Research areas
My scientific dream is a complete mathematical model of human body. In my research, I focus on two levels of mathematical description of living cells:
- conformational changes of biomolecules (protein / nucleic acid folding)
- interaction / reaction networks
In the past 5 years, I have learned that mathematical models used in theoretical chemistry are helpful when designing efficient solutions to problems in chemical engineering and vice versa. Therefore, I am enthusiastic about mathematical formulation of any real world phenomena.
Table of Contents
Current projects
Dynamics of rare events
Characteristic times of interesting processes increase roughly exponentially with the height of the corresponding barrier. Methods that would properly sample dynamics of rare events are highly desired, since they could enable computer simulation of any system of interest regardless the barrier heght within days of computer time. We have recently develped a new method for construction of a master equation (first order system of ordinary differential equations) from a set of relatively cheap molecular simulations. We hope that our approach will avoid problems faced by currently used methods for simulation of rare events and lead to more accurate results.
Molecular friction
We study effects of projecting a complex energy landscape onto a few collective coordinates on the observed dynamics. Roughness of the landscape slows down the motion in the direction of the collective coordinates and can be modeled as a random force. We use relaxation path sampling to study the molecular friction acting on various test systems, such as clusters of Morse particles and alanine dipeptide. The results of this research can help understanding dynamics of biological molecules and self-assembly of nanoparticles.
Energy landscapes
Energy landscapes of complex molecular systems can be expressed in terms of kinetic transition networks. These networks are sparse, yet too large to study via full matrix diagonalisation. We develop tools for extracting observable rates of processes from lerge kinetic networks obtained by basin sampling or discrete relaxation path sampling.
Properties of simple polymer chains
A homopolymer of Lennard-Jones beads is the most simple model of biomacromolecules that possesses desirable properties:
- is off lattice
- has attractive potential
- bonds between beads are flexible
There is scope for studies on similarities between clusters and homopolymers, phase transitions of unconstrained homopolymers and for reversal and translocation of polymers through pores.
Past projects
Stability and folding of proteins
Proteins are essential for almost any process in living organisms. During folding, linear genetic information translates into structural and functional aggregates for cellular machines.
Thermodynamics of protein folding is poorly understood, since proteins are marginally stable as a result of compensation of thousands of strong interactions. I have studied stability of native proteins by modeling representative subset of known globular protein structures.
Despite extensive effort, debates on folding dynamics remain unresolved. New insight can be brought by new modeling approach, such as Markov state models and energy landscapes approaches.
Complex reaction networks
The systems of kinetic equations of practical interest are usually non-linear, resulting in unintuitive behavior such as oscillations or Turing instabilities. At the Institute of Chemical Technology in Prague, I was developing a general approach to qualitative understanding of systems comprising up to ~100 reactions. The methods were applied to toy reaction networks, a model of the atmosphere and a cellular metabolic pathway.