Quantitative Biology

This paper compares a number of mathematical models for the Calvin cycle of photosynthesis and presents theorems on the existence and stability of steady states of these models. Results on five-variable models in the literature are surveyed. Next a number of larger models related to one introduced by Pettersson and Ryde-Pettersson are discussed. The mathematical nature of this model is clarified, showing that it is naturally defined as a system of differential-algebraic equations. It is proved that there are choices of parameters for which this model admits more than one positive steady state. This is done by analysing the limit where the storage of sugars from the cycle as starch is shut down. There is also a discussion of the minimal models for the cycle due to Hahn.

This document compares SRI's Pathway Tools (PTools) software with the Reactome software. Both software systems serve the pathway bioinformatics area, including representation and analysis of metabolic pathways and signaling pathways. The comparison covers pathway bioinformatics capabilities, but does not cover other major facets of Pathway Tools that are completely absent from the Reactome software: Pathway Tools genome-informatics capabilities, regulatory informatics capabilities, and table-based analysis tools (SmartTables). Our overall findings are as follows. (1) PTools is significantly ahead of Reactome in its basic information pages. For example, PTools pathway layout algorithms have been developed to an advanced state over several decades, whereas Reactome pathway layouts are illegible, omit important information, and are created manually and therefore cannot scale to thousands of genomes. (2) PTools is far ahead of Reactome in omics analysis. PTools includes all of the omics-analysis methods that Reactome provides, and includes multiple methods that Reactome lacks. (3) PTools contains a metabolic route search tool (searching for paths through the metabolic network), which Reactome lacks. (4) PTools is significantly ahead of Reactome in inference of metabolic pathways from genome information to create new metabolic databases. (5) PTools has an extensive complement of metabolic-modeling tools whereas Reactome has none. (6) PTools is more scalable than Reactome, handling 18,000 genomes versus 90 genomes for Reactome. (7) PTools has a larger user base than Reactome. PTools powers 17 websites versus two for Reactome. PTools has been licensed by 10,800 users (Reactome licensed user count is unknown).

Model-based prediction of stochastic noise in biomolecular reactions often resorts to approximation with unknown precision. As a result, unexpected stochastic fluctuation causes a headache for the designers of biomolecular circuits. This paper proposes a convex optimization approach to quantifying the steady state moments of molecular copy counts with theoretical rigor. We show that the stochastic moments lie in a convex semi-algebraic set specified by linear matrix inequalities. Thus, the upper and the lower bounds of some moments can be computed by a semidefinite program. Using a protein dimerization process as an example, we demonstrate that the proposed method can precisely predict the mean and the variance of the copy number of the monomer protein.

Development of fast methods to conduct in silico experiments using computational models of cellular signaling is a promising approach toward advances in personalized medicine. However, software-based cellular network simulation has run-times plagued by wasted CPU cycles and unnecessary processes. Hardware-based simulation affords substantial speedup, but prior attempts at hardware-based biological simulation have been limited in scope and have suffered from inaccuracies due to poor random number generation. In this work, we propose several hardware-based simulation schemes utilizing novel random update index generation techniques for step-based and round-based stochastic simulations of cellular networks. Our results show improved runtimes while maintaining simulation accuracy compared to software implementations.

An Elementary Flux Mode (EFM) is a pathway with minimum set of reactions that are functional in steady-state constrained space. Due to the high computational complexity of calculating EFMs, different approaches have been proposed to find these flux-balanced pathways. In this paper, an approach to find a subset of EFMs is proposed based on a graph data model. The given metabolic network is mapped to the graph model and decisions for reaction inclusion can be made based on metabolites and their associated reactions. This notion makes the approach more convenient to categorize the output pathways. Implications of the proposed method on metabolic networks are discussed.

We describe a mathematical model for the aggregation of starved first-stage C elegans larvae (L1s). We propose that starved L1s produce and respond chemotactically to two labile diffusible chemical signals, a short-range attractant and a longer range repellent. This model takes the mathematical form of three coupled partial differential equations, one that describes the movement of the worms and one for each of the chemical signals. Numerical solution of these equations produced a pattern of aggregates that resembled that of worm aggregates observed in experiments. We also describe the identification of a sensory receptor gene, srh-2, whose expression is induced under conditions that promote L1 aggregation. Worms whose srh-2 gene has been knocked out form irregularly shaped aggregates. Our model suggests this phenotype may be explained by the mutant worms slowing their movement more quickly than the wild type.

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.

Cancer disease occurs because of a disorder in the cellular regulatory mechanism, Which causes cellular malformation. The genes that start the malformation are called Cancer driver genes (CDGs) . Numerous computational methods have been introduced to identify cancer driver genes that use the concept of mutation.Regarding abnormalities spread in human cell and tumor development, CDGs are likely to be the potential types of gene with high influence in the network. This increases the importance of influence diffusion concept for the identification of CDGs.recently developed a method based on influence maximization for identifying cancer driver genes. One of the challenges in these types of networks is to find the power of regulatory interaction between edges.The current study developed a technique to identify cancer driver gene and predict the impact of regulatory interactions in a transcriptional regulatory network. This technique utilizes the concept of influence diffusion and optimizes the Hyperlink-Induced Topic Search algorithm based on the influence diffusion. The results suggest the better performance of our proposed technique than the other computational and network-based approaches.

Realistic description of patient-specific mechanical properties of clotting dynamics presents a major challenge. Available patient-specific data falls short of robustly characterizing myriads of complex dynamic interactions that happen during clotting. We propose a simplified switching model for a key part of the coagulation cascade that describes dynamics of just four variables. The model correctly predicts prolonged activity of thrombin, an important enzyme in the clotting process, in certain plasma factor compositions. The activity sustains beyond the time which is conventionally considered to be the end of clotting. This observation along with the simplified model is hypothesized as a necessary step towards effectively studying patient-specific properties of clotting dynamics in realistic geometries.

Motivation: Gene regulatory interactions are of fundamental importance to various biological functions and processes. However, only a few previous computational studies have claimed success in revealing genome-wide regulatory landscapes from temporal gene expression data, especially for complex eukaryotes like human. Moreover, recent work suggests that these methods still suffer from the curse of dimensionality if network size increases to 100 or higher. Result: We present a novel scalable algorithm for identifying genome-wide regulatory network structures. The highlight of our method is that its superior performance does not degenerate even for a network size on the order of 10 4 , and is thus readily applicable to large-scale complex networks. Such a breakthrough is achieved by considering both prior biological knowledge and multiple topological properties (i.e., sparsity and hub gene structure) of complex networks in the regularized formulation. We also illustrate the application of our algorithm in practice using the time-course expression data from an influenza infection study in respiratory epithelial cells. Availability and Implementation: The algorithm described in this article is implemented in MATLAB ® . The source code is freely available from this https URL. Contact: [email protected] http URL; [email protected] http URL Supplementary information: Supplementary data are available online.