Ising model – an analysis, from opinions to neuronal states

Here we have developed a mathematical model of a random neuron network with two types of neurons: inhibitory and excitatory. Every neuron was modelled as a functional cell with three states, parallel to hyperpolarised, neutral and depolarised states in vivo. These either induce a signal or not into their postsynaptic partners. First a system including just one network was simulated numerically using the software developed in Python. Our simulations show that under physiological initial conditions, the neurons in the network all switch off, irrespective of the initial distribution of states. However, with increased inhibitory connections beyond 85%, spontaneous oscillations arise in the system. This raises the question whether there exist pathologies where the increased amount of inhibitory connections leads to uncontrolled neural activity. There has been preliminary evidence elsewhere that this may be the case in autism and down syndrome [1-4]. At the next stage we numerically studied two mutually coupled networks through mean field interactions. We find that via a small range of coupling constants between the networks, pulses of activity in one network are transferred to the other. However, for high enough coupling there appears a very sudden change in behaviour. This leads to both networks oscillating independent of the pulses applied. These uncontrolled oscillations may also be applied to neural pathologies, where unconnected neuronal systems in the brain may interact via their electromagnetic fields. Any mutations or diseases that increase how brain regions interact can induce this pathological activity resonance. Our simulations provided some interesting insight into neuronal behaviour, in particular factors that lead to emergent phenomena in dynamics of neural networks. This can be tied to pathologies, such as autism, Down's syndrome, the synchronisation seen in parkinson's and the desynchronisation seen in epilepsy. The model is very general and also can be applied to describe social network and social pathologies

Tunable phenotypic variability through an autoregulatory alternative sigma factor circuit.

Genetically identical individuals in bacterial populations can display significant phenotypic variability. This variability can be functional, for example by allowing a fraction of stress prepared cells to survive an otherwise lethal stress. The optimal fraction of stress prepared cells depends on environmental conditions. However, how bacterial populations modulate their level of phenotypic variability remains unclear. Here we show that the alternative sigma factor σV circuit in Bacillus subtilis generates functional phenotypic variability that can be tuned by stress level, environmental history and genetic perturbations. Using single-cell time-lapse microscopy and microfluidics, we find the fraction of cells that immediately activate σV under lysozyme stress depends on stress level and on a transcriptional memory of previous stress. Iteration between model and experiment reveals that this tunability can be explained by the autoregulatory feedback structure of the sigV operon. As predicted by the model, genetic perturbations to the operon also modulate the response variability. The conserved sigma-anti-sigma autoregulation motif is thus a simple mechanism for bacterial populations to modulate their heterogeneity based on their environment

Biased generation and retention of oligonucleotide motifs in the human genome

During evolution, variation is created by mutational processes in an organism's genome, and then these variants remain or are purged as a result of selective pressures and drift. Mutation rates are biased at many scales across the genome, and the selective pressure acting on the generated variation as a result of mutations also varies greatly. One well studied example of mutational heterogeneity at single-base resolution concerns methylated cytosines, which mutate at an approximately 10-fold higher rate than their unmethylated counterpart. In Chapter 1, I demonstrate that cytosine methylation not only affects mutation risk at the methylated base but also exerts mutational effects on its neighbouring nucleotides. In human, bases surrounding the methylated cytosine accrue fewer SNPs than bases in the vicinity of unmethylated sites. In plants, on the other hand, I demonstrate that the opposite is true. I show that this difference is not driven by differential sampling of sequence or chromatin contexts, and is instead likely due to alternative lesion processing between the species. Regarding selective heterogeneity, studies in the past have largely focused on differential conservation of genetic elements between species, an approach ill-equiped to capture selection against gaining a novel deleterious function. In Chapter 2, I develop and validate a novel approach to interrogate selection against deleterious gain-of-function motifs in protein coding sequences, which is based on derived allele frequency distributions. I show how derived allele frequencies can be used to detect selection against particular amino acid motifs genome-wide. This thesis elucidates forces biasing the creation and persistence of genetic variation and highlights the entwined nature of mutational bias, selective pressures, and the technical challenges involved.Open Acces