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Register a new userThe case for algebraic biology: from research to education
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Though it goes without saying that linear algebra is fundamental to mathematical biology, polynomial algebra is less visible. In this article, we will give a brief tour of four diverse biological problems where multivariate polynomials play a central role -- a subfield that is sometimes called algebraic biology. Namely, these topics include biochemical reaction networks, Boolean models of gene regulatory networks, algebraic statistics and genomics, and place fields in neuroscience. After that, we will summarize the history of discrete and algebraic structures in mathematical biology, from their early appearances in the late 1960s to the current day. Finally, we will discuss the role of algebraic biology in the modern classroom and curriculum, including resources in the literature and relevant software. Our goal is to make this article widely accessible, reaching the mathematical biologist who knows no algebra, the algebraist who knows no biology, and especially the interested student who is curious about the synergy between these two seemingly unrelated fields.
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The concepts and methods of Systems Biology are being extended to neuropharmacology, to test and design drugs against neurological and psychiatric disorders. Computational modeling by integrating compartmental neural modeling technique and detailed kinetic description of pharmacological modulation of transmitter-receptor interaction is offered as a method to test the electrophysiological and behavioral effects of putative drugs. Even more, an inverse method is suggested as a method for controlling a neural system to realize a prescribed temporal pattern. In particular, as an application of the proposed new methodology a computational platform is offered to analyze the generation and pharmacological modulation of theta rhythm related to anxiety is analyzed here in more detail.
Innovation in synthetic biology often still depends on large-scale experimental trial-and-error, domain expertise, and ingenuity. The application of rational design engineering methods promise to make this more efficient, faster, cheaper and safer. But this requires mathematical models of cellular systems. And for these models we then have to determine if they can meet our intended target behaviour. Here we develop two complementary approaches that allow us to determine whether a given molecular circuit, represented by a mathematical model, is capable of fulfilling our design objectives. We discuss algebraic methods that are capable of identifying general principles guaranteeing desired behaviour; and we provide an overview over Bayesian design approaches that allow us to choose from a set of models, that model which has the highest probability of fulfilling our design objectives. We discuss their uses in the context of biochemical adaptation, and then consider how robustness can and should affect our design approach.
Computational intelligence is broadly defined as biologically-inspired computing. Usually, inspiration is drawn from neural systems. This article shows how to analyze neural systems using information theory to obtain constraints that help identify the algorithms run by such systems and the information they represent. Algorithms and representations identified information-theoretically may then guide the design of biologically inspired computing systems (BICS). The material covered includes the necessary introduction to information theory and the estimation of information theoretic quantities from neural data. We then show how to analyze the information encoded in a system about its environment, and also discuss recent methodological developments on the question of how much information each agent carries about the environment either uniquely, or redundantly or synergistically together with others. Last, we introduce the framework of local information dynamics, where information processing is decomposed into component processes of information storage, transfer, and modification -- locally in space and time. We close by discussing example applications of these measures to neural data and other complex systems.
Depression has been associated with impaired neural processing of reward and punishment. However, to date, little is known regarding the relationship between depression and intertemporal choice for gain and loss. We compared impulsivity and inconsistency in intertemporal choice for monetary gain and loss (quantified with parameters in the q-exponential discount function based on Tsallis statistics) between depressive patients and healthy control subjects. This examination is potentially important for advances in neuroeconomics of intertemporal choice, because depression is associated with reduced serotonergic activities in the brain. We observed that depressive patients were more impulsive and time-inconsistent in intertemporal choice action for gain and loss, in comparison to healthy controls. The usefulness of the q-exponential discount function for assessing the impaired decision-making by depressive patients was demonstrated. Furthermore, biophysical mechanisms underlying the altered intertemporal choice by depressive patients are discussed in relation to impaired serotonergic neural systems. Keywords: Depression, Discounting, Neuroeconomics, Impulsivity, Inconsistency, Tsallis statistics
The Chem2Bio2RDF portal is a Linked Open Data (LOD) portal for systems chemical biology aiming for facilitating drug discovery. It converts around 25 different datasets on genes, compounds, drugs, pathways, side effects, diseases, and MEDLINE/PubMed documents into RDF triples and links them to other LOD bubbles, such as Bio2RDF, LODD and DBPedia. The portal is based on D2R server and provides a SPARQL endpoint, but adds on few unique features like RDF faceted browser, user-friendly SPARQL query generator, MEDLINE/PubMed cross validation service, and Cytoscape visualization plugin. Three use cases demonstrate the functionality and usability of this portal.
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