Computational models in systems biology

A report of the 6th International Conference on Computational Methods in Systems Biology, Rostock, Germany, 12-15 October 2008.One of the chief goals of systems biology is to build mechanistic mathematical models of biological systems to further the understanding of biological detail. Such models often aim at predicting the outcome of potentially interesting biological experiments, and if such predictions are confirmed by wet-lab observations, an important step forward is made. How exactly such models are constructed and how predictions are computed were at the core of a recent conference on Computational Methods in Systems Biology that brought 80 participants to Rostock, Germany (for conference proceedings see volume 5307 of Lecture Notes in Bioinformatics http://dx.doi.org/10.1007/978-3-540-88562-7).A simplistic approach to model construction might be to capture everything that is known about a system and simulate it in supercomputers. While this is appropriate for some systems, it is impossible or highly impracticable for many others. This is mostly due to the complexity of biological systems, which demand simplification to make them amenable to modeling. Such simplifications have to capture the essence of the processes of interest, while neglecting as many of the less important details as possible. Thus, one can consider model building in systems biology as the art of building caricatures of life: capture the essence, ignore the rest.     

Computational models in systems biology

A report of the 6th International Conference on Computational Methods in Systems Biology, Rostock, Germany, 12-15 October 2008.     

Ranked retrieval of Computational Biology models

Background  

The study of biological systems demands computational support. If targeting a biological problem, the reuse of existing computational models can save time and effort. Deciding for potentially suitable models, however, becomes more challenging with the increasing number of computational models available, and even more when considering the models' growing complexity. Firstly, among a set of potential model candidates it is difficult to decide for the model that best suits ones needs. Secondly, it is hard to grasp the nature of an unknown model listed in a search result set, and to judge how well it fits for the particular problem one has in mind.     

Computational analysis of models for cotransport

A well-characterized crude peroxisomal fraction from brown adipose tissue was used to compare peroxisomal beta-oxidation with beta-oxidation in isolated mitochondria. The apparent Km and chain-length specificity for peroxisomal (acyl-CoA) and mitochondrial (acyl-carnitine) beta-oxidation were determined with saturated C4-C22 fatty acyls and some unsaturated fatty acyls. Peroxisomes showed the lowest Km for medium-chain (9:0-10:0) and mono-unsaturated long-chain (16:1-22:1) fatty acids, and highest oxidation rates with lauroyl-CoA (12:0). Mitochondria showed the lowest Km for long-chain fatty acids (16:0-18:0) and highest oxidation rates with 12:0-16:0 and with 18:2. These in vitro results offer an explanation of previous results obtained in situ by Foerster et al. (Foerster, E.-C., F?hrenkemper, T., Rabo, U., Graf, P. and Sies, H. (1981) Biochem. J. 196, 705-712) and indicate a role for peroxisomes in degradation of medium-chain and mono-unsaturated long-chain fatty acids. It is concluded that no mechanism, other than relative preferences, needs to be suggested for channelling of fatty acids between the two subcellular organelles.     

Computational models of collective foraging.

In this paper the behaviour of a bee colony is modelled as society of communicating agents acting in parallel and synchronising their behaviour. Two computational approaches for defining the agents behaviour are introduced and compared. Their common features as well as the complementary aspects making them suitable for merging together into a more complex model.     

Computational models of cells and tissues: machines, agents and fungal infection

Computational models have been of interest in biology for many years and have represented a particular approach to trying to understand biological processes and phenomena from a systems point of view. Much of the early work was rather abstract and high level and probably seemed to many to be of more philosophical than practical value. There have, however, been some advances in the development of more realistic models and the current state of computer science research provides us with new opportunities through both the emergence of models that can model seriously complex systems and also the support that modern software can give to the modelling process. This paper describes a few of the early simple models and then goes on to look at some new ideas in the area with a particular application drawn from the world of mycology. Some general principles relating to how new and emerging computational techniques can help to represent and understand extremely complex models conclude the paper.     

On evaluating models in Computational Morphodynamics

Recent advances in experimental plant biology have led to an increased potential to investigate plant development at a systems level. The emerging research field of Computational Morphodynamics has the aim to lead this development by combining dynamic spatial experimental data with computational models of molecular networks, growth, and mechanics in a multicellular context. The increased number of published models may lead to a diversification of our understanding of the systems, and methods for evaluating, comparing, and sharing models are main challenges for the future. We will discuss this problem using ideas originating from physics and use recent computational models of plant development as examples.     

Computational models of plant development and form

The use of computational techniques increasingly permeates developmental biology, from the acquisition, processing and analysis of experimental data to the construction of models of organisms. Specifically, models help to untangle the non-intuitive relations between local morphogenetic processes and global patterns and forms. We survey the modeling techniques and selected models that are designed to elucidate plant development in mechanistic terms, with an emphasis on: the history of mathematical and computational approaches to developmental plant biology; the key objectives and methodological aspects of model construction; the diverse mathematical and computational methods related to plant modeling; and the essence of two classes of models, which approach plant morphogenesis from the geometric and molecular perspectives. In the geometric domain, we review models of cell division patterns, phyllotaxis, the form and vascular patterns of leaves, and branching patterns. In the molecular-level domain, we focus on the currently most extensively developed theme: the role of auxin in plant morphogenesis. The review is addressed to both biologists and computational modelers.     

Network mechanisms of grid cells

One of the major breakthroughs in neuroscience is the emerging understanding of how signals from the external environment are extracted and represented in the primary sensory cortices of the mammalian brain. The operational principles of the rest of the cortex, however, have essentially remained in the dark. The discovery of grid cells, and their functional organization, opens the door to some of the first insights into the workings of the association cortices, at a stage of neural processing where firing properties are shaped not primarily by the nature of incoming sensory signals but rather by internal self-organizing principles. Grid cells are place-modulated neurons whose firing locations define a periodic triangular array overlaid on the entire space available to a moving animal. The unclouded firing pattern of these cells is rare within the association cortices. In this paper, we shall review recent advances in our understanding of the mechanisms of grid-cell formation which suggest that the pattern originates by competitive network interactions, and we shall relate these ideas to new insights regarding the organization of grid cells into functionally segregated modules.     

Computational models of epileptiform activity in single neurons

A series of original computational models written in NEURON of increasing physiological and morphological complexity were developed to determine the dominant causes of epileptiform behavior. Current injections to a model hippocampal pyramidal neuron consisting of three compartments produced the sustained depolarizations (SD) and simple paroxysmal depolarizing shifts (PDS) characteristic of ictal and interictal behavior in a cell, respectively. Our results indicate that SDs are the result of the semi-saturation of Na+, Ca2+ and K+ active channels, particularly the CaN, with regular Na+/K+ spikes riding atop a saturated depolarization; PDS rides on a similar semi-saturated depolarization whose shape depends more heavily on interactions between low-threshold voltage-gated Ca2+ channels (CaT) and Ca(2+)-dependent K+ channels. Our results reflect and predict recent physiological data, and we report here a cellular basis of epilepsy whose mechanisms reside mainly in the membrane channels, and not in specific morphology or network interactions, advancing a possible resolution to the cellular/network debate over the etiology of epileptiform activity.     

Computational models of molecular self-organization in cellular environments

The cellular environment creates numerous obstacles to efficient chemistry, as molecular components must navigate through a complex, densely crowded, heterogeneous, and constantly changing landscape in order to function at the appropriate times and places. Such obstacles are especially challenging to self-organizing or self-assembling molecular systems, which often need to build large structures in confined environments and typically have high-order kinetics that should make them exquisitely sensitive to concentration gradients, stochastic noise, and other non-ideal reaction conditions. Yet cells nonetheless manage to maintain a finely tuned network of countless molecular assemblies constantly forming and dissolving with a robustness and efficiency generally beyond what human engineers currently can achieve under even carefully controlled conditions. Significant advances in high-throughput biochemistry and genetics have made it possible to identify many of the components and interactions of this network, but its scale and complexity will likely make it impossible to understand at a global, systems level without predictive computational models. It is thus necessary to develop a clear understanding of how the reality of cellular biochemistry differs from the ideal models classically assumed by simulation approaches and how simulation methods can be adapted to accurately reflect biochemistry in the cell, particularly for the self-organizing systems that are most sensitive to these factors. In this review, we present approaches that have been undertaken from the modeling perspective to address various ways in which self-organization in the cell differs from idealized models.     

Computational models of signalling networks for non-linear control

Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.     

Computational models of spatial updating in peri-saccadic perception

Perceptual phenomena that occur around the time of a saccade, such as peri-saccadic mislocalization or saccadic suppression of displacement, have often been linked to mechanisms of spatial stability. These phenomena are usually regarded as errors in processes of trans-saccadic spatial transformations and they provide important tools to study these processes. However, a true understanding of the underlying brain processes that participate in the preparation for a saccade and in the transfer of information across it requires a closer, more quantitative approach that links different perceptual phenomena with each other and with the functional requirements of ensuring spatial stability. We review a number of computational models of peri-saccadic spatial perception that provide steps in that direction. Although most models are concerned with only specific phenomena, some generalization and interconnection between them can be obtained from a comparison. Our analysis shows how different perceptual effects can coherently be brought together and linked back to neuronal mechanisms on the way to explaining vision across saccades.     

Computational method for muscle-path representation in musculoskeletal models

 This paper presents a new and efficient method to calculate the line-of-action of a muscle as it wraps over bones and other tissues on its way from origin to insertion. The muscle is assumed to be a one-dimensional, massless, taut string, and the surfaces of bones that the muscle may wrap around are approximated by cross-sectional boundaries obtained by slicing geometrical models of bones. Each cross-sectional boundary is approximated by a series of connected line segments. Thus, the muscle path to be calculated is piecewise linear with vertices being the contact points on the cross-sectional boundaries of the bones. Any level of geometric accuracy can be obtained by increasing the number of cross sections and the number of line segments in each cross section. The algorithm is computationally efficient even for large numbers of cross sections. Received: 9 July 2001 / Accepted in revised form: 11 March 2002     

Computational models for the prediction of polypeptide aggregation propensity

In amyloid fibrils, beta-strand conformations of polypeptide chains, or segments thereof, are perpendicular to the fibril axis, but knowledge of their three dimensional structure at atomic level of detail is scarce. Two types of computational approaches have been developed recently for investigating the aggregation propensity of peptides and proteins and identifying the segments most prone to form fibrils (hot spots). The physicochemical properties of the natural amino acids (e.g. beta-propensity, hydrophobicity, aromatic content and charge) have been used to derive phenomenological models able to predict changes in aggregation rate upon mutation, as well as absolute rates and hot spots. Applications of these models to entire proteomes have provided evidence that intrinsically disordered proteins are less amyloidogenic than globular proteins. In the second type of approach, amyloidogenic polypeptides have been decomposed into overlapping segments, and atomistic simulations of three or more copies of each segment have been performed to obtain insights into aggregation propensity and structural details of the ordered aggregates (e.g. turn regions).     

Computational models of temporal processing in the auditory thalamus

Previous work has shown that neurons in the medial geniculate body (MGB) of the echolocating bat, Myotis lucifugus, display response properties that are distinguishable from those of their afferents in the inferior colliculus (IC). Specifically, MGB neurons display phasic temporal discharge patterns, poor entrainment to trains of constant-amplitude sound pulses, and facilitated responses to amplitude-modulated trains of sound pulses (Llano and Feng 1999). In this study we used a modeling approach to examine the relative contributions of different known sources of inhibition on the temporal response properties of auditory thalamocortical neurons. We found that GABA_A-mediated post-excitatory inhibition resulting from coactivation of thalamocortical neurons and local inhibitory interneurons (in a triadic arrangement) is sufficient to reproduce many of the temporal response properties of MGB neurons. Addition of long-duration GABA_B-mediated inhibition gave the thalamocortical neuron temporal response characteristics that more closely resemble those seen in the experimental data. Neither recurrent inhibition from the thalamic reticular nucleus nor post-synaptic nonlinear mechanisms were necessary to reproduce the temporal transformations between the IC and MGB. This work suggests that feed-forward inhibitory circuitry, coupled with slow GABA_B-mediated inhibition, can emulate temporal information processing at the MGB. The transformation taking place in the MGB can be used to extract salient features from complex, time-varying stimuli, such as echoes returning from moving prey. Received: 11 August 1999 / Accepted in revised form: 5 April 2000     

Computational models of motivated action selection in corticostriatal circuits

Computational models of the basal ganglia have matured and received increasing attention over the last decade. This article reviews some of the theoretical advances offered by these models, focusing on motor and cognitive action selection, learning, and the interaction between multiple corticostriatal circuits in selection and learning.