PhD: Large-Scale Parallelised Boundary Element Method Electrostatics for Biomolecular Simulation
![macromolecular crowding](images/cytosol.png)
All life is based on the interactions between biological molecules (e.g. proteins, nucleic acids), which in human cells coexist in a complicated and crowded mixture. It is extremely difficult to directly measure the interactions between individual biomolecules in the lab because of the very small length-scale and short time-scale over which these processes occur. Computer simulations which model these interactions can improve our understanding and suggest avenues for further experiment. With increased knowledge of how biomolecules interact comes better understanding of what happens in illnesses where biomolecules misbehave, and ultimately leads to progress in medical science and the treatment of disease.
In order to carry out large-scale simulations, we need to be able to calculate the electrostatic force between proteins (like that between a positive and negative charge). This can be found by solving the Poisson-Boltzmann Equation (PBE), but unfortunately the process is generally non-trivial.
![acetylcholinesterase and fasciculin](images/ache-fas.png)
I have written a program called BEEP which solves the linearised PBE using the "boundary element method" (BEM) with a linearly-scaling fast multipole method (FMM) . I improved and parallelised these highly complex algorithms, using a number of open source tools and libraries along the way (e.g. Boost, OpenCL, OpenMP). BEEP now runs on both desktop computers and HPC clusters, and uses GPUs to accelerate the near-field integration terms of the BEM.
Our results of running BEEP on proteins show that the stability and numerical accuracy of the combined BEM/FMM method is extremely sensitive to the choice of surface representation and integration method. I used a curved triangulated surface to improve numerical stability and accuracy, and conclude that it is practicable to use the total electrostatic solvation energy calculated by BEEP to drive a Monte-Carlo simulation of protein-protein interactions.
MRes: Modelling Biological Complexity
![hippocampal neuron](images/neuron.gif)
CASE Essay 1: Motion tracking of fluorescently tagged receptor proteins
This essay discusses the experimental process of tracking the diffusion of GABAA receptors in the
cell membrane of neuronal cells by fluorescent confocal microscopy, and the mathematical issues
arising from the interpretation of the results – i.e. the motion tracking task of converting
a video of the movement of blurry ‘blobs’ into estimates of underlying diffusion
coefficient distribution.
download as pdf
![hepatocytes under a confocal microscope](images/hepatocytes.jpg)
CASE Essay 2: Simplification of biological models using Voronoi compression technique
This essay shows how phase plane analysis of biological models (in this case, the Morris-Lecar
barnacle giant muscle fibre, and a model for hepatocyte calcium oscillations following Höfer) can be
carried out using a novel Voronoi 'compression' technique. The result is simplification of the
model without loss of useful information, such as location in phase space of fixed points, limit
cycles etc.
download as pdf
![hypolimnas bolina](images/hbolina.png)
CASE Essay 3: Sperm modelling of butterflies
Bacterial infections such as the male-killing Wolbachia can infect butterflies and cause
distortions in the operational sex ratio (OSR) of the population by increasing the number
of females relative to males. The excess of females leads to increased opportunities for
males to mate, and alters the optimum sperm allocation strategy. Mutant males who have a
strategy which fertilises more eggs than will have an immediate advantage over rival
males, and such mutations would be expected to fixate rapidly leading to fast evolution
of sperm strategy towards the new optimum. This essay presents a model of both female and
male mating behaviour which is solved using a method of dynamic programming combined with
simulation to yield the optimal sperm strategy for a given initial OSR.
download as pdf
![Mars](images/mars.jpg)
MRes Summer Project: Modelling extraterrestrial radiation environments for astrobiology
This project is concerned with estimating the probability of bacteria being able to survive beneath the surface of Mars, given the harsh environmental conditions which exist there. To make such an estimate at least two things must be known: the level of ionizing radiation at the surface of Mars due to both solar and galactic radiation; and the capacity of biological material to survive the radiation. Correspondingly this project is divided into two parts: firstly the simulation of the radiation environment on Mars, using a Monte-Carlo simulation program based upon the Geant4 physics framework; secondly a set of biological experiments which aim to link the damage caused by desiccation to the damage caused by radiation, using Antarctic extremophile bacteria as proxies for hypothetical Martian bacteria.
The results of our desiccation experiments were published in Antarctic Science and are also available in the project report.