David R. Gilbert

Approaches to the automatic discovery of patterns in biosequences.

This paper surveys approaches to the discovery of patterns in biosequences and places these approaches within a formal framework that systematises the types of patterns and the discovery algorithms. Patterns with expressive power in the class of regular languages are considered, and a classification of pattern languages in this class is developed, covering the patterns that are the most frequently used in molecular bioinformatics. A formulation is given of the problem of the automatic discovery of such patterns from a set of sequences, and an analysis is presented of the ways in which an assessment can be made of the significance of the discovered patterns. It is shown that the problem is related to problems studied in the field of machine learning. The major part of this paper comprises a review of a number of existing methods developed to solve the problem and how these relate to each other, focusing on the algorithms underlying the approaches. A comparison is given of the algorithms, and examples are given of patterns that have been discovered using the different methods.

Computational modelling of the receptor-tyrosine-kinase-activated MAPK pathway

The MAPK (mitogen-activated protein kinase) pathway is one of the most important and intensively studied signalling pathways. It is at the heart of a molecular-signalling network that governs the growth, proliferation, differentiation and survival of many, if not all, cell types. It is de-regulated in various diseases, ranging from cancer to immunological, inflammatory and degenerative syndromes, and thus represents an important drug target. Over recent years, the computational or mathematical modelling of biological systems has become increasingly valuable, and there is now a wide variety of mathematical models of the MAPK pathway which have led to some novel insights and predictions as to how this system functions. In the present review we give an overview of the processes involved in modelling a biological system using the popular approach of ordinary differential equations. Focusing on the MAPK pathway, we introduce the features and functions of the pathway itself before comparing the available models and describing what new biological insights they have led to.

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how qualitative descriptions are abstractions over stochastic or continuous descriptions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks.

Cell fate decisions are specified by the dynamic ERK interactome.

Extracellular signal-regulated kinase (ERK) controls fundamental cellular functions, including cell fate decisions. In PC12, cells shifting ERK activation from transient to sustained induces neuronal differentiation. As ERK associates with both regulators and effectors, we hypothesized that the mechanisms underlying the switch could be revealed by assessing the dynamic changes in ERK-interacting proteins that specifically occur under differentiation conditions. Using quantitative proteomics, we identified 284 ERK-interacting proteins. Upon induction of differentiation, 60 proteins changed their binding to ERK, including many proteins that were not known to participate in differentiation. We functionally characterized a subset, showing that they regulate the pathway at several levels and by different mechanisms, including signal duration, ERK localization, feedback, crosstalk with the Akt pathway and differential interaction and phosphorylation of transcription factors. Integrating these data with a mathematical model confirmed that ERK dynamics and differentiation are regulated by distributed control mechanisms rather than by a single master switch.

The Mammalian MAPK/ERK Pathway Exhibits Properties of a Negative Feedback Amplifier

Analysis of ERK pathway circuitry suggests appropriate targets for inhibition, providing a guide for drug development. Biological Circuits Inform Drug Development The mitogen-activated protein kinase (MAPK) pathway involves a three-tiered kinase module, which amplifies the signal. Many cells also have negative feedback loops from the last kinase in the module to various points upstream in the pathway. Sturm et al. showed that, with negative feedback loops, the MAPK module results in a system like that of a negative feedback amplifier (NFA), which is an engineering design that smoothens the output to changes in input and makes a system robust to change. These NFA-like properties may explain why some cells are sensitive to inhibition of the second kinase in the cascade (they lack feedback loops), whereas other cells are resistant to inhibition at this point (their feedback loops are intact). These results also have implications for drug development, because inhibitors that target components that are outside the NFA are more effective at inhibiting the pathway. Three-tiered kinase modules, such as the Raf–MEK (mitogen-activated or extracellular signal–regulated protein kinase kinase)–ERK (extracellular signal–regulated kinase) mitogen-activated protein kinase pathway, are widespread in biology, suggesting that this structure conveys evolutionarily advantageous properties. We show that the three-tiered kinase amplifier module combined with negative feedback recapitulates the design principles of a negative feedback amplifier (NFA), which is used in electronic circuits to confer robustness, output stabilization, and linearization of nonlinear signal amplification. We used mathematical modeling and experimental validation to demonstrate that the ERK pathway has properties of an NFA that (i) converts intrinsic switch-like activation kinetics into graded linear responses, (ii) conveys robustness to changes in rates of reactions within the NFA module, and (iii) stabilizes outputs in response to drug-induced perturbations of the amplifier. These properties determine biological behavior, including activation kinetics and the response to drugs.

When kinases meet mathematics: the systems biology of MAPK signalling

The mitogen activated protein kinase/extracellular signal regulated kinase pathway regulates fundamental cellular function such as cell proliferation, survival, differentiation and motility, raising the question how these diverse functions are specified and coordinated. They are encoded through the activation kinetics of the pathway, a multitude of feedback loops, scaffold proteins, subcellular compartmentalisation, and crosstalk with other pathways. These regulatory motifs alone or in combination can generate a multitude of complex behaviour. Systems biology tries to decode this complexity through mathematical modelling and prediction in order to gain a deeper insight into the inner works of signalling networks.

Representing and analysing molecular and cellular function using the computer.

Abstract Determining the biological function of a myriad of genes, and understanding how they interact to yield a living cell, is the major challenge of the post genomesequencing era. The complexity of biological systems is such that this cannot be envisaged without the help of powerful computer systems capable of representing and analysing the intricate networks of physical and functional interactions between the different cellular components. In this review we try to provide the reader with an appreciation of where we stand in this regard. We discuss some of the inherent problems in describing the different facets of biological function, give an overview of how information on function is currently represented in the major biological databases, and describe different systems for organising and categorising the functions of gene products. In a second part, we present a new general data model, currently under development, which describes information on molecular function and cellular processes in a rigourous manner. The model is capable of representing a large variety of biochemical processes, including metabolic pathways, regulation of gene expression and signal transduction. It also incorporates taxonomies for categorising molecular entities, interactions and processes, and it offers means of viewing the information at different levels of resolution, and dealing with incomplete knowledge. The data model has been implemented in the database on protein function and cellular processes ‘aMAZE’ (http://www.ebi.ac.uk/research/pfbp/), which presently covers metabolic pathways and their regulation. Several tools for querying, displaying, and performing analyses on such pathways are briefly described in order to illustrate the practical applications enabled by the model.

Motif-based searching in TOPS protein topology databases.

MOTIVATION TOPS cartoons are a schematic ion of protein three-dimensional structures in two dimensions, and are used for understanding and manual comparison of protein folds. Recently, an algorithm that produces the cartoons automatically from protein structures has been devised and cartoons have been generated to represent all the structures in the structural databank. There is now a need to be able to define target topological patterns and to search the database for matching domains. RESULTS We have devised a formal language for describing TOPS diagrams and patterns, and have designed an efficient algorithm to match a pattern to a set of diagrams. A pattern-matching system has been implemented, and tested on a database derived from all the current entries in the Protein Data Bank (15,000 domains). Users can search on patterns selected from a library of motifs or, alternatively, they can define their own search patterns. AVAILABILITY The system is accessible over the Web at http://tops.ebi.ac.uk/tops

A unifying framework for modelling and analysing biochemical pathways using Petri nets

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how qualitative descriptions are abstractions over stochastic or continuous descriptions, and show that the stochastic and continuous models approximate each other. A key contribution of the paper consists in a precise definition of biochemically interpreted stochastic Petri nets. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks.

TOPS: an enhanced database of protein structural topology

The TOPS database holds topological descriptions of protein structures. These compact and highly abstract descriptions reduce the protein fold to a sequence of Secondary Structure Elements (SSEs) and three sets of pairwise relationships between them, hydrogen bonds relating parallel and anti- parallel beta strands, spatial adjacencies relating neighbouring SSEs, and the chiralities of selected supersecondary structures, including connections in betaalphabeta units and between parallel alpha helices. The database is used as a resource for visualizing folding topologies, fast topological pattern searching and structure comparison. Here, significant enhancements to the TOPS database are described. The topological description has been enhanced to include packing relationships between helices, which significantly improves the description of protein folds with little beta strand content. Further, the topological description has been annotated with sequence information. The query interfaces to the database have been improved and the new version can be found at http://www.tops.leeds.ac.uk/.