... understanding life in molecular detail

Dr Sergei Krivov

Protein folding, Free energy landscapes, Computational Biology, Biophysics

We are interested in rigorous quantitative analysis of complex dynamics of (biological) systems by determining the underlying free energy landscapes. The approach has been developed originally for the analysis of the protein folding dynamics. Later it was generalised to analyse other types of complex dynamics such as disease dynamics or dynamics of the game of chess.

Current major projects include:
  • Free energy landscape analysis of protein folding dynamics
  • Methodological development of the free energy landscape framework
  • Quantitative analysis of disease dynamics.
  • Analysis of the game of chess

Life manifests itself through complex dynamics across many scales. From “wiggling and jiggling of atoms” (protein folding) to the transcription dynamics in gene regulatory networks, disease dynamics and the population dynamics at the top. Advances in the experimental techniques and computer simulations resulted in availability of multidimensional, time-resolved data about the dynamical processes. A very important practical problem is the development of rigorous algorithms for proper quantitative analysis of the data.

Free Energy Landscape Analysis of Protein Folding Dynamics.

One of the reasons that the protein folding problem still interests researchers, is that it is difficult to get direct and unambiguous answers about the basic questions of how proteins fold, due to the limited spatial and temporal resolution of state of the art experimental techniques. In principle, the detailed picture of how proteins fold can be obtained by simulation. Recent advances in the computer hardware, simulation methodology and force-field  accuracy made realistic simulation of the folding of small fast-folding proteins computationally affordable. With the steady progress in the simulation of protein folding the rigorous quantitative analysis of the obtained data becomes all the more important. In our group we analyze the dynamics by determining the underlying free energy landscapes. The approach developed in our group, is arguably, the only rigorous approach that allows one to rigorously determine free energy landscape that provide accurate quantitative description of the folding dynamics.

Free energy landscape of Fip35 protein - first realistic simulation of protein folding. Red line shows the free energy landscape along the optimal reaction coordinate while green shows that for a sub-optimal coordinate.

Methodological development of the free energy landscape framework.

The determination of the optimal reaction coordinate, which accurately represents the multidimensional folding dynamics, is the most challenging part of the approach. A poorly chosen coordinate can hide the complexity of the dynamics, decrease the height of the folding barrier, and make the dynamics sub-diffusive.  Once the optimal coordinate has been found, one can determine the associated free energy landscape and the position dependent diffusion coefficient, which completely specify the dynamics. We have introduced the notion of cut-based free energy profile and shown that the optimal coordinate is the one with the highest cut-based profile. These profiles are used to efficiently compute the diffusion coefficient.

Free Energy Landscape Analysis of Disease Dynamics

The responses of an individual to an infection, to pharmacological treatment or to surgery are examples of time dependent stochastic processes characterized by complex dynamics. An increasing amount of time-resolved data is available reporting on the unique chemical fingerprints that specific cellular processes leave behind. Quantitative description of this process in real-time by a single, clinically measurable parameter (biomarker) would be helpful for early, informed and targeted treatment. We suggested that an optimal biomarker can be obtained if it is defined and determined as an optimal reaction coordinate that provides a complete (Markovian) description of the dynamics as diffusion on the associated free energy landscape. Such predictive biomarkers have potentially unlimited applications as diagnostic tools.

Analysis of the game of chess.

To emphasize the power and generality of the approach the game of chess has been analyzed. Its complex dynamics is not generated by a physical system and thus applicability of the free-energy landscape framework is no evident. The optimal reaction coordinate and the associated free energy landscape has been determined, which provide accurate description of the dynamics. In particular, given a position on a chess board one can predict the probability of winning starting from the position. The analysis of the chess game shows that the approach can quantitatively describe the dynamics where human decision-making plays a central role, e.g., financial and social dynamics.

Free energy landscape for the game of chess. Smaller right barrier indicates that white has more chances to win.

Detailed research programme                  Close ▲

RCUK Academic Research Fellow (Leeds) 2008-present
PhD (Novosibirsk State University Russia)

Postdoc (University Louis Pasteur, Strasbourg) 2001-2008

Astbury 8.111
School of Molecular and Cellular Biology
0113 3433141

Selected Publications

  1. Krivov, S.V. (2012) On reaction coordinate optimality J. Chem. Theory Comput. 9, 135

  2. Banushkina, P.V. & Krivov, S.V. (2013) HIgh-Resolution Free-Energy Landscape analysis of alpha-Helical Protein Folding: HP35 and its Double Mutant.  J. Chem. Theory Comput. 9, 5257

  3. Krivov, S.V. ; Fenton, H; Goldsmith, PJ; Prasad RK; Fisher, J; Paci, E (2014) Optimal Reaction Coordinate as a Biomarker for the Dynamics of Recovery from Kidney Transplant. PLoS Comput. Biol. 10, e1003685

  4. Banushkina, P.V. & Krivov, S.V. (2015) Nonparametric variational optimization of reaction coordinates.  J. Chem. Phys. 143, 184108