Fritz-Haber-Institut der Max-Planck-Gesellschaft  Department of Physical Chemistry
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Complex Dynamics.
Studies of complex dynamics in chemical and biophysical systems are performed by two groups and build on the tradition of research on nonlinear dynamics and spatiotemporal pattern formation established in the department.
  1. Complex Nonlinear Dynamics in Biophysical Systems
  2. Electrochemical Dynamics

1. Ultrafast Dynamics in
2. Molecular Processes at
3. Complex Dynamics



Activity reports

1. Complex Nonlinear Dynamics in Biophysical Systems

Rapid development of experimental methods in recent years has led to essential progress in molecular biophysics. Today, one cannot only observe single biological molecules, but also dynamically monitor their functional behavior or investigate the functional responses of protein machines to specific perturbations. Furthermore, non-invasive high-resolution optical methods provide the possibility to observe how spatial distributions of chemical species are dynamically evolving within living biological cells, and to investigate how such complex spatiotemporal processes are linked to the principal operation aspects of a biological cell. In essence, molecular cell biology is increasingly approaching a status of quantitative science, with the understanding being so profound that specific predictions become possible and the tools to control and steer biophysical processes can be developed. While molecular biophysics has started with the attempts to understand actual biological processes, the attention now gets shifted to synthetic and constructive biology and also to the design of artificial systems, such as protocells, which would reproduce certain properties of real biological objects and living biological cells.

The Complex Systems Group headed by Alexander Mikhailov is actively involved in these developments. In the last two years, firm contacts with leading international centers involved in the experimental and theoretical research on molecular biophysics have been established. Here, one should particularly stress the importance of collaborations with the recently founded RIKEN Center for Quantitative Biology in Kobe, Japan, and its director, Prof. T. Yanagida. In a joint project, the group aims to substantially deepen the understanding of how molecular motors, such as myosin, generate forces ultimately responsible for muscle contraction. Joint investigations, employing coarse-grained elastic-network dynamical descriptions of proteins, have allowed us to interpret the important experimental observations, indicating that myosin and, possibly, other protein motors are acting as molecular strain-sensors, so that their conformational responses to mechanical perturbations are central for their operation. As has been shown, mechano-chemical conformational dynamics in myosin and kinesin is intrinsically nonlinear and behavior of such motors cannot be understood with the usual normal-mode analysis [1].

Continuing previous research for another molecular motor, hepatitis C virus helicase, the group has finally produced numerical simulations which — for the first time for any molecular motor — reproduce in a structurally resolved dynamical way the entire operation cycles of this extensively studied protein machine, including its interactions with the double-strand DNA [2]. Proceeding further, conformational dynamics in several other helicase proteins has been analyzed in a comparative study.

Fig. 10: Numerical simulations of adenylate kinase (ADK). ADK is an enzyme catalyzing the reaction ATP + AMP 2 ADP. Right: Sequence of conformational transitions inside the turnover cycle. The protein includes three distinct domains: CORE (green), LID (blue) and NMP (light blue). In the free enzyme (A), both domains LID and NMP are open. Binding of ATP induces closing of domain LID (B); subsequent binding of AMP leads to closing of domain NMP (C). In the fully closed state C, catalytic conversion takes place. After that, first LID gets open (D) and then also NMP, restoring the original free state A. Left: Probability distribution in the plane of distances RLC and RLN between the centers of mass of the CORE and LID and CORE and NMP domains, respectively. From Ref. [3].

In a collaboration with Prof. R. Kapral, the head of the Chemical Physics Theory Group in the University of Toronto, the group has been working on the combination of the elastic-network coarse-grained descriptions for protein with the coarse-grained hydrodynamic description of the solvent. In this direction, important progress could beachieved. Incorporating available experimental data, catalytic turnover cycles of the enzyme adenylate kinase (ADK) in the presence of solvent have been reproduced [3]. Figure 10 shows the principal conformational states of this enzyme inside its turnover cycle and the computed probability density in the plane corresponding to distances between the principal protein domains. The current joint research, where scientists from the National Central University of Taiwan are additionally participating, is intended to enlarge coarse-grained descriptions, allowing us to consider operation of membrane-based protein machines in the presence of solvent.

At the next level of structural biological hierarchy, complex nonlinear dynamics of genetic regulation and protein signal transduction networks have been investigated. In an international project supported by the Volkswagen Foundation, the aim is to understand the origins of extreme robustness of real biological network-based systems to local structural perturbations and distributed noise. Here, the group collaborates with the RIKEN Center for Developmental Biology in Kobe, with the universities of Kyoto and Hokkaido, and with the Department of Mathematics in the Arizona State University. The first results include the model design [4] of synthetic oscillatory genetic networks able to maintain a required oscillation period with the accuracy of one percent despite the twenty-percent random variations of regulatory interaction strengths or knock-out of individual genes. Model signal-transduction networks with robust time-programmed functional responses have been designed and statistically investigated.

Going further to multi-cellular organisms, complex nonlinear dynamics in networks of diffusively coupled chemical microreactors has been theoretically considered. Together with Prof. H. Nakao from the Department of Physics of the Kyoto University (now in the Tokyo Institute of Technology), a detailed numerical study and statistical analysis of self-organized Turing patterns in network-based activator-inhibitor systems has been performed [5]. This work has attracted broad attention, since it clearly demonstrates the existence of rich self-organization behavior in biochemical networks.

[1]   Y. Togashi, T. Yanagida, A. S. Mikhailov, PLoS Comp. Biol. 6, e1000814 (2010).
[2]   H. Flechsig, A.S. Mikhailov, Proc. Natl. Acad. Sci. USA 107, 20875 (2010).
[3]   C. Echeverria, Y. Togashi, A. S. Mikhailov, R. Kapral, PCCP 13,10527 (2011).
[4]   Y. Kobayashi, T. Shibata, Y. Kuramoto, A. S. Mikhailov, Phys. Rev. E (2011, in press).
[5]   H. Nakao, A. S. Mikhailov, Nature Physics 6, 544 (2010).
2. Electrochemical Dynamics

The group of Markus Eiswirth, studying electrochemical systems, has concentrated on possible gains in efficiency under oscillatory conditions in fuel cells as well as on spatiotemporal pattern formation on electrodes.

In general, dissipation in a process is given by the product of the flux and the driving force; for an electrochemical reaction these correspond to the current and overvoltage. The efficiency is then just the difference between the theoretically achievable energy gain (thermodynamic limit) and the dissipation. In a nonlinear system, during forced or autonomous oscillations, flux and driving force can be out of phase (or even anti-phase), which lowers the average dissipation compared to the stationary state. This idea was tested for electrochemical systems. The experiments were carried out in cooperation with Hamilton Varela (University of Sao Paulo at Sao Carlos, Brazil, and Ertl Center for Electrochemistry and Catalysis, Gwangju, Korea).

For any oscillator with hidden negative differential resistance (HNDR) it could be shown that the efficiency always increases at the onset of potentiostatic oscillations, since the negative differential resistance (where voltage and current are anticorrelated) appears only on a sufficiently fast timescale, which is exactly the scale on which oscillations set in. For galvanostatic conditions, the situation is more complicated; the result crucially depends on the shape of the nonlinear oscillations.

As an experimental example, the oxidation of hydrogen containing trace amounts of CO (which is realistic for technical fuel cells in which the hydrogen is obtained from methanol) was chosen, with pure oxygen as oxidant.

The dissipation for oscillatory conditions was calculated by integrating over several periods and subtracted from the equilibrium enthalpy of the total gas flux through the chamber to obtain the efficiency. A typical result is reproduced in Fig. 11, together with the data for pure hydrogen (for which the constant-current and constant-voltage data are identical and stationary). The presence of CO led to a significant decrease in efficiency due to partial poisoning of the active surface. However, for oscillatory (constant-current) conditions the efficiency significantly increased again, almost reaching the levels of pure hydrogen.

Fig. 11: Comparison of the efficiency of a fuel cell operated with pure hydrogen and hydrogen containing trace amounts of CO. The former could only be operated under stationary conditions, while the latter also exhibited oscillations when drawing a constant current leading to a significant increase in efficiency. The inset shows the highly nonlinear nature of the oscillations.

Research on spatiotemporal self-organization was continued using formic acid oxidation on a Pt ring. A number of new patterns were obtained such as localized bursts, standing domains and oscillating 4-domain patterns. Mechanistic studies of electrochemical processes were carried out in close cooperation with the Department of Inorganic Chemistry, starting with water splitting on platinum single crystals.

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