# Research

### Stochastic Models for transitions in heterogeneous cell populations

- University of Warwick, UK
- Netherlands Cancer Institute (NKI), Amsterdam

###### Supervisors

*Sach Mukherjee (Statistics, Complexity Science DTC and NKI Amsterdam)*, *Mario Nicodemi (INFI, Italy)*

###### Main collaborators

*Krishanu Saha , **Bas Van Steensel*

The project will focus on a recently discovered biological phenomenon called stem cell reprogramming. Reprogramming refers to the process by which a differentiated or specialized adult cell is transformed back into a pluripotent stem cell, i.e. a cell that has the ability to mature into any cell type. Reprogramming was first demonstrated (1) in 2006 by the group of Shinya Yamanaka at Kyoto. There has since been much research activity in this area (1-3). The collaborating group at MIT are world leaders in this field (2,3). Recently, experimental results (3) have suggested that the process by which cells change state during reprogramming is stochastic in nature. However, the details of the underlying process remain unclear. The aim of this project is to provide a more detailed characterization of this process than has so far been available, by using tools from probability, statistics and statistical physics to interpret diverse high-throughput data that are currently being generated by the collaborating group at MIT.

*K. Takahashi and S. Yamanaka, Cell 126, 663-676 (2006)**M. Wernig et al., Nature 448, 318-324 (2007)**J. Hanna et al., Nature 462, 595-601 (2009)*

### Stochastic synaptic integration in a spatial neuron with voltage activated currents (Project 1)

- University of Warwick

###### Supervisors

*Magnus Richardson (Systems Biology DTC), **Yulia Timofeeva (Department of Computer Science, Complexity Science DTC)*

The spatially extended structure of pyramidal dendrites in the neocortex can not be modelled by a single compartment model. Therefore the problem considered is modelling stochastic synaptic input into spatially extended dendrites. We modelled each synaptic impulse to lead to a change in post-synaptic conductance, the resulting model takes the form of a diffusion like cable equation with a term proportional to white noise in time and space. The equation can be solved using Green's functions convoluted with the white noise term. We calculate the covariance and variance of the voltage exactly and this can be compared to a numerical solution of the cable equation.

### X-chromosome dosage compensation in mammals and C. elegans (Project 2)

- University of Warwick

###### Supervisors

*Mario Nicodemi (Universita' di Napoli "Federico II", Dipartimento di Scienze Fisiche), **Sach Mukherjee (Department of Statistics, Complexity Science DTC)*

We investigate the mechanism for X-chromosome dosage compensation in female mammalian cells and hermaphrodite C. elegans. The X-chromosome inactivation in mammals is studied in the mean field approximation. We investigate some limiting cases for the binding energies and find probabilities for a molecular complex to form on either of the chromosomes. By approximating equal binding energies we also find analytical solutions. For hermaphrodite C. elegans a half down-regulation of X-chromosomes is observed experimentally. We propose a statistical mechanics model with two factors one of which is excitatory and the other is inhibitory, and show that the proposed models indeed fulfils this requirement. We then investigate the stability of the solution under fluctuations of the probability. By comparing the areas covered in parameter space for different limits we find the binding energies for which the solutions is most stable and how this relationship changes with increasing fluctuation.

### Fractal quantum transport in the presence of underlying mixed classical phase space

- Imperial College London
- Institut für Theoretische Physik, Universität Heidelberg

###### Supervisor

*Sandro Wimberger - Universität Heidelberg*

The aim of this project is to study the complexity of the quantum kicked rotor system in cases where the classical counterpart shows a transition from mixed regular-chaotic to purely chaotic phase space. The complexity of the system is analysed by investigating the parametric fractal fluctuations of the survival probability of the quantum mechanical -kicked rotor. The survival probability is obtained by studying quantum transport in the presence of absorbing boundary conditions in momentum space. Recent work (of regimes where the classical analogue is completely chaotic) is substantially extended to a broader range of parameters. The fractal dimension, a measure of complexity of quantum transport, is systematically analysed for fixed underlying phase space and fixed interaction times, measured in number of kicks. It is shown that the fractal dimension, for varied underlying phase space, increases and finally saturates in crossing from a mixed to a completely chaotic regime.