Thesis opportunities

Coupling of intrinsic and extrinsic noise in biological systems

Models for biological processes on a molecular level consist of elementary or complex reaction networks that describe the interactions between key components of a process in question. The basis for these models is the chemical master equation. It describes the time evolution of the probability that each component has a specified copy number at a given time.

In most cases, the probabilistic chemical master equation cannot be solved exactly so it is necessary to apply a systematic approximation. In general, the description is split into a deterministic differential equation for the macroscopic dynamics and so-called intrinsic fluctuations. The intrinsic fluctuations are significant in case of small copy numbers and they are relatively well understood. However, cellular variation is predominantly generated by extrinsic fluctuations that non-specifically affect many system components, for example fluctuations of the number of ribosomes. Many mathematical tools have been developed for the treatment of intrinsic noise. Although extrinsic noise is attracting increasing interest, the mathematical treatment is still in the beginning and mainly based on simulations. In this master thesis project we investigate a perturbative approach to understanding the interplay between intrinsic noise on a short time scale and slowly fluctuating extrinsic variations. The work will be based on a previous master thesis done in this group and will consist of investigating through computer simulations the quality and also the limitations of the already derived systematic expansion.

Methods

Master equation, Time-scale separation, Asymptotic expansion, Stochastic differential equations, Stochastic simulation, C/C++ programming.

Literature

D.T. Gillespie. Stochastic simulation of chemical kinetics. Annual Review of Physical Chemistry, 58(1):35–55, 2007. doi: 10.1146/annurev.physchem.58.032806.104637.

V. Shahrezaei, J.F. Ollivier, and P.S. Swain. Colored extrinsic fluctuations and stochastic gene expression. Mol Syst Biol, 4:196, 2008. doi: 10.1038/msb.2008.31.

Michael B. Elowitz, Arnold J. Levine, Eric D. Siggia, and Peter S. Swain. Stochastic gene expression in a single cell. Science, 297(5584):1183–1186, 2002. doi: 10.1126/ science.1070919.

J. Elf and M. Ehrenberg. Fast evaluation of fluctuations in biochemical networks with the linear noise approximation. Genome Res, 13(11):2475–84, 2003. doi: 10.1101/gr.1196503.

Miscellaneous

This project is done in close collaboration with the group of Dr. Ramon Grima form Edinburgh, UK (http://grimagroup.bio.ed.ac.uk/index.html).

Interested?

Please write an email to: christian.fleck@wur.nl

Implementation of a 3-dimensional modeling framework for plants

Virtual Leaf is a modeling framework to implement dynamic models in a larger system describing growing plant tissue. The framework is capable of simulating plant cell growth and cell division according to kinetic reactions taking place in every single cell at the same time. This system was initially constructed by the group of Roeland Merks in Amsterdam to model the development of plant leaves and leaf vein formation. In our group we use the framework to model the vascular initiation during embryogenesis in plants. Whereas for leaf development it is sufficient to use only a two-dimensional model for most applications in plant modeling there is much benefit from using a three-dimensional model. That's why we started to extend the existing framework to simulate three-dimensional domains. The work we are offering here is to implement this software; the scope of the project will depend on the background and the skills of the student. The framework is written in C++ so the student should have some experience in C++ and/or other object-oriented programming languages. Knowledge of cellular mechanics and/or biophysics and a solid background in math is preferred but not essential. If wanted, there could also be some modeling work in the area of development of plant vasculature included in the project.

Methods

C++ programming, Monte-Carlo-Simulation, Cell mechanics, Ordinary differential equations.

Literature

R.M.H. Merks, M. Guravage, D. Inzé and G.T.S. Beemster. VirtualLeaf: an open/source framework for cell-based modeling of plant tissue growth and development. Plant physiology, 155:656-66, 2011

Miscellaneous

This project is done in close collaboration with the group of Dr. Roeland Merks, CWI, Amsterdam, NL (http://biomodel.project.cwi.nl) and Prof. Jan Broekhoven, CoMP at University Antwerp, BE (https://www.uantwerpen.be/en/rg/comp/).

Interested?

Please write an email to: christian.fleck@wur.nl

Quantifying patterns: analyzing a mechanistic model of vasculature formation in Arabidopsis embryo

Developmental biology is concerned with processes that give rise to tissue and organs and define the form and geometry of multicellular organisms. Plant embryos are ideal platforms to study developmental processes, due to their small size and rigid cell walls that inhibit cell-movement.

In collaboration with the group of Prof. Dolf Weijers we have developed a model of growing plant cells that captures the formation of hormonal response zone that lead to formation of vasculature in Arabidopsis embryo. The model output is a qualitative pattern of hormonal response in a cross section of the embryo. Due to the absence of quantitative data regarding the cell-by-cell readouts of hormonal responses, the model output cannot be assessed against quantitative data. However we have GFP-readout data available, which can be used to estimate the relative level of hormonal responses in the cells.

The project would involve the development of methods to recognize and score the patterns of hormonal responses generated by the model against the available data. Such methods would then be implemented in a cost function, which would be use to analyze the model behavior via parameter sweeping, sensitivity analysis and optimization.

Methods

Computer simulations, Ordinary differential equations, Parameter sampling, Spatial pattern analysis, Optimization, Python and/or C++ programming.

Literature

Merks, Roeland MH, et al. "VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development." Plant Physiology 155.2 (2011): 656-666.

De Rybel, Bert, et al. "A bHLH Complex Controls Embryonic Vascular Tissue Establishment and Indeterminate Growth in Arabidopsis." Developmental cell 24.4 (2013): 426-437.

Kremling, Andreas. Systems Biology: Mathematical Modeling and Model Analysis. CRC Press, 2013.

Miscellaneous

This project is done in close collaboration with the group of Prof. Dolf Weijers (http://www.wur.nl/en/Expertise-Services/Chair-groups/Agrotechnology-and-Food-Sciences/Laboratory-of-Biochemistry/Research/Plant-Development.htm)

Interested?

Please write an email to: christian.fleck@wur.nl

Determining binding rates of light-regulated protein complexes

In plants, development and growth is tightly controlled by the external environment. Upon exposure to light, plants begin photomorphogenesis resulting in reduced stem elongation and increased amounts of chlorophyll. One key pathway that controls this light-triggered developmental switch are the red/far-red light-regulated phytochromes. The phytochrome proteins switch reversibly between two conformational states: an active state that occurs upon exposure to red light and an inactive state upon exposure to far-red light. Once activated, the phytochromes enter the nucleus of plant cells and alter the gene expression pattern.

However, not all phytochromes strictly follow this simplified system. One phytochrome, phyA, is able to enter the nucleus and regulate plant development upon exposure to far-red light despite only ~3% of phyA proteins being in the active state. Therefore it is of interest to our group to determine how phyA is able to have such a strong effect in far-red light. Recent research has demonstrated how the formation of a protein complex between phyA and FHY1 (FAR RED ELONGATED HYPOCOTYL 1) in far-red light conditions is important for phyA function (Hiltbrunner et al., 2006; Rausenberger et al., 2011). However, the kinetics of association and dissociation between these proteins has yet to be elucidated.

In this project, we wish to investigate the binding kinetics of phyA and FHY1 using microscopy techniques such as FRET-FLIM (Fšrster resonance energy transfer – fluorescence lifetime imaging; Laptenok et al., 2013). By performing experiments on plants under different light regimes, we will be able to determine how much of the phyA protein forms complexes with FHY1. Using these results we wish to infer the rates of association and dissociation between phyA and FHY1.

Methods

Plant growth, microscopy, FRET-FLIM, data analysis, parameter estimation

Literature

Hiltbrunner, A. et al. (2006) FHY1 and FHL act together to mediate nuclear accumulation of the phytochrome A photoreceptor. doi: 10.1093/pcp/pcj087

Rausenberger, J. et al. (2011) Photoconversion and nuclear trafficking cycles determine phytochrome A's response profile to far-red light. doi: 10.1016/j.cell.2011.07.023

Laptenok, S.P. et al. (2013) Global analysis of FRET-FLIM data in live plant cells. In ÔMethods in Molecular Biology (2013)Õ

Miscellaneous

This is a joint project between our group (Theoretical Systems and Synthetic Biology Group) and the group of Dr. Jan Willem Borst (https://www.wur.nl/en/Persons/dr.ing.-JW-Janwillem-Borst.htm).

Interested?

Write an email either to: christian.fleck@wur.nl or janwillem.borst@wur.nl.