Abstracts from completed PhD's by CoMPLEX students.
Scale-Space and the Implicit Coding of Luminance in V1
Ioannides, Alex, 2006
PhD, London,
University College London
Abstract This thesis pursues a single line of enquiry: lightness, brightness, and visual illusions. In particular, it focuses on White's effect, simultaneous brightness contrast, and theories that can account for both phenomenon.
In the first part (Chapters 1-3), the problem-space is defined before a review of lightness and brightness theories from both low- and high-level vision.
In the second part (Chapter 4), the only two low-level V1 models of brightness, capable of accounting for both White's effect and simultaneous brightness contrast, are shown to be reliant on the amplification of low spatial frequency information, to accurately reconstruct images and account for the illusory brightness apparent in both effects. It is argued that this low spatial frequency information is not available to V1. Hence, it is concluded that these models are not biologically plausible. In the third part (Chapter 5), the issue of recovering low spatial frequency information without explicitly sampling it is considered. The problem is formally defined in the Scale- Space framework and solved analytically. That is, an algorithm for recovering local mean luminance (and low spatial frequencies), from the information implicit in contrast coding cells typically found in V1, is constructed, and is referred to as the Implicit Luminance Coding (ILC) model.
It is argued that the ILC model is not biologically-plausible. Subsequently, a new algorithm is proposed, based on a numerical approximation to the analytical solution. The biologically plausible ILC algorithm is developed into a complete low-level model of brightness, which makes use of the information present in multiple scale channels. The model is shown to be capable of accounting for both White's effect and simultaneous brightness contrast, by means of an interplay between two independent assimilation and contrast mechanisms.
The final part (Chapter 6), is concerned with the application of the model to visual phenomenon synonymous with lightness and brightness, including all known variants of White's effect and simultaneous brightness contrast, and some effects that are traditionally accounted for by appealing to mechanisms from high-level vision. The biologically-plausible ILC model is shown to be in good accordance with experimental data.
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Modelling Electrical Current Flow
in the Mammalian Cochlea Mullaley Christopher John, 2006 Ph.D., London, University College
Abstract
This thesis examines the way in which mathematical and computational modeling can be used to advance the understanding of biophysical mechanisms in the mammalian inner ear. It shows how experimental results from a variety of sources can be integrated to describe electrical current flows within the cochlea.
A software framework is developed which allows the construction of complex, multi variable models from descriptions of the components. By taking advantage of the geometry of the cochlea, these descriptions can be simplified and the number of free parameters in the models reduced. The software framework handles the parsing of these descriptions, manipulation of the parameters through a simple graphical user interface (GUI) and interfacing to the MatLab programming environment for numerical simulation.
Static models are developed where the cochlea is represented as a network of resistive elements and voltage sources. From these models, estimates of the space constants for the organ of Corti are deduced and the consequences of blocking gap junctions are studied. It is predicted that, in terms of short term effects on endocochlear potential, selectively blocking the gap junctions in the stria vascularis is likely to have a much greater effect than blocking those in the organ of Corti.
Dynamic models are also developed, incorporating a biophysical description of the travelling wave within the cochlea with appropriate phase relationships. The simulations indicate how the interaction of out-of-phase current flows in adjacent regions of the cochlea may help to maintain active amplification at high frequencies.
Finally, the electrophysiology of the stria vascularis is modelled in greater detail as a multi-layered structure with different ion channels and pumps in each different layer.
The behaviour of this system is compared that of the simple resistance and voltage
representation used in the other models.
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Comparisons of Parsimony and Likelihood-based methods in Phylogenetic analysis
Dale Dave, 2006 Ph.D., London, University College
Abstract
This work provides a defence of the claim that likelihood based methods provide a better framework for performing phylogenetic analyses on molecular sequences than do parsimony based methods under the conditions studied.
Novel work introduced in the thesis includes simulation studies that examine the performance of likelihood based and parsimony based methods at high evolutionary distances. At these distances, many changes accumulate at a single site causing a catastrophic collapse in the performance of the parsimony analysis. In contrast a well understood mathematical theory involving the use of Fisher’s information measure describes the decline in performance of likelihood methods.
Further work compares the performance of likelihood based methods and parsimony methods under heterotachous conditions, i.e. conditions under which a single site will alter its rate of evolution relative to other sites. A recent claim that parsimony based analyses outperform likelihood is rebutted and a likelihood model is introduced and its performance analysed.
Finally likelihood based methods are defined in terms of rates. A method for turning these rates into a probability distribution describing the number of changes of interest across a phylogeny is described. This is then compared to the number of changes inferred under a parsimony analysis. When the true model is known, it is shown that the counts of changes inferred under a parsimony based analysis have a low probability of being correct. It is argued that this accounts for the poor performance of parsimony.
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The Population Biology of Multispecies Helminth Infection
Bottomley, Herbert Christian, 2006
Ph.D., London, University College
Abstract
Vertebrate hosts are frequently infected with multiple helminth species. There is a body of experimental evidence to suggest that infection with one parasite species can have either an antagonistic or synergistic effect on another species; such interactions may occur through parasite establishment, survival and fecundity. The extent to which such interactions are involved in the organization of helminth communities is largely unknown. Mathematical models based on Markov processes are used to explore two themes:
1) The effect of interspecific interactions on the joint distribution of helminth parasites in a population of hosts, and 2) conditions under which interacting species can coexist. To explore the former, models are formulated that describe the process by which helminths of two species are acquired and lost in a cohort of ageing hosts. In these models, the interspecific interaction occurs at the point of parasite establishment within the host such that the rate of establishment depends on the current worm burdens of the two species. The results are used to highlight some of the difficulties associated with inferring interspecific interactions from ecological data. The relationship between competition and species coexistence is investigated using models of the long-term dynamics of interacting species. Models are developed in which there is a free-living larval stage whose population size is dependent on the size of the adult worm population. The models are analyzed using ëhybridí and ëmoment-closureí approximations; the former involves replacing stochastic components of the model with deterministic approximations, and the latter assumes a functional relationship between higher and lower order moments based on a specified distribution. The Lotka-Volterra model of competition is derived for the case where hosts are equally exposed to parasites of the same species. Coexistence of two competing species is promoted by heterogeneous host exposure to each parasite species, provided that the rates of exposure to the two parasite species are not perfectly, positively correlated, and provided that the degree of heterogeneity in host exposure is similar for both species. In addition, it is shown that the conditions required for coexistence are the same regardless of whether competition occurs at the point of parasite establishment within the host or via parasite fecundity. These results are discussed within the context of helminth community ecology.
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Branching Process Models of T Cell Selection
Moon Simon Peter, 2006 Ph.D., London, University College
Abstract
Cell division history can be examined with the fluorescent dye: 5- (and 6-) carboxyflourescein diacetate succinimidyl ester (CFSE). Modelling the data produced by flow cytometric analysis of CFSE has recently been an active area of research and promises to give new insight into the behaviour of dividing populations of cells. Initially, this thesis describes how CFSE data can be modelled with discrete time multi-type branching processes. This approach has not previously been used where CFSE data is concerned, although branching process models of cell division have an established history of producing simple tractable models that yield biologically relevant results. In particular, these models can be adapted to staged behaviour. We therefore use a multi-type model in an attempt to isolate the phenotypic stage at which negative selection occurs in the thymus. In doing so we re-examine published experimental data that analyses the fate of positively selected double positive (DP CD69+) thymocytes during and after their transition to single positive (SP) stage. We analyse the data with respect to two alternative hypotheses: 1. Death occurs at the DP CD69+ stage and not at the SP stage and 2. Death occurs at the SP stage and not at the DP CD69+ stage and it occurs concurrently with division. We conclude that the second model fits the data better than the first. Motivated to avoid the discrete time assumption that division behaviour is synchronous, the thesis shows how a continuous time branching process model of CFSE can be obtained. The results of a subsequent re-analysis of the published data conflict with our discrete time modelling. Upon further investigation, we conclude that the continuous time model is a poorer model of the data. Finally, the effect of negative selection in combination with division on the thymocyte repertoire is modelled with a discrete time branching process. The results of our analysis suggest that there may be an advantage to division and selection being a combined process.
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Modelling the p53 Gene Regulatory Network
Brewer Daniel, 2006 Ph.D., London, University College
Abstract
p53 is the central protein in the DNA damage response and is part of a complex and extensive gene regulatory network. This network integrates a variety of stress signals to produce the up-regulation of active p53 and a range of effects including apoptosis, growth arrest and DNA damage repair. The p53 system has typically been studied qualitatively as a linear pathway, however this approach is insufficient to gain a full functional understanding of the dynamic nature of the network. In this work a better description of the DNA damage response will be constructed through the use of mathematical techniques.
Ordinary differential equations models of the p53 network between DNA damage and p53 up-regulation are proposed, including a model that takes into account various localisation mechanisms. Parameter estimation is required to validate these models with biological data. A number of established techniques are examined along with a novel method based on linear algebra, collocation and B-splines. To examine the network downstream of p53 and the global response to DNA damage, a “G” time profile (Gg(t)) quantifying the activity driving the formation of each gene is constructed. This is derived from a model of gene transcription, microarray data and mRNA degradation rates.
The new parameter estimation technique developed works significantly better than the other techniques examined. Also, it was found that the mechanisms that control the location of p53 significantly contribute to the rapid DNA damage response. The G time profiles suggest that there are four principal transcription activities in the DNA damage response: p53, an early peaking response (possibly AP-1), stopping and restarting the cell cycle, and a double peaked response. The G time profile in combination with a training set of genes can be used to successfully find confirmed p53 targets.
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Clocks, gradients, and molecular networks:
mathematical models for morphogenesis
Cinquin Olivier, 2005. Ph.D., London, University College
Abstract
The acquisition of a spatial structure during embryo development involves the differentiation of cells, often according to positional information. The complexity of the molecular networks regulating differentiation and of the mechanisms generating positional information makes it necessary to study them by means of mathematical modeling. Vertebrate embryos also acquire a segmented structure during somitogenesis; this requires spatial and temporal variations in gene expression, which mathematical modeling can also help understand.
A molecular mechanism for the somitogenesis clock is proposed, which accounts for intercellular synchronisation, and is based on positive feedback, even though it is compatible with all experimental data interpreted as showing that the clock is based on negative feedback. Experiments proposed to test this model involve real-time clock reporters, as well as inducible systems to induce spatially-controlled perturbations.
Theoretical and experimental results have led to conflicting ideas as to how useful positional information can be established. In particular, it has been pointed out that some
models of extracellular diffusion of morphogen exhibit inadequate traveling waves of receptor saturation. Two alternative (but not mutually exclusive) models are proposed, which are based on recent experimental results highlighting the roles of extracellular glycoproteins and morphogen oligomerization.
The readout of positional information is translated to a discrete set of gene expression
patterns. Intriguingly, it has been observed in numerous contexts that genes regulating differentiation are initially co-expressed in progenitors despite their antagonism. We characterise conditions under which three classes of generic ”master regulatory networks” can behave as a ”multi-switch”, directing differentiation in an all-or-none fashion to a specific cell-type chosen among more than two possible outcomes. bHLH dimerisation networks can readily display coexistence of many antagonistic factors when competition is low. Decision-making can be forced by a transient increase in competition, which could correspond to some unexplained experimental observations related to Id proteins.
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Evolution of gene networks in sex determination.
MacCarthy Banos, T. A., 2005, F2d
Ph.D., London, University College, 54-16022 (BL: DXN088239)
Abstract
In this work, the evolution of sex determination gene networks is investigated using a modelling approach. Sex determination mechanisms offer a good model for studying gene network evolution because, among other reasons, they evolve rapidly. In chapter 2, the potential for evolutionary change of the existing Drosophila sex determination gene network is considered. With the aid of a synchronous logical model, theoretical concepts such as a network-specific form of mutation are defined, as well as a notion of functional equivalence between networks. Applying this theoretical framework to the sex determination mechanism, it is found that sex determination networks generally exist within large sets of functionally equivalent networks all of which satisfy the sex determination task. These large sets are in turn composed of subsets which are mutationally related, suggesting a high degree of flexibility is available without compromising the core functionality. The technique for finding functional equivalence between networks suggests a general method for gene network reconstruction, which is explored in chapter 3. Lastly, in chapters 4 and 5, a hierarchical model is presented which integrates population genetics techniques with network dynamics. This model consists of a core population genetics simulation within which parameters such as genotype sex fitness are calculated from the corresponding network dynamics. The model is used to investigate the early evolution of sex determination networks. Following from a hypothesis proposed by Wilkins (1995), the assumption is made that sex determination networks have evolved in a retrograde manner from bottom to top. Starting from a simplest possible ancestral system, based on a single locus, we explore the way in which more complex systems, involving two or three loci, could have evolved.
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The kinetics of T cell responses.
Allan, M.J., 2005, G6d
Ph.D., London, University College, 54-16581 (BL: DXN087747)
Abstract
The first aim of this thesis is to identify the most plausible mechanism that could regulate the T cell kinetics during an acute response. Using an ODE compartmental model to keep track of the number of cells in each generation, the predictions of a number of plausible regulatory mechanisms are compared to experimental data to determine the potential of each to regulate cell number. One revealing conclusion is that all successful mechanisms progressively increase the apoptosis rate during the response. The most plausible mechanisms are then further assessed to determine which produces the least wasteful response (in terms of unnecessary T cell death). It is concluded that the most plausible mechanism is one that progressively increases death rates and decreases division rates.
The second aim of this thesis is to investigate how the programmed nature of the regulatory mechanism affects the outcome of infection. Two aspects of the outcome of infection are considered: the size of the generated memory population, and the success, or otherwise, of pathogen clearance. The previous compartmental model is extended to incorporate the formation of memory cells, and the impact of the program parameters on the final memory size following an acute infection is established. Situations when the pathogen can persist beyond the acute phase are then considered, and a discrete-time population model is developed to predict the long-term behaviour of the response. It is found that if the developmental program always produces a net increase in cell population size then pathogen clearance is guaranteed. A further conclusion is that during this long-term infection the sensitivity of the specific memory cells to re-stimulation diminishes.
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Kernel-based classification of protein structure and function from amino acid sequences.
Ward, J. J., 2005, F6d Ph.D., London, University College, 54-16116 (BL: DXN088341)
Abstract
The thesis describes the application of kernel methods and, in particular, the support vector machine (SVM) to the classification of protein structure and function. The thesis is divided into two related halves and chapters 2 and 3 containing descriptions of methods for predicting different aspects of protein structure. Chapter 4 investigates the functions of disorder in the proteome of a model eukaryote and Chapter 5 describes algorithms and data sources for inferring protein function. The data sources include structure predictions and other properties that can be derived directly from amino acid sequences.
Chapter 2 describes a new method for the prediction of secondary structure using an SVM learning algorithm. This is presented as a guide to the application of SVMs to problems in bioinformatics, and includes a discussion of the positive and negative aspects of the technique. The final prediction method is shown to have comparable performance to several of the most accurate modern methods.
The third chapter discusses the development of a method to recognize native disorder from amino acid sequences. This predictor (DISOPRED2) is shown to be the most accurate contemporary method on targets from the fifth CASP experiment. The false positive rate of DISOPRED2 is determined using ordered structures from the Protein Data Bank, and the classifier is then used to estimate the frequency of disorder in complete genomes. The final part of this chapter presents the design and implementation of a publicly-available web service for disorder prediction.
The fourth chapter describes the use of DISOPRED2 to investigate the functional annotations that are associated with long predictions of disorder in the proteome of the model organism Saccharmoyces cerevisiae.
The final research chapter discusses the development of machine learning methods for determining the function of anannotated proteins.
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A computational and psychophysical study of motion induced distortions of perceived location.
Durant, S., 2004, B2d
Ph.D., London, University College, 54-12788 (BL: DXN086537)
Abstract
In this thesis I begin by extending previous psychophysical research on the effects of visual motion on spatial localisation. In particular, I measured the perceived spatial shift and briefly presented stationary objects adjacent to a moving stimulus. It was found that the timing of the presentation of stationary objects with respect to nearby motion was crucial. I also found a decrease of this motion induced spatial displacement with the increasing distance of stationary objects from motion, suggesting a local effect of motion. The induced perceptual shift could also be reduced by introducing transient stimuli (flickering dots) in the background of the display.
The next stage was to construct a computational model to provide a mechanism that could facilitate such shifts in position. To motivate our combined model of motion computation and spatial representation we considered what functions could be attributed to V1 cells on the basis of their contrast sensitivity functions. I found that functions based on sums of differential of Gaussian operators could provide good fits to previously found V1 data.
The properties of V1 cells as derivatives of Gaussian kernel filters on an image were used to build a spatial representation, where position is represented in the weighting of these filter outputs, rather than in a one-to-one isomorphic representation of the scene. This image representation can also be used along with temporal derivatives to calculate motion using the Multi-Channel Gradient Model scheme (Johnston et al, 1992). I demonstrate how this framework can incorporate motion signals to produce “in place” shifts of visual location. Finally a combined model of motion and spatial location is outlined and evaluated in relation to the psychophysical data.
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Detecting Positive Selection in Protein Coding Genes Anisimova Maria, 2003
Ph.D., London, University College
Abstract
Selective pressure at the protein level is typically measured by the nonsynonymous / synonymous rate ratio (ω = dN/dS), with ω <1, =1, and >1 indicating purifying selection, neutral evolution, and positive selection, respectively. Methods that detect positive selection using this criterion are reviewed. I focus on maximum likelihood (ML) methods based on codon substitution models accounting for heterogeneous selective pressure across sites. If ML estimates indicate presence of positive selection and the likelihood ratio test (LRT) is significant, Bayes prediction can be used to identify sites under positive selection.
I examine the accuracy and power of LRTs for positive selection and Bayes prediction of residues under positive selection. The use of X2 for significance testing makes the LRT conservative, especially for small samples of closely related lineages. Nevertheless, if a large number of lineages of sufficient divergence are analyzed, the power of the LRT can be as high as 100%. Both accuracy and power of Bayes prediction are low for data containing only few similar sequences. But sampling a large number of lineages improves the performance substantially. Multiple models of heterogeneous selective pressure among sites should be applied in real data analysis.
ML models are phylogeny-based and do not incorporate recombination.
To evaluate the effect of recombination on the LRTs and Bayes prediction, data are simulated using a coalescent model with recombination. The LRT is found to be robust to low recombination rates. However, for higher rates, the type-I error rate can be very high. Identification of sites under positive selection by the Bayes method is less affected by recombination than is the LRT. Finally, the hepatitis D antigen gene (HDAg) is tested for positive selection. Sites predicted to evolve under positive selection are found in immunogenic domain and in the N-terminus region with reported antigenic activity. No significant evidence of recombination is found.
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