the comparison of networks in terms of their underlying role-structure.

physics.soc-ph↗

arXiv2011

Semi-Markov models of mRNA-translation

Translation is the cellular process in which ribosomes make proteins from information encoded on messenger RNA (mRNA). We model translation with an exclusion process taking into account the experimentally determined, non-exponential, waiting time between steps of a ribosome. From numerical simulations using realistic parameter values, we determine the distribution P(E) of the number of proteins E produced by one mRNA. We find that for small E this distribution is not geometric. We present a simplified and analytically solvable semi-Markov model that relates P(E) to the distributions of the times to produce the first E proteins.

q-bio.MN↗

arXiv2011

Recursive Shortest Path Algorithm with Application to Density-integration of Weighted Graphs

Graph theory is increasingly commonly utilised in genetics, proteomics and neuroimaging. In such fields, the data of interest generally constitute weighted graphs. Analysis of such weighted graphs often require the integration of topological metrics with respect to the density of the graph. Here, density refers to the proportion of the number of edges present in that graph. When topological metrics based on shortest paths are of interest, such density-integration usually necessitates the iterative application of Dijkstra's algorithm in order to compute the shortest path matrix at each density level. In this short note, we describe a recursive shortest path algorithm based on single edge updating, which replaces the need for the iterative use of Dijkstra's algorithm. Our proposed procedure is based on pairs of breadth-first searches around each of the vertices incident to the edge added at each recursion. An algorithmic analysis of the proposed technique is provided. When the graph of interest is coded as an adjacency list, our algorithm can be shown to be more efficient than an iterative use of Dijkstra's algorithm.

q-bio.MN↗

arXiv2014

The "Machinery" of Biocomplexity: understanding non-optimal architectures in biological systems

One popular assumption regarding biological systems is that traits have evolved to be optimized with respect to function. This is a standard goal in evolutionary computation, and while not always embraced in the biological sciences, is an underlying assumption of what happens when fitness is maximized. The implication of this is that a signaling pathway or phylogeny should show evidence of minimizing the number of steps required to produce a biochemical product or phenotypic adaptation. In this paper, it will be shown that a principle of "maximum intermediate steps" may also characterize complex biological systems, especially those in which extreme historical contingency or a combination of mutation and recombination are key features. The contribution to existing literature is two-fold: demonstrating both the potential for non-optimality in engineered systems with "lifelike" attributes, and the underpinnings of non-optimality in naturalistic contexts. This will be demonstrated by using the Rube Goldberg Machine (RGM) analogy. Mechanical RGMs will be introduced, and their relationship to conceptual biological RGMs. Exemplars of these biological RGMs and their evolution (e.g. introduction of mutations and recombination-like inversions) will be demonstrated using block diagrams and interconnections with complex networks (called convolution architectures). The conceptual biological RGM will then be mapped to an artificial vascular system, which can be modeled using microfluidic-like structures. Theoretical expectations will be presented, particularly regarding whether or not maximum intermediate steps equates to the rescue or reuse of traits compromised by previous mutations or inversions. Considerations for future work and applications will then be discussed, including the incorporation of such convolution architectures into complex networks.

q-bio.QM↗

arXiv2011

Boundedness of trajectories for weakly reversible, single linkage class reaction systems

This paper is concerned with the dynamical properties of deterministically modeled chemical reaction systems with mass-action kinetics. Such models are ubiquitously found in chemistry, population biology, and the burgeoning field of systems biology. A basic question, whose answer remains largely unknown, is the following: for which network structures do trajectories of mass-action systems remain bounded in time? In this paper, we conjecture that the result holds when the reaction network is weakly reversible, and prove this conjecture in the case when the reaction network consists of a single linkage class, or connected component.

math.DS↗

arXiv2017

Parallelism and Time in Hierarchical Self-Assembly

We study the role that parallelism plays in time complexity of Winfree's abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the "hierarchical" aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the "seeded" aTAM, tiles attach one at a time to a growing assembly. Adleman, Cheng, Goel, and Huang ("Running Time and Program Size for Self-Assembled Squares", STOC 2001) showed how to assemble an n x n square in O(n) time in the seeded aTAM using O(log n / log log n) unique tile types, where both of these parameters are optimal. They asked whether the hierarchical aTAM could allow a tile system to use the ability to form large assemblies in parallel before they attach to break the Omega(n) lower bound for assembly time. We show that there is a tile system with the optimal O(log n / log log n) tile types that assembles an n x n square using O(log^2 n) parallel "stages", which is close to the optimal Omega(log n) stages, forming the final n x n square from four n/2 x n/2 squares, which are themselves recursively formed from n/4 x n/4 squares, etc. However, despite this nearly maximal parallelism, the system requires superlinear time to assemble the square. We extend the definition of *partial order tile systems* studied by Adleman et al. in a natural way to hierarchical assembly and show that no hierarchical partial order tile system can build any shape with diameter N in less than time Omega(N), demonstrating that in this case the hierarchical model affords no speedup whatsoever over the seeded model. We strengthen the Omega(N) time lower bound for deterministic seeded systems of Adleman et al. to nondeterministic seeded systems. Finally, we show that for infinitely many n, a tile system can assemble an n x n' rectangle, with n > n', in time O(n^{4/5} log n), breaking the linear-time lower bound.

cs.CC↗

arXiv2011

Mining Temporal Patterns from iTRAQ Mass Spectrometry(LC-MS/MS) Data

Large-scale proteomic analysis is emerging as a powerful technique in biology and relies heavily on data acquired by state-of-the-art mass spectrometers. As with any other field in Systems Biology, computational tools are required to deal with this ocean of data. iTRAQ (isobaric Tags for Relative and Absolute quantification) is a technique that allows simultaneous quantification of proteins from multiple samples. Although iTRAQ data gives useful insights to the biologist, it is more complex to perform analysis and draw biological conclusions because of its multi-plexed design. One such problem is to find proteins that behave in a similar way (i.e. change in abundance) among various time points since the temporal variations in the proteomics data reveal important biological information. Distance based methods such as Euclidian distance or Pearson coefficient, and clustering techniques such as k-mean etc, are not able to take into account the temporal information of the series. In this paper, we present an linear-time algorithm for clustering similar patterns among various iTRAQ time course data irrespective of their absolute values. The algorithm, referred to as Temporal Pattern Mining(TPM), maps the data from a Cartesian plane to a discrete binary plane. After the mapping a dynamic programming technique allows mining of similar data elements that are temporally closer to each other. The proposed algorithm accurately clusters iTRAQ data that are temporally closer to each other with more than 99% accuracy. Experimental results for different problem sizes are analyzed in terms of quality of clusters, execution time and scalability for large data sets. An example from our proteomics data is provided at the end to demonstrate the performance of the algorithm and its ability to cluster temporal series irrespective of their distance from each other.

q-bio.QM↗

arXiv2011

Extremal Properties of Complex Networks

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks.

q-bio.MN↗

arXiv2012

Biochemical network decomposition reveals absolute concentration robustness

Robustness of biochemical systems has become one of the central questions in Systems Biology, although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the stoichiometry of the underlying interrelated components, but also on a multitude of kinetic parameters. For given parameter values, recent findings have aimed at characterizing the property of the system components to exhibit same concentrations in the resulting steady states, termed absolute concentration robustness (ACR). However, the existing method for determining system components exhibiting ACR is applicable only to one class of mass-action networks for which this property can be confirmed, but not discarded. Here we design a new method which relies on biochemical network decompositions into subnetworks, called elementary flux modes, to identify ACR in a broader class of mass-action networks by using only the given stoichiometry. This approach reduces the problem of determining ACR to that of solving parameterized systems of linear equations, rendering it amenable to networks of larger sizes. Our unified framework will be helpful in analyzing this biologically important type of robustness as well as detection of novel systemic properties independent of the kinetic parameters for more complex biochemical networks.

q-bio.MN↗

arXiv2011

A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks

We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a new variational principle for biochemical networks that can be implemented in a computationally tractable manner. We derive the Lagrange dual of the optimization problem and use strong duality to demonstrate that a biochemical analogue of Tellegen's theorem holds at optimality. Each optimal flux is dependent on a free parameter that we relate to an elementary kinetic parameter when mass action kinetics is assumed.

q-bio.MN↗

arXiv2011

Existence of Positive Steady States for Mass Conserving and Mass-Action Chemical Reaction Networks with a Single Terminal-Linkage Class

We establish that mass conserving single terminal-linkage networks of chemical reactions admit positive steady states regardless of network deficiency and the choice of reaction rate constants. This result holds for closed systems without material exchange across the boundary, as well as for open systems with material exchange at rates that satisfy a simple sufficient and necessary condition. Our proof uses a fixed point of a novel convex optimization formulation to find the steady state behavior of chemical reaction networks that satisfy the law of mass-action kinetics. A fixed point iteration can be used to compute these steady states, and we show that it converges for weakly reversible homogeneous systems. We report the results of our algorithm on numerical experiments.

q-bio.MN↗

arXiv2011

Nonlinear regulation of commitment to apoptosis by simultaneous inhibition of Bcl-2 and XIAP in leukemia and lymphoma cells

Apoptosis is a complex pathway regulated by the concerted action of multiple pro- and anti-apoptotic molecules. The intrinsic (mitochondrial) pathway of apoptosis is governed up-stream of mitochondria, by the family of Bcl-2 proteins, and down-stream of mitochondria, by low-probability events, such as apoptosome formation, and by feedback circuits involving caspases and inhibitor of apoptosis proteins (IAPs), such as XIAP. All these regulatory mechanisms ensure that cells only commit to death once a threshold of damage has been reached and the anti-apoptotic reserve of the cell is overcome. As cancer cells are invariably exposed to strong intracellular and extracellular stress stimuli, they are particularly reliant on the expression of anti-apoptotic proteins. Hence, many cancer cells undergo apoptosis when exposed to agents that inhibit anti-apoptotic Bcl-2 molecules, such as BH3 mimetics, while normal cells remain relatively insensitive to single agent treatments with the same class of molecules. Targeting different proteins within the apoptotic network with combinatorial treatment approaches often achieves even greater specificity. This led us to investigate the sensitivity of leukemia and lymphoma cells to a pro-apoptotic action of a BH3 mimetic combined with a small molecule inhibitor of XIAP. Using computational probabilistic model of apoptotic pathway, verified by experimental results from human leukemia and lymphoma cell lines, we show that inhibition of XIAP has a non-linear effect on sensitization towards apoptosis induced by the BH3 mimetic HA14-1. This study justifies further ex vivo and animal studies on the potential of the treatment of leukemia and lymphoma with a combination of BH3 mimetics and XIAP inhibitors.

q-bio.MN↗

arXiv2011

Replica procedure for probabilistic algorithms as a model of gene duplication

In the present paper we propose to describe gene networks in biological systems using probabilistic algorithms. We describe gene duplication in the process of biological evolution using introduction of the replica procedure for probabilistic algorithms. We construct the examples of such a replica procedure for hidden Markov models. We introduce the family of hidden Markov models where the set of hidden states is a finite additive group with a p-adic metric and build the replica procedure for this family of markovian models.

q-bio.MN↗

arXiv2011

Controlling Complex Networks with Compensatory Perturbations

The response of complex networks to perturbations is of utmost importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that the perturbation of one node can affect other nodes, in a process that may cause the entire or substantial part of the system to change behavior and possibly collapse. Recent research in metabolic and food-web networks has demonstrated the concept that network damage caused by external perturbations can often be mitigated or reversed by the application of compensatory perturbations. Compensatory perturbations are constrained to be physically admissible and amenable to implementation on the network. However, the systematic identification of compensatory perturbations that conform to these constraints remains an open problem. Here, we present a method to construct compensatory perturbations that can control the fate of general networks under such constraints. Our approach accounts for the full nonlinear behavior of real complex networks and can bring the system to a desirable target state even when this state is not directly accessible. Applications to genetic networks show that compensatory perturbations are effective even when limited to a small fraction of all nodes in the network and that they are far more effective when limited to the highest-degree nodes. The approach is conceptually simple and computationally efficient, making it suitable for the rescue, control, and reprogramming of large complex networks in various domains.

q-bio.MN↗

arXiv2011

A machine learning pipeline for discriminant pathways identification

Motivation: Identifying the molecular pathways more prone to disruption during a pathological process is a key task in network medicine and, more in general, in systems biology. Results: In this work we propose a pipeline that couples a machine learning solution for molecular profiling with a recent network comparison method. The pipeline can identify changes occurring between specific sub-modules of networks built in a case-control biomarker study, discriminating key groups of genes whose interactions are modified by an underlying condition. The proposal is independent from the classification algorithm used. Three applications on genomewide data are presented regarding children susceptibility to air pollution and two neurodegenerative diseases: Parkinson's and Alzheimer's. Availability: Details about the software used for the experiments discussed in this paper are provided in the Appendix.

q-bio.MN↗

arXiv2011

Molecular Codes in Biological and Non-Biological Reaction Networks

Can we objectively distinguish chemical systems that are able to process meaningful information from those that are not suitable for information processing? Here, we present a formal method to assess the semantic capacity of a chemical reaction network. The semantic capacity of a network can be measured by analyzing the capability of the network to implement molecular codes. We analyzed models of real chemical systems (Martian atmosphere chemistry and various combustion chemistries), bio-chemical systems (gene expression, gene translation, and phosphorylation signaling cascades), as well as an artificial chemistry and random networks. Our study suggests that different chemical systems posses different semantic capacities. Basically no semantic capacity was found in the atmosphere chemistry of Mars and all studied combustion chemistries, as well as in highly connected random networks, i.e., with these chemistries molecular codes cannot be implemented. High semantic capacity was found in the bio-chemical systems, as well as in random networks where the number of second order reactions is at the number of species. Hypotheses concern the origin and evolution of life. We conclude that our approach can be applied to evaluate the information processing capabilities of a chemical system and may thus be a useful tool to understand the origin and evolution of meaningful information, e.g., at the origin of life.

q-bio.MN↗

arXiv2011

Dynamic modeling of gene expression in prokaryotes: application to glucose-lactose diauxie in Escherichia coli

Coexpression of genes or, more generally, similarity in the expression profiles poses an unsurmountable obstacle to inferring the gene regulatory network (GRN) based solely on data from DNA microarray time series. Clustering of genes with similar expression profiles allows for a course-grained view of the GRN and a probabilistic determination of the connectivity among the clusters. We present a model for the temporal evolution of a gene cluster network which takes into account interactions of gene products with genes and, through a non-constant degradation rate, with other gene products. The number of model parameters is reduced by using polynomial functions to interpolate temporal data points. In this manner, the task of parameter estimation is reduced to a system of linear algebraic equations, thus making the computation time shorter by orders of magnitude. To eliminate irrelevant networks, we test each GRN for stability with respect to parameter variations, and impose restrictions on its behavior near the steady state. We apply our model and methods to DNA microarray time series' data collected on Escherichia coli during glucose-lactose diauxie and infer the most probable cluster network for different phases of the experiment.

q-bio.MN↗