2015 Project Proposals

47 Bateman Street
CB2 1LR

Regulatory logic of transcription

This project would involve working with Dr Tanya Ronson, a senior postdoc and the group’s crystallography expert, to analyse our library of crystal structures in order to quantify the geometrical parameters characteristic of a stable structure. This process will likely involve abstraction of key features of the geometries of molecular building blocks and the metal ions that link them together and analysis of the degrees of freedom explored by the system during self-assembly. Statistical analysis would likely be undertaken upon geometry data extracted from X-ray crystal structures.

We would aim to generate a model able to predict how a given set of building blocks and metal ions are likely to self-assemble, if at all. A high-impact publication is likely to result

A universal description of these phenomena is provided by a stochastic partial differential equation called the KPZ equation (after its inventors: Kardar, Parisi, and Zhang). While the KPZ equation provides a overarching framework, a lot of progress has arisen from the analysis of specific models. The goal of this project is to use one such model, called Polynuclear Growth (PNG) to study the effect of changes in the random nucleation events that cause the interface to grow.

This will involve numerical simulation of the model — which is easy as it has very simple rules — coupled with a theoretical analysis of the simulation data to extract the universal scaling functions describing the sensitivity to disorder.

Some useful background can be found in Section 1 of Viktor S Dotsenko 2011 Phys.-Usp. 54 259 http://iopscience.iop.org/1063-7869/54/3/R02/

You can play with Java simulations of the model (and others) at http://wt.iam.uni-bonn.de/ferrari/research/#animations

Optoacoustic tomography is an emerging imaging modality using nanosecond laser pulses to precisely map the location of absorbing molecules in living subjects, and in particular, blood oxygenation. Excited molecules emit ultrasound waves allowing us to pinpoint their location using standard detection techniques with high precision. Image quantification relates the signal intensity to the actual concentration of the absorbing molecules in a given tissue.

As in other tomographic modalities, a 3D image is formed by combining data from 2D slices together. However, the limited focusing ability of the acoustic transducers means that some regions of the imaged slice receive signal contributions from pixels from nearby slices, distorting the intensity map in the final image and in turn affecting our ability to accurately quantify the concentrations of the absorbing molecules in the slice.

This project aims to evaluate for each pixel of the slice the amount of signal intensity coming from nearby slices and apply a global correction matrix to the image to compensate for this effect. The goal is to achieve a more accurate signal intensity map for image quantification. To realise this goal, it will be necessary to apply the Boltzmann equation to calculate the scattered light intensity in neighbouring planes, and use acoustic wave propagation to find which out-of-plane pixels are relevant for corrections and map them to the related slice pixels.

Hunter Group
Department of Chemistry
Lensfield Road
Cambridge CB2 1EW

Molecular electrostatic potentials (MEP) are three dimensional maps which indicate the potential a proton would feel in the region around a molecule and can be calculated using quantum mechanical methods. From this continuum, specific regions that interact with other molecules, in a non-covalent manner, may be identified and abstracted as a set of, coarser, discrete interaction sites, termed surface site interaction points (SSIPs). In turn, useful macro scale properties, such as the molecule’s free energy of solvation may be inferred by the interactions between an ensemble of SSIPs[1].

The algorithm for determining the location of SSIPs can be considered a constrained optimisation. For a typical molecule, quantum chemistry calculations produce a MEP surface described by thousands of xyz coordinates each with an electrostatic potential. The number of SSIPs required is approximately 100-fold smaller, and we require a method to identify which sites we should pick from the MEP. The optimal set of SSIPs are the set of points from the MEP that maximize the sum of the electrostatic potentials.

The current algorithm we are using is very inefficient and produces a best guess rather than a defined solution. The result is that for certain molecular topologies, unphysical artifactual anisotropies manifest. We have already attempted ensure rotational invariance by sampling multiple molecular orientations when generating the starting MEP, but we would like to investigate the SSIP selection method from a formal mathematical point of view.