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Case studies

These 3 case studies were written as part of my MRes year. They are extended literature reviews that examine a particular biological question. They evaluate the current research regarding this question and suggest ideas for future modelling or experimental work that would help to answer it. In many cases there was also the opportunity to do some basic original modelling to further explore some of these ideas.

1: Modelling the effect of morphogens in the development of the Drosophila wing disc [pdf]

This case study explores how two key Drosophila morphogens, Decapentaplegic (Dpp) and Wingless (Wg), control the expression of two wing disc transcription factors, Vestigial (Vg) and Distalless (Dll). Two simple models for the potential control of Vg and Dll expression by Dpp and Wg in the mature steady state Drosophila wing pouch are explored. Firstly, a model based on the activation mechanism for Dll in the leg disc was evaluated and dismissed. Secondly, a simple caricature model of Vg activation, based on different thresholds for the contribution of Dpp and Wg to Vg activation, is explored. Although it is limited to modelling the effects of Dpp and Wg, and ignores many other elements later identified as critical to the Vg regulatory pathway, initial analysis suggests that it may be possible to model Vg distribution in the mature wing pouch relatively well using such a simplified steady state model. Further analysis is required to validate the model as it has so far only been assessed against the data used to fit the model parameters. A fuller system of Vg development is then described and the implications for modelling this more complex system discussed.

2: Modelling peripheral homeostasis of Naive CD4+ T-cells [pdf]

T-cells play a crucial regulatory role in the immune system. Understanding the mechanisms underlying the homeostasis of the healthy T-cell pool is expected to provide insight into the apparent deregulation of this process in many auto-immune diseases, including HIV. Naive CD4 + T-cells form a significant fraction of the overall T-cell pool, and it has been observed that the average lifetime of these cells increases with the age of an individual. This case essay explores a simple potential mechanism for this increase in lifetime. This mechanism assumes a static distribution of lifetimes for all T-cells newly exported from the Thymus, corresponding to a static distribution of "fitness" for survival. The model hypothesises that the accumulation of long-lived survivors in the T-cell pool over time will result in the observed increase in average lifetime. Initial evaluation of the model determines that it does not explain the observed increase in lifetime in its current form. However, potential adjustments to the model are suggested that might result in a closer fit to the data.

3: Understanding the Rotating Snakes illusion [pdf]

This paper explores potential mechanisms underlying Rotating Snakes - a piece of Op-Art by Kitaoka evoking a striking apparent motion illusion. The Op-Art is based on an illusion developed by Kitaoka & Ashida (2003) and is similar to previous illusions developed by Fraser & Wilcox (1979), Faubert & Herbert (1998) and Naor-Raz & Sekuler (2000). The subsequent illusions, including Rotating Snakes are considered by their authors to be related to the original Fraser & Wilcox "Escalator" illusion and are collectively termed Peripheral Drift illusions. Despite their similarities, none of the mechanisms proposed to date can explain both the "single gradient" members of this class of illusion (exemplified by the Faubert & Herbert illusion) and the "double gradient" members of this class (namely the Rotating Snakes illusion). A mechanism based on luminance-dependent latency proposed by Faubert & Herbert explains the "single gradient" illusions well but does not explain the "double gradient" illusions. It is also not clear how biologically plausible such a mechanism is given the centre-surround structure of retinal ganglion cell receptive fields. Two similar mechanisms based on contrast-dependent latency explain the "double gradient" illusions but fail to explain the single gradient illusions. Conway et al (2005) describe the effect of this latency in terms of forward and reverse phi motion, while Backus and Oruc (2005) explicitly model the temporal response of V1 neurons as a function of contrast. It is likely that these two approaches are describing the same underlying mechanism. Johnston et al (1998; 2003) have developed a high-level Gaussian derivative model of motion, which has successfully detected "illusory" contrast-driven second order motion in moving patterns. The contrast- dependent latency described above could be considered a gradual switch from an input dominated by high- contrast elements to one dominated by low-contrast elements. Therefore a simplified Rotating Snakes pattern was contrast-modulated and passed through the Gaussian derivative model to see if any motion was detected. Despite preliminary theoretical analysis suggesting that the model would detect motion in the direction of the illusion for a stimulus decreasing in contrast over time, the motion reported by the model was excessively large and inconsistent in direction. It seems likely that any perceived motion is an artefact of the model. Further work will be necessary to identify and eliminate any causes of any anomalous motion before conclusions can be drawn regarding whether a Gaussian derivative based motion model will see the Rotating Snakes Illusion.

3D representation of the expression of the morphogen Vestigial across the developing Drosophila wing disc

3D representation of the expression of the morphogen Vestigial across the developing Drosophila wing disc