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Dennis Bray (Dept of Zoology)
Do E. coli play dice? Deterministic
vs stochastic modelling.
Carl Jason Morton-Firth (Dept of Zoology)
23 October 1997
Response of simple neurones to random
and regular stimulation
Jianfeng Feng and David Brown (Babraham
Institute)
20 November 1997
The relationship between input and output of simple model neurones is currently a topic of interest amongst modellers, focussing on whether neurones use a firing rate code or not. The talk will outline some of our recent work relating input to output for some simple input patterns, and for some basic neuronal models: e.g. the leaky and non-leaky integrator and FitzHugh-Nagumo models.
Modelling the effects of surface
tension in the lung
Oliver Jensen (Dept of Applied Mathematics
and Theoretical Physics)
22 January 1998
The airways of the lung are lined with a thin layer of liquid, so that within the lung is a highly curved air-liquid interface with a huge surface area. Consequently, surface tension forces acting at this interface can have a major effect on the mechanics of respiration. This talk will provide a brief survey of some simple computational models used to understand the effects of elevated levels of surface tension (a major problem for very premature infants) and the role of surfactants (either natural or artificial) in reducing surface tension to healthy levels.
Walk: a stochastic simulation of
the G-protein cascade
Trevor Lamb (Dept of Physiology) and
Lucian Wischik (Computer Laboratory)
26 February 1998
Trevor Lamb will briefly summarise current knowledge of the molecular reactions in G-protein cascades of signal transduction. Such cascades underlie phototransduction, olfactory transduction, the B-adrenergic receptor system, and many other biological signalling systems. He will outline the requirements of a computer program to simulate the molecular interactions. Lucian Wischik will describe the realisation of a Windows-based program "Walk" that simulates the stochastic nature of the molecular interactions, and that provides a very friendly interface for the user.
Modelling retinal processing - is
information theory informative?
Simon Laughlin (Dept of Zoology)
19 March 1998
It is widely held that the function of the nervous system is to process information but Information Theory has done remarkably little to advance our understanding of neural function. I will use examples drawn from insect vision to demonstrate circumstances in which information theory is informative, in the sense that it tells us what neurons are doing and how well they are doing it. Although increasingly popular, the application of information theory is hardly a major growth area in contemporary neuroscience - why?
Molecular motors at work
Tom Duke (Cavendish Laboratory)
23 April 1998
Motor proteins are enzymes which use chemical energy, derived from ATP hydrolysis, to produce force and motion. How do they work? There is currently a concerted experimental effort to answer this question, using micromanipulation techniques to probe the action of individual molecules. I will describe stochastic simulations of motor proteins which help to interpret the experimental data and which indicate how large collections of enzymes may act together to drive muscle contraction.
Optimisation by evolution
Dennis Bray and Matthew Levin (Dept
of Zoology)
21 May 1998
Dennis Bray will describe a technique for optimising networks of reactions through an evolutionary strategy of mutation and selection, and show how this approach can be used to train a simple, model signalling pathway to respond in the desired way over a range of initial concentrations of ligand and also over timecourses involving single pulses of ligand. Matthew Levin will describe the successful application of this technique in simulating the formation of the ternary signalling complex that mediates the chemotactic response of coliform bacteria.
The theory and practice of modelling
sequence evolution
Ewan Birney (Sanger Centre)
18 June 1998
The ferocious pace of DNA sequencing in the genome projects has emphasised the need for fast and effective ways to characterize sequences. By far the fastest way to find function for a sequence is to show homology to an already characterized sequence using sequence similarity measures on a computer.
To produce an effective measure of sequence similarity one needs to model the evolution of biological sequences. In the methodology that I work in the models of evolution are made as probabilistic models that can be easily handled both theoretically - using principally Bayesian modeling methods - and computationally. In the talk I will describe how I go through the process of deciding on the probabilistic model to applying it in a large scale production environment. The real examples I will give will be comparing a protein domain directly to genomic DNA and comparing two pieces of genomic DNA to each other.
Computer modelling of the flagellar
motor
Richard Berry (Dept of Physics, University
of Oxford)
23 July 1998
I'll introduce the bacterial flagellar motor, review existing models, and discuss the pros and cons of different types of simulation, using a few of the models as examples.
Computational models of developing
neural systems: from growth cones to neuronal networks
Tim Hely (Centre for Cognitive Science,
University of Edinburgh)
20 August 1998
This talk introduces two computational models which simulate different aspects of developmental neurobiology. The first half of this talk will concentrate on a computational model of the cellular mechanisms underlying growth cone dynamics. The second half of the talk introduces a model of the emergent synchronization of spike firing which occurs during the development of neurons in culture.
During brain development a huge number of cells have to be organised together into the coherent neuronal network seen in the adult. In order to achieve this extensive wiring task each developing neuron creates a structure called the *growth cone*. The growth cone forms at the tip of the elongating axon (the neuronal output fibre) and guides the axon along an often complicated route to its target cells. On arrival at the target the growth cone remodels itself to form a synapse (neuronal connection). The talk introduces a new computational model of growth cone dynamics. The model shows how *microtubules* and *actin* proteins interact in the growth cone to control axonal elongation and turning.
The second half of the talk will concentrate on the phenomenon of *emergent synchronization* of spike firing during the development of neurons in culture. Initially the cells fire independently but gradually over a few weeks of development cells begin to fire simultaneously. The talk introduces a computational model which extends a mechanism initially put forward to explain the synchronization of firefly flashing. In the model the frequency and phase of cell firing is modified by the pattern of input signals received by the cell through local connections. This mechanism alone can result in synchronous oscillation of the entire network of cells.
It is hoped that both models will show that computational approaches to developmental biology can provide useful and often non-intuitive results.
Three colours red, white and blue:
what mechanisms drive ecological interactions?
Pej Rohani (Dept of Zoology)
17 September 1998
Mechanisms responsible for the irregular fluctuations observed in natural populations have been at the centre of a long debate in contemporary theoretical ecology. These irregular patterns were initially mostly attributed to environmental factors. In the mid-1970s, however, it was proposed that these fluctuations may be generated intrinsically by the underlying non-linearities in population processes. In recent years, the focus of this argument has turned increasingly towards the statistical properties of population fluctuations. Many of these studies show that ecological systems tend to be dominated by low-frequency or long-term dynamics, termed 'red' noise. Currently, the source of the 'redness' in ecological time-series is hotly debated, with the general consensus that environmental variables are the major driving force. In this talk, I will show that three classic laboratory populations which display irregular fluctuations also have reddened spectra, in the absence of environmental forcing. Furthermore, the dynamics of these populations show very well-defined generic scaling properties, in the form of power laws. These results imply that long-term influences in ecological systems may well be the product of intrinsic dynamics. I conjecture that ecological red noise may result from the interaction between demographic stochasticity and density dependence. I will also discuss how this work relates to recent non-linear phenomena in the physical sciences.
E-CELL: A generic software environment
for modelling and simulation of intracellular molecular processes
Tom Shimizu (Dept of Zoology)
22 October 1998
Genome sequencing projects and further systematic functional analyses of complete gene sets are producing an unprecedented mass of molecular information for a wide range of model organisms. This provides us with a detailed account of the cell with which we may begin to build models for simulating intracellular molecular processes to predict the dynamic behaviour of living cells. Previous work in biochemical and genetic simulation have isolated well-characterised pathways for detailed analysis, but methods for building comprehensive models of the cell that incorporate gene metabolism, regulation and signalling have not been established. The E-CELL project, initiated at Keio University in Japan, develops general-purpose software for building models of intracellular molecular processes based on gene sets, and simulating biological experiments. The E-CELL project so far has concentrated on modelling prokaryotic metabolism, and we have constructed a hypothetical model cell with a "minimal" metabolism, which has only 127 genes selected from the gene complement of Mycoplasma genitalium. In this talk, I will give a brief description of E-CELL, compare it with other biochemical simulation systems, and discuss our present results, as well as future applications.
Scaling and dynamically generated
variability in plant-pathogen systems
Adam Kleczkowski (Dept of Plant Sciences)
19 November 1998
A combination of chance and nonlinearity can produce unexpected and highly variable results in the transient behaviour of ecological and biological systems. Very often these transients are more important than the equilibrium behaviour (on which most of the work has concentrated so far). Thus, small differences in the initiation of epidemics can be magnified later in the season by the nonlinear character of the infection process. This can lead to large variability in and an apparent unpredictability of the disease spread. The variability becomes an important part of the dynamics that can and must be incorporated into the description and explained rather than removed from the analysis. The dynamics of the variability can occur at different levels of ecosystems, ranging from plant-microbes and plant-plant interactions through to ecosystems at a field and continent level. There has recently been a marked interest in the area of 'scaling-up' - predicting the behaviour at higher levels of ecosystem description from the knowledge of processes at lower levels. In particular, models are being developed to provide a bridge between interactions of individual plants (the scale at which most experimental work is done) and a population level (where the experiments are difficult to be carried over). While the models are relatively successful in predicting the mean behaviour, the link between the dynamics and the variability has still to be explored. Yet, it is the variability that is often affecting our perception of the system, with treatments aimed at maintaining diversity (as in conservation strategies) or reducing it (for example in order to obtain a uniform crop in horticultural practice).
Functional concerted motions of
proteins: analysis by the "essential dynamics" method
Pak-Lee Chau (Dept of Biochemistry)
17 December 1998
This work illustrates the method of "essential dynamics" in the study of protein motions. The large concerted motions in the apo/holo bovine serum retinol-binding protein were studied using crystal data, molecular dynamics simulation and "essential dynamics" analysis. Initially, concerted motions were calculated from conformational differences between various crystal structures. The dynamic behaviour of the protein in the configurational space directions, described by these concerted motions, is analysed. This reveals that the large backbone dynamics of the protein is not influenced by the presence of retinol. Study of free retinol dynamics and retinol in the retinol binding site reveals that the protein binds retinol in a favourable conformation, as opposed to what has been previously described for the bovine cellular retinol-binding protein.
Virtual zoology
Steven Grand - Creator of "Creatures"
(former Chief Technology Officer, Cyberlife Technology Ltd.)
4 February 1999
Alan Turing and Fibonacci phyllotaxis:
the first ever computer model in biology
Jonathan Swinton (Dept of Zoology
and King's College)
25 March 1999
Alan Turing is well known in mathematical biology for discovering the Turing instability, which generates pattern in reaction-diffusion systems, and as a pioneer in the development of the computer.
Less well known is that he spent the last few years of his life (1950-1954) using the new Manchester computer to generate solutions to reaction-diffusion systems and generating results which, though never published, have been preserved in the archives of King's. One problem he was trying to solve was the appearance of Fibonacci numbers in the structures of plants, and I will describe this problem and speculate about how far he succeeded with it.
The acetylcholine receptors: subunit
sequences and structures
Nicolas Le Novère (Institut
Pasteur, Paris, France)
29 April 1999
The nicotinic acetylcholine receptors are pentameric transmembrane proteins. The subunits are disposed symmetrically around a cationic pore. The equilibrium between opened and closed states is affected by the binding of ligands such as acetylcholine and nicotine.
The nicotinic receptor subunits are encoded by a multigene family, i.e. a group of genes descending from a common ancestor, and are hypothesised to share the same overall tri-dimensional structure.
Numerous subunits have been identified in the last two decades, most of them expressed in neurones. According to the recently completed Caenorhabditis genome, the diversity could be even more important than previously thought.
Such a diversity emphasises the importance of large-scale analyses, able to uncover essential features from noisy variability.
This lecture will present sequence analyses performed on the nicotinic receptor subunits, and the consequences they have had on the framework of nicotinic experimental work.
The study of evolutionary relationship between subunit genes will be first presented. In the second part, it will be shown how the wealth of homologous sequences can help to predict some structural features of the subunits.
Simulating the lytic-lysogenic switch
in phage l
Robert Andrews (European Bioinformatics
Institute)
20 May 1999
A computer-based simultation of the lytic-lysogenic decision in bacteriophage l has been built. The simulation uses information from the l sequence, as well as kinetic and thermodynamic data from phage experiments, to model l growth.
This work has involved three stages
of investigation:
(1) Building the model from what we
know - our knowledge of l
and its behaviour.
(2) Testing the model against what
we know - in vivo versus in silico analysis.
(3) Using the model to perform our
own experiments.
Analysis of DNA and protein sequences
by 2D pattern formation with coloration
Kenji Oosawa (Graduate School of Polymathematics,
Nagoya University, Japan)
29 July 1999
I will outline the method and desribe the results from searching for tandem repeats in the E. coli genome by using this method, some results from the application of this method to protein sequence analysis, and other possible applications. By using this method, we found about 50 tandem repeats with periods ranging from 30 to longer than 1200 nucleotides. In addition, some differences between coding and non-coding regions of cDNA sequence, and protein structural features, such as coiled-coil structure, globular and rod structures, were visualised.
A cellular-automaton approach to
modelling intracellular structures
Lois Le Sceller (University of Rouen,
France)
28 October 1999
It has recently become evident that bacteria are highly structured. Large intracellular structures probably exist comprising proteins and other molecules that interact within the structure to perform a particular function. To model the formation of these structures, I have written a program that models in 3-D the diffusion and localisation of proteins in the inner membrane and the cytoplasm of a cell. The program offers the prospect of the exploration of the range of parameters and their values required for the formation of structures in prokaryotic and eukaryotic cells.
Our complete DNA sequence, now in
sight: the analysis of the human genome
Tim Hubbard (Wellcome Trust Genome
Campus)
4 November 1999
Mathematical modelling of the eukaryotic
cell cycle
Béla Novák (Dept of
Agricultural Chemical Technology, Technical University of Budapest, Hungary)
20 January 2000
Metabolic control analysis
Guy Brown (Dept of Biochemistry)
17 February 2000
Metabolic control analysis is a form of sensitivity analysis for quantifying and explaining control and regulation properties of complex systems. Originaly it was used to quantify rate-limitation by different enzymes over the steady-state rate of metabolic pathways. Now the theory has been extended to analyze a wide-variety of control and regulation properties of organisms, cells, metabolic pathways, signal transduction pathways, enzyme reactions, chamical reactions, and computer models.
Discrete cell models in pattern
formation and wound healing
Jonathan Sherratt (Dept of Mathematics,
Heriot-Watt University)
23 March 2000
Biological cells are discrete objects, and yet, traditionally, most mathematical models for cell populations neglect this discreteness, and use continuum averages, leading to partial differential equations for cell densities. Although such models have been highly successful, it is increasingly clear that in a number of biomedical contexts, discrete cellularity plays a crucial role. I will discuss two such cases: juxtacrine pattern formation and scar tissue formation. Recent experimental data implicates direct cell--cell (`juxtacrine') communication as playing an important role in the epidermis. This occurs via growth factors that are bound in the cell membrane binding to receptors on neighbouring cells. I will show that mathematical modelling of this situation reveals counter-intuitive behaviour, in particular the formation of long-wavelength patterns. I will also discuss a discrete-cell computational model for scar tissue formation, which involves a complex interplay between cells and their environment. In this model, the movement of individual cells is represented within a continuous network of protein fibres. The model is able to represent in detail the scarring process, and makes new predictions on the potential for anti-scarring clinical therapies.
Reverse engineering a genetic regulatory
network
Hamid Bolouri (Science & Technology
Research Centre, University of Hertfordshire)
21 September 2000
Embryonic development of the pacific purple sea urchin embryo offers a unique opportunity for understanding genetic regulatory networks. The fully formed embryo is a free living organism, but is extremely simple: less than 1500 cells and a dozen cell types. Extensive experimental work over the past 150 years suggests that cell differentiation along the animal-vegetal axis of the embryo is primarily due to a relatively shallow genetic regulatory network activated by asymmetrically distributed maternal factors.
I will describe a collaborative project with Eric Davidson (Biology, Caltech) which aims to construct a network model of the above interactions. The project started by building a hypothetical network model that satisfies all observations reported in the literature. We are now carrying out detailed experiments using cDNA macroarray technology, gene regulatory domain sequence data, and artificial reporter gene constructs to quantify our hypothetical model.
In the process, we are discovering we need various computational aids not currently available. I will point to some of these needs and outline some of the tools we are developing.
Juxtacrine intercellular signalling
Nick Monk (Mathematical Modelling
and Genetic Epidemiology Group, University of Sheffield)
19 October 2000
Juxtacrine signalling, in which cells in close contact communicate via membrane-bound ligand and receptor, plays a significant role in many processes during metazoan development. I will review recent models of juxtacrine signalling in epithelial sheets, and then describe extensions to these models in which dynamic cell polarisation contributes to the signalling process.
Qualitative analysis of gene regulatory
networks
Matthieu Louis (European Bioinformatics
Institute)
14 December 2000
In Biology, regulation is mainly achieved
by complex networks comprising intertwined feedback loops. To study the
dynamical properties of regulatory systems, it is usually required to describe
the systems by models and to perform formal analyses. Up to now, several
modelling methods have been proposed. In this talk, the logical formalism
developed by the group of R. Thomas will be introduced. The application
of the logical formalism to simple gene regulatory networks will help us
to understand:
- How a model can be described in
terms of a set of logical equations.
- How a state table can be derived
from the logical equations.
- How the trajectories of the model
can be computed in the phase space.
In particular, the biological roles
of individual positive and negative feedback loops will be discussed.
Signal quality and cost-efficiency
in neurons
Gonzalo Garcia-De-Polavieja (Dept
of Zoology)
30 January 2001
Signal quality and cost-efficiency in neurons could be maintained by the underutilisation of the signals that are noisiest for each cell and by the underutilisation of the expensive signals, respectively. To test these two principles I have built a model that assumes a maximisation of the signal quality while maintaining cost-efficiency. The predictions of this model are shown to correspond to measurements in visual cortex neurons.
Cell-surface receptor clustering
Jacki Goldman (Computing Laboratory,
University of Kent)
20 March 2001
The erbB family of receptor tyrosine kinases can be important in the genesis of several common solid tumour types. It has been demonstrated that ligand binding induces clustering of these receptors on the cell surface, which (with the exception of erbB1), is not a precursor to internalisation. We wish to learn more about clustering as it may be important in signal transduction. I will describe a computer program which simulates two-dimensional Brownian motion and aggregation of receptor molecules. The data generated by these simulations may be useful in future for analysis of clustering behaviour under different conditions to aid in determining the characteristics of molecules which are important for clustering.
Integrating gene transcription,
molecular signalling and cell motion in computer models of development
Michel Kerszberg (Institut Pasteur,
Paris, France)
24 April 2001
I will present a computer program which attempts to integrate, in a fairly simple way, the effects of combinatorial gene transcription control, cell-cell signalling and cell motility in the solution of problems in developmental biology. By "fairly simple", I mean that a biologist, helped initially by someone reasonably conversant with C++ notation, might be able to use the program to enter a description of some experimental situation of interest and, by running the program, gain a better understanding of the biological problems involved. I will describe applications of the program to the propagation of morphogens, to neurogenesis, and to the segmentation of insects. I shall also invite suggestions as to how the program ought to evolve in the future.
Periodic haematological disease:
pathology, mathematical modelling and treatment
Michael Mackey (Centre for Nonlinear
Dynamics, McGill University, Montréal, Canada and University of
Oxford)
15 May 2001
There are a number of interesting periodic haematological diseases [Haurie et al. Blood (1998), 92, 2629-2640] and some are understood through mathematical modelling [M.C. Mackey. ``Mathematical models of hematopoietic cell replication and control", pp. 149-178 in The Art of Mathemtical Modelling: Case Studies in Ecology, Physiology and Biofluids (H.G. Othmer, F.R. Adler, M.A. Lewis, and J.C. Dallon eds.) Prentice Hall (1997)]. Cyclical neutropenia is one of these diseases. In this disorder, patients show oscillations of leukocytes, reticulocyte and platelet numbers with periods ranging from 18 to 40 days. This disease is most certainly due to a Hopf bifurcation in the haematopoietic stem cell compartment caused by an elevation of the rate of apoptosis.
This talk will focus on the insight into these diseases obtained from mathematical modelling, and the necessity to extend these models to the molecular level, e.g. to the regulation of apoptosis.
Molecular discrimination analysis
of purine nucleotide binding sites
James Smith (Unilever Cambridge Centre
for Molecular Informatics, Dept of Chemistry)
26 June 2001
The discrimination between possible drug receptors requires reliable methods to compare between different protein surfaces. Structural diversity within binding sites with similar catalytic activity has received little attention and almost no systematic analysis in relation to the problem of computer-aided drug design or receptor prediction. Previous studies have been unable to consider multiple sites from orthologues and paralogues simultaneously.
Systematic comparisons of binding sites can reveal the identification of discriminatory interactions. Conventional approaches exploit protein homology modelling namely the three-dimensional alignment and superposition of entire C-alpha backbones. However, this is limited to shape similarity and not local functionality; problems arise when considering binding sites with no obvious correspondence between atoms, or when the ligands have different binding modes and conformations.
Following a crystal survey of wild-type proteins bound to purine di- & tri- phosphate nucleotides, the ligand conformational approach provided an immediate tool for the discrimination of receptors according to their shape. The presentation will introduce a ligand-centric molecular similarity approach for the statistical classification of proteins. Superposed binding sites are processed after they have been divided unambiguously into ligand conformational groups using step-wise significance testing - a form of recursive partitioning. Incorporating parameterised inter-molecular contacts allows the scoring of energetically favourable interactions.
This work was developed in the former Drug Design Group, Department of Pharmacology, and recently submitted for a Ph.D. The subject areas in the presentation will include the exploitation of the growing number of protein crystal structures from the Protein Data Bank (http://www.rcsb.org/pdb/) and the comparisons of GTPase and ATPase binding sites. Conformationally derived motifs will also be introduced which are currently being evaluated for their ability to predict the shape of binding sites from other proteins independent of protein sequence similarity.
Computational biology of the dying
heart
Arun Holden (School of Biomedical
Sciences, University of Leeds)
24 July 2001
During the last few minutes of life, the rhythmic pumping of the heart is lost; the ventricular muscles no longer contract synchronously but fibrillate. This mechnical fibrillation is a consequence of a loss of order (arrhythmia) in the electrical signals controlling the heart muscle. In re-entrant arrhythmias, the same piece of ventricular tissue is repeatedly re-excited by the same wave of excitation, as a vortex of electrochemical activity in a stationary medium. Such re-entant arrhythmias are a major cause of premature death.
We model the electrical activity of single cardiac cells by high-order, stiff, ordinary differential systems, and the propagation of activity by linearly coupled cell models (in a coupled, ordinary-differential-equation lattice) or by partial differential equations of the reaction-diffusion type. The stiff, nonlinear reaction terms describe membrane excitability, and the linear diffusion terms the spread of voltage through the tissue. In such homogenous, isotropic excitable-media models, re-entry appears as a spiral wave in a two-dimensional medium, and as a scroll wave in a three dimensional medium. Heterogenities, anisotropy and medium motion produce movement and breakdown of these vortices. Although monodomain models are adequate for endogenous activity and arryhthmias, the effects of externally applied shocks (as applied by pacemakers or defibrillators) require bidomain models.
I will consider the effects of parametric heterogeneities observed by molecular mapping of the sinoatrial node (the pacemaker of the heart); the meander of spiral waves in homogenous, isotropic atrial and ventricular tissue, a speculative explanation for the relative lethality of arrhythmic episodes in the LQT1, LQT2 and LQT3 syndromes; and three-dimesnional, nonlinear wave behaviour during fibrillation. Where possible, computational results are related to experimental and clinical observations.
Computational modelling of physiology
using continuum models, with examples from the heart, lungs and musculo-skeletal
systems
Peter Hunter (Bioengineering Research
Group, University of Auckland, New Zealand)
18 September 2001
Modern medicine is currently benefitting both from the development of new genomic and proteomic techniques, based on our recently discovered knowledge of protein-encoding sequences in the human genome, and from the development of ever more sophisticated clinical imaging devices (MRI, microCT, ultrasound imaging, electrical field imaging, optical tomography, etc). This will mean that the clinical assessment of a patient's medical condition could, in the near future, include information from both diagnostic imaging and DNA or protein expression data. To relate these two ends of the spectrum, however, will require very comprehensive integrative mathematical models of human physiology based on patient-specific quantitative descriptions of anatomical structures and models of biophysical processes which reach down to the genetic level. This talk will discuss the use of continuum models in this so-called "Physiome Project" and give examples from the work at the University of Auckland on modelling the heart, lungs and the musculo-skeletal system.
How nematode sperm cells crawl
Alexander Mogilner (Dept of Mathematics
and Institute of Theoretical Dynamics, University of California, Davis,
USA)
16 October 2001
Motility of animal cells is fundamentally important and is the most striking process underlying the phenomena of wound healing, morphogenesis and cancerogenesis. Despite recent radical advances in cell biology and the biophysics of the motile cell, we still do not have a complete picture of how animal cells move across surfaces. One reason for this is that a huge variety of molecular mechanisms are involved in locomotion, which leads to a multiplicity and redundancy in force generation machineries and regulatory pathways. Theoretical modelling helps to search for truth in this situation.
Amoeboid motility, in all its forms save one, is associated with the actin cytoskeleton. The crawling sperm of nematodes are the exception. An intriguing aspect of nematode sperm motility is that these cells discard their actin-based cytoskeleton and deploy an entirely new motility machinery based on a major sperm protein. Nematode sperm offer at least one advantage for investigating principles of cell crawling: these cells are remarkably simple and dedicated entirely to locomotion, yet their migrating behaviour is essentially indistinguishable from that of actin-based cells.
We have constructed the computational
model of the sperm in two projections: a top and side view. This is because
a true 3-dimensional simulation is far more complicated than the two projections,
and except for its visual impact, probably doesn't carry much more information.
The computational model has several ingredients, or submodels, that determine
the forces and chemical signals which control the locomotion:
1. The protrusion forces at the leading
edge that push out the cell frontier.
2. The contractile forces near the
cell body that pull the cell forward.
3. The adhesion forces to the substratum
4. The pH gradient that determines
the zones of polymerisation and depolymerisation and contraction. Each
of these submodels determines a local behaviour which is then incorporated
into a computational subroutine and assembled into the model that describes
the global behaviour of the crawling sperm.
At the leading edge, MSP dimers assemble into linear polymers. These polymers are semi-flexible and tend to contract entropically. However, because the filaments are hydrophobic and basic, they tend to aggregate laterally into higher order fibres. This condensation process holds the individual filaments to a length longer than their rest length, which both pushes the cell membrane forward, and 'locks in' a tensile stress in the gel. That is, the energy of hydrophobic and electrostatic association is converted into a force of protrusion and tensile stress. Lower pH near the cell body leads to de-crosslinking of the fibres. Thus, at the rear the tensile stress is released later performing the work of pulling the cell forward.
We solve partial differential equations of the 1-D model in a side view analytically, and simulate 2-D finite elements model on a domain with a moving boundary of the cell in a top view numerically. The models are consistent with experimental data. They re-create sperm-like shapes, movements and forces and advance our understanding of the principles of cell locomotion.
Signal transduction and behavioural
response in E. Coli: a model system for understanding macroscopic
patterns from microscopic rules
Hans Othmer (Dept of Mathematics,
University of Minnesota, Minneapolis, USA)
20 November 2001
Chemotaxis in the bacterium E. coli is widely studied because of its accessibility and because it incorporates processes that are important in the response of numerous sensory systems to stimuli: signal detection and transduction, excitation, adaptation, and a change in behaviour. Quantitative data on the change in behaviour is available for this system, and the major biochemical steps in the signal transduction/processing pathway have been identified. In this talk, I will discuss a mathematical model of single cells that can reproduce many of the major features of signal transduction, adaptation and aggregation, and which incorporates the interaction of the chemotactic protein CheYp with the flagellar motor. I shall then address the problem of how to obtain macroscopic equations for population-level behaviour that incorporate certain features of the microscopic model.
A dynamic model for determining
the middle of E. coli
Karsten Kruse (Max Planck Institute
for Complex Systems, Dresden, Germany)
29 January 2002
Proper placement of the division septum is an essential part of bacterial cell division. In E. coli, this process depends crucially on the proteins MinC, MinD, and MinE. The detailed mechanism by which these proteins determine the correct position of the division plane is currently unknown, but observed pole-to-pole oscillations of the corresponding distributions are thought to be of functional importance. Here, a theoretical approach towards an explanation of this dynamical behaviour is reported. Emphasizing generic properties of the protein dynamics, two features are found to be sufficient for generating oscillations: first, a tendency of membrane bound MinD to cluster, and, second, attachment to as well as detachment from the cell wall, that depends on the amount of molecules already attached. The model is in qualitative agreement with the presently existing experimental results and further tests of the underlying model assumptions are suggested. Finally, based on the analysis of the model, a simple mechanism is proposed of how these proteins might initiate septal growth. In addition, to ensure correct positioning of the septum, the MinCDE complex could therefore also play an important role in cell cycle control.
Dissecting silicon mice: speech
recognition using spiking neurons
Seb Wills (Cavendish Laboratory)
26 February 2002
I will describe an artificial system capable of recognising spoken words. The system consists of a network of roughly 1000 integrate-and-fire neurons and a pre-processing unit. The network formed the winning solution to a competition set by John Hopfield in 2000. It has a vocabulary of 10 words, is trained on a single example of each word, and can recognise the words when spoken by a speaker other than that of the training example. The design of the network exploits the transient coincidence of several decaying quantities in a way which results in time-warp invariance, i.e. the ability to recognise words whether spoken slowly or quickly. It also makes use of the transient synchrony of collections of spiking neurons, a feature of many biological systems.
Morphogenetic algorithms
Richard Adams (Dept of Biology and
Biochemistry, University of Bath)
26 March 2002
The most striking feature of the development of multicellular organisms is their generation of form from a population of proliferating precursors. How cells reorganise to achieve this is a central problem in developmental biology. The zebrafish embryo provides us with an excellent model organism to study these events; it is transparent, so all of its cells can be visualised, and it develops rapidly so that significant periods of change can be followed continuously. We have used time-lapse microscopy to ask how cells reorganise during gastrulation and neurulation to form the earliest organs of the body. Tracking the movements of many hundreds of cells in parallel allows us to address firstly the question of how cells reorganise over time and by looking at how cell behaviours change in time and space, gives us clues about how they might generate forces to achieve this. In the future, a significant way to test these hypotheses will be to construct mechanically-realistic simulations of cell networks and ask if the rules we identify from our analyses can produce the emergent morphogenesis that we see in the embryo.
Feedback and cooperativity in T
cell activation
Cliburn Chan (Dept of Immunology,
Imperial College)
23 April 2002
The interaction between the T cell and antigen-presenting cell (APC) is central in the generation of an adaptive immune response. At the molecular level, the T cell receptor (TCR) recognises foreign peptide presented by a major histocompatibility complex (MHC) on the APC. This interaction has been demonstrated experimentally to be an extremely sensitive, specific and reliable process, despite the fact that ligand (i.e., peptide-MHC) binding to the TCR occurs in a noisy background and is a stochastic, low-affinity event lasting only a few seconds. I discuss some problems with the standard model used by immunologists to explain this, and how an alternative model for TCR activation based on feedback might be more useful for explaining TCR specificity, as well as provide a framework for understanding biochemical signalling networks. Coupling a population of these individual TCR models allows a Monte Carlo simulation of recently discovered signalling cross-talk between receptors. This reveals that the specificity of T cell ligand discrimination can be further enhanced with such cross-talk.
Modelling stem cell clusters in
the epidermis
Nick Savill (Dept of Mathematics,
Heriot-Watt University, Edinburgh)
7 May 2002
The skin is renewed by cell proliferation in the basal layer of the epidermis. This layer of cells consists of three basic cell types: stem, transit amplifying and postmitotic cells. Stem cells can divide indefinately. These cells can differentiate into transit amplifying cells that divide for about 3-5 generations before differentiating into postmitotic cells that migrate from the basal layer and up through the epidermis until they are finally shed at the skin surface. It has recently been shown that the stem cells form small clusters surrounded by a network of transit and postmitotic cells. The regulation of division and differentiation in these clusters is only just beginning to be understood; cell-cell signalling via the Delta-Notch mechanism seems to play an important role. In this talk, I will present preliminary theoretical and simulation work that looks at which mechanisms may be important in keeping these stem cell clusters stable in a dynamic environment of cell division, differentiation and migration.
The evolution of personality differences
Rufus Johnstone (Dept of Zoology)
18 June 2002
Humans and other animals display distinct personality profiles. In other words, individuals of a given species exhibit differences in behaviour that are consistent throughout life, and that cut across age, sex and size classes. Adaptive explanations for these differences are lacking. Game-theoretical models do provide an explanation for the maintenance of behavioural variation, in terms of frequency-dependent selection of alternative tactics - e.g. the classic 'Hawk-Dove' game can account for variation in aggressiveness - but do not explain the evolution of consistent differences between individuals. I will argue that it is social interaction that drives the evolution of personality differences. I develop an extension of the Hawk-Dove game in which individuals may observe fights between others, and adjust their own behaviour in response to the previous history of an opponent. I show that under these circumstances, any variation in individual aggression, however slight, is sufficient to favour individuals that attend to the past behaviour of opponents. Such social sensitivity, in turn, favours greater inter-individual variation in aggression. This positive feedback drives a population towards a polymorphic equilibrium featuring consistently aggressive and cautious individuals. I conclude that consideration of the social environment in which agonistic interactions occur can provide an adaptive explanation for the evolution of distinct personality types.
Ion and water transport in the lens
Stephen Baigent (Centre for Non-linear
Dynamics and Its Applications, University College London)
30 July 2002
In the interests of maintaining a high refractive index, the inner fibre cells of the avascular lens are packed tightly together and lack the usual complement of organelles. To ship nutrients and waste products in and out, the lens uses a network of passive and active transport mechanisms, metabolically driven in part by the lens surface epithelial cells. When this network fails, the lens homeostasis can be severely challenged, and can lead to structural damage, such as osmotically induced cell rupture. Often the lens can survive a single challenge, but falls to multiple challenges. As a first step in a study of how the lens responds to various injuries, I am extending the basic continuum model for lens transport of Rick Mattias to incorporate more biophysically detailed descriptions of the transport network components, as well as their highly localised distributions. I will present the lens model, some example computations, and outline planned work.
Molecular puzzle of how bacteria
guzzle
Tom Shimizu (Dept of Zoology)
20 August 2002
Hungry bacteria are "clever" enough to swim towards food and away from toxins in their environment. The remarkably simple biochemical pathway that mediates this response is arguably the best understood cell signalling system so far studied. However, even though all the components have been identified, sequenced and kinetically characterised, models still fail to reproduce the quantitative behaviour of the living cell satisfactorily. These discrepancies highlight the limits of both our current knowledge and accepted biochemical formalisms. In this talk, I will describe our attempts to shed light on some of the unsolved puzzles in bacterial chemotaxis by focusing on the role that spatial organisation of molecules in the cell might play in the pathway. In this regard, my own work has concentrated on a plausible, though as yet unverified, consequence of the clustering of receptors in the membrane - a phenomenon that has only only come to light during the past decade. I will concentrate on three puzzles whose origins and solutions are thought to lie within this particular spatial structure: (i) how bacteria achieve their exquisite sensitivity to substances in their environment, (ii) how the component proteins of the receptor cluster are arranged in space, and (iii) how the movement and activity of two other components of the pathway may be affected not only by the spatial arrangement of the receptors themselves but also by specific aspects of their structure.
Validating drug targets in silico:
a role for control analysis and computer simulation
David Fell (School of Biological &
Molecular Sciences, Oxford Brookes University)
24 September 2002
Genomics has led to the identification of too many potential new targets for drugs than it is feasible to pursue, and a major problem in drug development is how to choose the best candidates for further investigation. One problem when inhibiting a metabolic or signal transduction pathway is that even when an enzyme is an essential component, the drug dose required to inhibit the pathway is far higher than expected from the affinity of the drug for the enzyme. Metabolic control analysis offers a theoretical framework for understanding this, and for characterizing the targets with the highest potential. Similar principles apply in signal transduction, as will be illustrated with a computer simulation of the EGF pathway that successfully predicts the unexpected effects of a candidate drug. The potential and challenges for in silico development of therapies will be discussed and illustrated.
Studying the balance of forces in
the mitotic spindle with computer simulations
François Nédélec
(EMBL, Heidelberg, Germany)
5 November 2002
For their division, eukaryotic cells need to produce opposite forces on each pair of sister chromatins to ultimately segregate them. These forces are applied through a structure, called the mitotic spindle, made of chromosomes, microtubules and many other proteins of the cytoskeleton. The spindle is not a static structure but rather a dynamic steady state which can however pull with continuous forces on the chromosomes. Essential to the self-organization of the spindle are the molecular motors, which can bind and move on the microtubules. I have used simulations to explore if a dynamic equilibrium can be produced solely by motor proteins between two asters of microtubules. Computers are used to systematically explore the space of reasonable parameter values, and yield several possible ways to build an equilibrium. With the kind of motors that are found, microtubules will automatically organize into a stable and sustained equilibrium with great internal tension.
Ref: Computer simulations reveal motor properties generating stable anti-parallel microtubule interactions, to appear in the Journal of Cell Biology, September 2002.
Diffusion and reaction - complex
dynamics from simple processes
Steve Andrews (Dept of Zoology)
10 December 2002
A tremendous amount of biochemistry is based on nothing more than diffusion and on the reversible binding of molecules. This talk will explore some of the interesting dynamics that arise from these processes, focusing on the E. coli chemotactic receptor cluster. The cluster forms through the aggregation of receptors - proteins that diffuse in the two dimensional inner membrane of the cell. Even when this aggregation has reached equilibrium, there are wide varieties of cluster sizes and shapes. The bacterium detects extracellular aspartate (an attractant) through its reversible binding to these receptors. Because of the clustering, any molecule of aspartate that is detected once is usually detected several more times, before the molecule finally diffuses away. Meanwhile, cytosolic proteins are also binding repeatedly to the inside of the receptor cluster. This complex interplay of diffusion and reversible binding leads to biochemical noise, a type of chemical memory, and spatially heterogeneous binding patterns.
Mechanics of biomolecular assemblies
L Mahadevan (Dept of Applied Mathematics
and Theoretical Physics)
18 February 2003
The borders between atomic phenomena and macroscopic processes pose many interesting challenges in understanding the coupling between structure and function in biology. In the context of the mechanical behaviour of the cytoskeleton, treated at a collective level, I will discuss some experimental and theoretical aspects of force generation in two actin-based systems: (1) polymerisation-driven motion in Listeria monocytogenes and (2) polymorphism-driven motion in the acrosome of Limulus polyphemus sperm.
From genes to patterns: developmental
and genetic implications of the dynamic structure of genetic networks
Pablo Padilla (Centre for Mathematical
Biology, University of Oxford)
18 March 2003
One of the main problems in developmental
biology is the precise understanding of pattern formation in terms of the
structure of the genetic network. We present a methodology which allows
us to construct a dynamical system given a genetic network. We show that
the dynamic structure has definite
developmental and morhpogenetic implications. The case of the subnetwork
responsible for the flowering process in Arabidopsis thaliana is
studied in detail.
Molecular limits to wiring density
in the brain
Aldo Faisal (Dept of Zoology)
15 April 2003
The small diameter and high density of neurons in brains suggest that, as in electronics, miniaturisation improves efficiency. I developed a stochastic neural simulator to show how random fluctuations in signalling proteins limit miniaturisation in the nervous system. Neurons communicate by sending a voltage pulse, the action potential (AP), along specialised signalling cables, axons. The AP is mediated by the concerted action of protein molecules, so called voltage-gated ion channels, that open and close to control ion flow across the axon membrane. Thermodynamic fluctuations in the molecular conformation of ion channels lead to random changes in transmembrane current, called channel noise. I modelled unmyelinated axons and find that channel noise is able to generate spontaneous APs in very fine axons. These spontaneous APs degrade communication, like letters inserted randomly in an email transmission. I find that spontaneous AP rate increases exponentially at about 0.1 micron diameter. This critical diameter is set by the physical properties of an axon’s basic components (protein, bilipid-membrane and cytoplasm). Reviewing studies from widely different species and taxa I find a common minimum axon diameter at 0.1 micron. This suggests that channel noise limits the wiring density of the brain.
Cells in telecommunications
Richard Tateson (Intelligent Systems Lab, BTexact)
20 May 2003
There are many examples of the natural world providing inspiration for human engineers and designers. Cell biology is one branch of the natural sciences which has not yet been widely exploited in this way, but which has great potential for application, particularly in the telecommunications area. The features of cells correspond strikingly well to some of the challenges in current engineering and design for telecommunications systems. The autonomy, evolution, adaptivity and self-organisation of cells are all desirable for the complex, dynamic and geographically distributed networks we are now constructing and using.
Three examples of current research illustrate how analogies from cells can lead to radically different telecommunications systems. Cell-to-cell interaction in fruitfly development has inspired a new, decentralised approach to managing mobile phone networks. Morphogenetic events in early embryos point to new design methods which add depth to the established, and also biologically-inspired, techniques of evolutionary optimisation. Genetic control pathways in bacteria inspire implicit learning techniques which allow individual 'cells' in simulation to discover adaptive behaviour without an explicit definition of "fitness".FitzHugh-Nagumo models.
Signalling at the synapse: too noisy
to think?
Upinder Bhalla (National Centre for
Biological Sciences, Bangalore, India)
1 July 2003
Many critical signalling molecules at the synapse are present in small numbers. We have analyzed computationally what may happen to typical signalling pathways at these small volumes, both in isolation and in networks. Not surprisingly, there are many effects of stochasticity both in terms of steady state and also dynamic computation. Not all these effects lead to degradation of the response. In particular, I report the phenomenon of stochastic amplification, similar to stochastic resonance, that actually improves tuning to input patterns. We have performed hippocampal slice recording experiments to test mass-action and stochastic predictions of synaptic computations in the time domain. These experiments provide some support for predicted temporal computation mechanisms, and may further refine the role of specific pathways. Some of our findings may be consistent with a role for stochastic amplification in synaptic change.
Gene dosage sensitivity and genome
evolution
Balázs Papp (Dept of Plant
Taxonomy and Ecology, Eötvös University, Budapest, Hungary)
26 August 2003
Several lines of evidence suggest that an altered balance in the concentrations of subunits of a stoichiometric protein complex can be harmful. Our analysis of recent large-scale fitness measurements of yeast deletion mutants supports this idea. We find that both underexpression and overexpression of genes are more likely to be deleterious if the encoded proteins are subunits of protein complexes. Although numerous different molecular mechanisms can be envisaged to explain the pattern, the generality of any of these mechanisms remains to be seen. However, given this source of dosage sensitivity, we expect adaptations at the level of both transcriptional and post-transcriptional regulation to minimize the degree of imbalance. By taking a genomic approach in yeast, we show indeed that the strength of transcriptional co-regulation of interacting subunits reflects their dosage sensitivities. A number of other putative cellular adaptations against imbalance are also discussed. Moreover, if enhanced gene dosage of a given protein is harmful, then single gene duplication, increasing dosage, is likely to be counter-selected in the short term. Hence, dosage sensitivity might affect the size of gene families and therefore constrain genome evolution. As expected, we find that members of large gene families are rarely involved in protein complexes. Furthermore, we present evidence that the gene copy number of interacting subunits co-evolve.
Induction of specificity as a mechanism
for the development of topographically ordered maps of nerve connections
David Willshaw (Institute for Adaptive
and Neural Computation, University of Edinburgh)
16 December 2003
The discovery of Eph receptors in the vertebrate retina and their associated ligands, the ephrins, in the optic tectum or superior colliculus, provides new constraints for contemporary models of the mechanisms for the formation of patterned neural connections.
In this talk I show what happens when the model for the formation of retinotectal nerve connections by means of the induction of molecular markers from retina onto tectum (developed originally by myself and Christoph von der Malsburg) is brought up-to-date.
I will consider three issues:
1. How ordered connections can form between two two-dimensional arrays of cells, which themselves are developing as the connections are being formed
2. How the basic model can be adapted to deal with the induction of counter-gradients as implied by recent experiments on Eph/ephrin interactions in the visual system.
3. The development of various types of map in genetically altered visual systems.
Providing a specific model at this level of detail enables predictions to be made of the distribution of Ephs/ephrins over the retina and the tectum, for any given map of connections observed.
Simplifying complexity with modular
regulation analysis
Keira Curtis (Dept of Clinical Biochemistry)
27 January 2004
Modular regulation analysis is a subset of metabolic control analysis. The approach involves grouping components such as enzymes together into reaction blocks or modules. The coefficients of control analysis then apply to the module as a whole. Modular regulation analysis can be used to find and quantify the different pathways by which a response is produced. This has many potential applications, such as finding drug targets. The approach has been used to look at, among others, mitochondrial metabolism, cell signalling and gene expression.
I have been applying modular regulation analysis to microarray data, in order to find and quantify mRNAs that are important for biological responses such as growth. The system is first simplified, by grouping genes with similar expression into clusters. How a stimulus (e.g. addition of a drug or nutrient, or a change in growth conditions) affects gene expression is described using integrated response coefficients. How gene expression affects the response (e.g. metabolite concentration, enzyme rate, growth rate) from the system is described using elasticity coefficients. The product of these coefficients describes how much of the response to the stimulus is mediated through each mRNA cluster.
Subcellular protein localisation
in bacteria: diverse mechanisms for precise positional targeting
Martin Howard (Dept of Mathematics,
Imperial College)
24 February 2004
I will discuss the physical principles lying behind the acquisition of accurate positional information in bacteria. A good application of these ideas is to the rod-shaped bacterium E. coli which divides precisely at its cellular midplane. This positioning is controlled by the Min system of proteins: MinC, MinD, and MinE. These proteins coherently oscillate from end to end of the bacterium. I will present a reaction-diffusion model that describes the diffusion of the Min proteins, and their binding/unbinding from the cell membrane. The system possesses an instability that spontaneously generates the Min oscillations, which then control the accurate placement of the midcell division site. I will then discuss the role of fluctuations in protein dynamics, and examine the extent to which fluctuations can set optimal protein concentration levels. Finally I will examine cell division in a different bacteria, B. subtilis. Although two of the three proteins involved are the same as in E. coli, quite different physical principles are used to regulate protein localisation.
Ab initio conformational sampling
for protein structure determination and prediction
Mark DePristo (Dept of Biochemistry)
30 March 2004
I describe a program, called rapper, that couples an ab initio conformational sampling engine for polypeptides to a general restraint satisfaction system that incorporates extensive knowledge of protein structure. The sampling engine employs a novel algorithm based on a multi-start tree-pruning technique. A diverse range of restraints is supported, from local restraints such as ideal geometry, fine-grained phi/psi state sets, and side chain rotamer libraries to global restraints such as hard-sphere excluded volume, compatibility with a protein fold, and consistency with an experimental electron density map. rapper has been successfully applied to model loop conformations, to regenerate all-atom models from limited structural information, to sample neighbouring conformations of a particular structure, to build homology models, to assess the accuracy of X-ray crystal structures, and finally for automated model building and refinement in X-ray crystallography.
Consciousness in brains - and in
computers?
Rodney Cotterill (Dept of Physics,
Technical University of Denmark)
27 April 2004
There is much speculation, these days, about whether and when there will be conscious computers. Some feel that this is premature, given that science has not even produced a definition of consciousness. There may be major surprises in store for those studying the subject, and it will be suggested that one of these could involve doing away with a paradigm that has been virtually unchallenged since the time of Aristotle: the stimulus-response paradigm. I will suggest an alternative approach, and discuss whether it is likely to open the way to decisive progress with the issue.
Towards a unified stochastic systems
biology
Johan Paulsson (Dept of Applied Mathematics
and Theoretical Physics)
18 May 2004
All life processes directly or indirectly depend on molecules present in low numbers per cell. The resultant 'noise' can randomise developmental pathways, disrupt cell cycle control or force metabolites away from their optimal levels. It can also be exploited for non-genetic individuality or even for more reliable and deterministic control. The first part of the talk will review recent progress in the field, and show how the different studies can be unified by the Fluctuation-Dissipation Theorem. The second part will focus on how homeostatic feedback loops deal with different types of fluctuations, and how efficiently suppressing one type necessarily amplifies others, similarly to robust-yet-fragile phenomena in control theory. Finally, I will discuss how cells solve this problem using noise-suppression-by-noise schemes, double-layered feedback loops, and molecular senescence. Examples are chosen from gene expression, metabolism and replication control.
Role of multiple molecular motors
and poleward flux in anaphase
Alex Mogilner (Dept of Mathematics
and Center for Genetics and Development, University of California, Davis,
USA)
8 June 2004
During mitosis, tubulin subunits within microtubules (MTs) move from the equator to the spindle poles, in a process termed poleward flux. The precise role of this flux is unknown. We develop a quantitative description of the relationship between spindle pole dynamics, poleward flux and MT-MT sliding within interpolar MT bundles during anaphase B. To test the idea that a switch from poleward flux to MT-MT sliding within ipMT bundles is responsible for activating anaphase B spindle elongation, we experimentally inhibited the flux-to-sliding switch that normally occurs at anaphase B onset and observed a corresponding inhibition in the rate of spindle elongation. The form and variance of the data obtained are concordant with a quantitative force-balance model according to which KLP61F motors generate MT-MT sliding at spindle equator, and KLP10A motors depolymerize MTs at the spindle poles, while KLP3A motors play a role of organizing ipMT bundles and indirectly regulating the flux-to-sliding switch.
How microtubule dynamics are regulated
during mitosis: integrated computational and fluorescence microscopy studies
of budding yeast mitosis
David Odde (Dept of Anatomy)
27 July 2004
The self-assembly and disassembly dynamics of microtubules (MTs) are central to the proper segregation of chromosomes during mitosis. In particular, a so-called kinetochore microtubule (kMT) physically associates with a chromosome via its plus end to then mediate chromosome movement, coupled to the addition and loss of tubulin subunits from the kMT plus end. Given its importance to mitotic chromosome movement, we asked whether tubulin addition and loss from kMTs is regulated in any way. To address this question we developed a Monte Carlo simulation of the kMT dynamics assuming that they obey "dynamic instability", the stochastic biphasic switching from a persistent assembling state to persistent disassembling state ("catastrophe") and back again ("rescue"). With this model we could predict the distribution of kMT plus ends, which was then compared to the observed distribution obtained by fluorescence microscopy of budding yeast that express a GFP fusion of a key kinetochore component (Cse4p). We found that simple dynamic instability failed to account for the observed distribution, regardless of the parameter values. Instead, we found that kMT dynamics are influenced by two phenomena: 1) catastrophe that increases with increasing distance from a pole (i.e. a "catastrophe gradient") and 2) rescue that increases with increasing tension between sister kinetochores. We speculate that the catastrophe gradient originates from a pole-bound kinase antagonized by a nucleoplasmic phosphatase, that both operate on a kMT assembly regulator whose activity is dependent on its phosphorylation state. We further speculate that the tension-dependent rescue effect is at least partially mediated by physical constriction of the kinetochore around the kMT to promote protofilament straightening. Together, these two phenomena enable the characteristic bi-oriented spindle to form, and explain how tension is generated consistently across all sister chromatid pairs, which is an important characteristic of proper spindle assembly used by the spindle checkpoint. The two phenomena also serve to illustrate general mechanisms of MT-mediated intracellular morphogenesis where spatial gradients in MT regulation control the orientation of the MT array.
In silico dynamics of biological
networks
Lukasz Salwinski (Institute for Genomics
and Proteomics, Univerisity of California, Los Angeles, USA)
29 September 2004
Biological regulatory systems are composed of a large number of simple modules linked together to form complex networks capable of reacting to diverse stimuli. Individual elements of these networks - the numerous molecules and molecular complexes within a cell - perform simple computational tasks, such as amplification or integration of a signal, whereas the complexity of the response is the result of the structure and dynamics of the entire network. In order to fully understand and predict the behaviour of such networks, efficient simulation algorithms are reqired.
Realistic simulation of biological networks requires computationally expensive stochastic approaches, because of the small number of molecules in cells. The high computational cost of stochastic simulation on conventional microprocessor-based computers arises from the intrinsic disparity between the sequential nature of a microprocessor program and the highly parallel nature of the information flow within biochemical networks. This disparity is reduced with the Field Programmable Gate Array (FPGA)-based approach. The parallel architecture of FPGAs, which can simulate the basic reaction steps of biological networks, can attain simulation rates at least an order of magnitude greater than currently available microprocessors.
Modelling cell homeostasis: how
cells regulate their intracellular environments
Virgilio Lew (Dept of Physiology)
26 October 2004
All cells have the capacity to regulate their intracellular environments, a function referred to as cellular homeostasis. Homeostatic control is implemented by the combined performance of membrane transporters, cell buffers, soluble proteins, and regulatory molecular ensembles. Homeostatic control is thus a complex cell function which involves the combined operation of many cell components, even in the simplest of cells.
In recent decades, much information has been gathered about the molecular nature and kinetic modality of the homeostatic components present in many diverse cell types. However, this information is not sufficient for understanding cell homeostasis and for predicting how cells would react to physiological or pathological stimuli because homeostasis inherently involves the integration of numerous and diverse cellular mechanisms, on a complexity scale beyond intuitive grasp. By the late seventies, confusion in this field made it clear to us that the development of integrated mathematical models of cell and epithelial homeostasis was a clear necessity. In this talk I will describe our pioneering efforts in this field, and will illustrate the results with three examples in which the application of integrated homeostatic models proved critical to resolve long-standing issues on epithelial function, on the mechanism of sickle cell dehydration and on the strategy applied by malaria parasites to prevent the lysis of the host cell during their asexual reproduction cycle.
Modelling and image understanding
for biological development: the case of a plant shoot meristem
Eric Mjolsness (Institute for Genomics
and Bioinformatics, Univerisity of California, Irvine, USA)
29 March 2005
The Computable Plant project is a systematic effort to advance the understanding of the shoot apical meristem (SAM) of Arabidopsis thaliana through imaging and computational modelling of developmental processes. Interesting and generic mathematical problems arise within the computational approach. For example, to quantify the growth of the SAM and its cell lineages requires tracking multiple features in 3D image sequences; we approach this problem through nonlinear optimization. Also, fitting the resulting data to dynamical models requires a flexible modelling framework for coupled mechanical and regulatory networks. For these problems we develop a mathematical foundation based on the use of a "dynamical grammar" capable of representing discrete-time events such as cell division that change the number of objects and their relationships, as well as continuous-time processes arising from regulatory networks and mechanical interactions. The resulting algorithms are being used to assist experimental research on mechanisms of meristem maintenance and phyllotaxis.
Theoretical models for understanding
the development of retinal mosaics
Stephen Eglen (Dept of Applied Mathematics
and Theoretical Physics)
19 April 2005
The vertebrate retina contains around five major cell classes, and each class is divided into many different functional types. The cell bodies of many types of retinal cell are arranged in semi-regular patterns across the retina, presumably to ensure that the visual field is efficiently sampled and that there are no "holes" in visual space. In this talk I will use computational models to investigate the contribution of different developmental mechanisms (including lateral migration, cell fate and cell death) upon cellular positioning in the retina. I will also compare the usefulness of phenomenological and mechanistic models in this area.
Epitheliome: an agent-based model of epithelial cells
Dawn Walker (Dept of Computer Science, University of Sheffield)
17 May 2005
Traditionally, computational models in biology consist of sets of differential equations that represent the averaged behaviour of the system, such as chemical reactions in intracellular signalling pathways or population growth in cells and organisms. These models are usually efficient to solve, but are adequate only when the behaviour of individual components of the system, such as cells or proteins, are not of interest.
We have developed Epitheliome, an agent-based model of epithelial growth and regeneration which allows the granularity of the tissue to be resolved at the single cell level. Each biological cell is represented by an individual software agent that changes its state (e.g. cell cycle position, number of bonds) according to a number of pre-programmed rules. Geometrically, cells are represented as ellipsoids that exert repulsive forces on one another to prevent overlap. This model has previously been applied to simulate growth and wound healing in urothelial cell monolayer cultures with varying levels of exogenous calcium. We have now extended the model to represent the behaviour of keratinocytes by including new rules to simulate features such as the differentiation and stratification of cells.
The results of our simulations give a good qualitative fit with those obtained from in vitro experiments on urothelial cells and keratinocytes, demonstrating that it is possible to simulate the behaviour of different cell types simply by changing rule sets and specific model parameters. This simple proof-of-concept model is totally extensible in that existing rules can be replaced with more sophisticated models of intracellular events such as signal transduction and changes in gene expression. We are currently extending Epitheliome to incorporate a more sophisticated biomechanical model of cell behaviour, as well as a number of critical signalling pathways.
Quantitative analysis of signal
transduction in bacterial chemotaxis
Victor Sourjik (ZMBH, University of
Heidelberg, Germany)
7 June 2005
Chemotaxis in Escherichia coli is the most thoroughly studied signal transduction pathway, and thus an excellent model system for quantitative analysis. All of the reaction rates and binding constants have been measured in vitro, and the average intracellular concentrations of signalling proteins have been determined. We supplement this knowledge with analyses of temporal and spatial dynamics of the pathway within the cell, using fluorescence resonance energy transfer (FRET), fluorescence recovery after photobleaching (FRAP), and other fluorescence techniques. This allows us to study quantitative aspects of signal processing such as amplification and integration of stimuli, precise adaptation, the role of spatial organisation in signal transduction, and robustness to cell-to-cell variations in protein levels. Our results suggest a strong evolutionary pressure on the pathway design to optimise sensitivity, dynamic range, and robustness of the output, while maintaining minimal network complexity.
Biological systems as reactive systems
Luca Cardelli (Microsoft Research)
6 July 2005
Systems Biology is a new discipline aiming to understand the behaviour of biological systems resulting from the (non-trivial, "emergent") interaction of biological components. I will discuss some biological networks that are characterized by simple components but complex interactions. The components are separately described in stochastic pi-calculus, which is a "programming language" that should scale up to describing large systems. The components are then wired together, and their interactions are studied by stochastic simulation. Subtle and unexpected behaviour emerges even from simple circuits, and yet stable behaviour emerges too, giving some hints about what may be critical and what may be irrelevant in the organisation of biological networks.
How does a protein find its binding
site on DNA?
Leonid Mirny (Harvard-MIT Division
of Health Sciences and Technology, Massachusetts Institute of Technology,
USA)
27 July 2005
Recognition and binding of specific sites on DNA by proteins is central for many cellular functions such as transcription, replication and recombination. In the process of recognition, a protein rapidly searches for its specific site on a long DNA molecule and then strongly binds this site. We aim to find a mechanism that can provide both a fast search (1-10 sec) and high stability of the specific protein-DNA complex.
Earlier studies have suggested that rapid search involves the sliding of a protein along the DNA. Here we consider sliding as a one-dimensional (1D) diffusion in a sequence-dependent rough-energy landscape. We demonstrate that, in spite of the landscape's roughness, rapid search can be achieved if 1D sliding is accompanied by 3D diffusion. We estimate the range of the specific and non-specific DNA-binding energy required for rapid search and suggest experiments that can test our mechanism. We show that optimal search requires a protein to spend half of time sliding along the DNA and half diffusing in 3D. We also establish that, paradoxically, realistic energy functions cannot provide both rapid search and strong binding of a rigid protein. To reconcile these two fundamental requirements, we propose a search-and-fold mechanism that involves the coupling of protein binding and partial protein folding.
The proposed mechanism has several important biological implications for search in the presence of other proteins and nucleosomes, simultaneous search by several proteins, etc. It also provides a new framework for interpretation of experimental, chromatin-IP and structural data on protein-DNA interactions.
Fluctuations and correlations in
stochastic lattice models for predator-prey interactions
Uwe Täuber (Department of Physics
and Center for Stochastic Processes in Science and Engineering, Virginia
Polytechnic Institute and State University, USA)
29 March 2006
The deterministic Lotka-Volterra model for two-species predator-prey competition/coexistence can be found in many textbooks on nonlinear kinetics, population dynamics, ecology, etc., but is often criticised on the grounds of being biologically unrealistic and mathematically unstable. Indeed, introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical Lotka-Volterra mean-field picture. Moreover, site occupation constraints, modelling locally limited resources, lead to the emergence of a continuous active-to-absorbing state transition. The universal properties near the extinction threshold for the predator population are governed by the directed percolation universality class. In the active state, where predators and prey coexist, the classical centre singularities in phase space are replaced by either nodes or foci, and the system displays complex and correlated spatio-temporal patterns of competing fronts of activity. Finite systems near stable foci are characterized by irregular population-number oscillations, whose features are determined by the intrinsic interaction rates rather than initial conditions. Other model variants that include next-nearest neighbour interactions can lead to even richer scenarios, including the possibility of first-order phase transitions.
Multicellular computation of plant
morphogenesis
Lionel Dupuy (Dept of Plant Sciences)
26 April 2006
Simulation tools and methods are essential to explore, and improve our understanding of, the mechanisms of development in plants. We have been developing dynamic methods for computation of plant morphogenesis at a cellular level.
Different steps need to be completed prior to realistic modelling of morphogenesis: first, segmentation of live microscopy data was used to estimate the model parameters; second, morphogenetic, transport and biomechanical models of cell wall expansion were developed in order to analyse coupled mechanisms in morphogenesis. Most importantly, a software platform was developed to provide a flexible environment for the development and the coupling of gene-regulatory, spatio-mechanical, and signal-transduction models at different levels of plant structure (e.g plant, cell, wall).
Mathematical modelling of protein networks regulating cell movement
Najl Valeyev (Dept of Biochemistry, University of Oxford)
17 May 2006
Cell migration plays a central role in a variety of physiological processes regulating embryonic development, wound healing, immune defence, and cancer metastasis. Numerous intracellular proteins have been shown to regulate cell migration, but here we focus on the calcium-dependent enzyme calpain. Impairment of calpain activation leads to pathological modes of cell migration and results in human disease; it has, for example, been reported to be a target for limiting prostate cancer invasion. I will talk about our recent work on a mathematical model that describes the Ca2+- and calpain-dependent regulation of cell locomotion and will also show various aspects of mathematical modelling of calcium-dependent cell movement in solution.
Ligand detection and discrimination
by spatial relocalisation: the complexities of T cell activation
Nigel Burroughs (Dept of Mathematics,
University of Warwick)
28 June 2006
We analyse a theory of ligand triggering based on receptor relocation to regions of low phosphatase activity. The application is cell:cell communication and receptors where there is no known conformation change, but possessing short ectodomains. Through spatial segregation of long and short bonds/molecules in the cell:cell interface, large phosphatases can be excluded from regions of close contact. In these regions small receptors get trapped by binding to their ligands. We examine the sensitivity and specificity of such as system using a spatial lattice model and molecule diffusion and the requirements for it to have efficient detection characteristics.
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Last updated: 28
June 2005