# Research of the Theoretical and Computational Biophysics Group - Helmut Grubmüller

The aim of the theoretical biophysics group is to contribute to the understanding of the physics and function of biomolecules - particularly proteins - at the atomic level. Here, two lines of questions span the field at the interface between physics, molecular biochemistry and computer science:

(1) What structural and dynamical properties are common to proteins? How can these highly organized, but irregular pieces of condensed matter be described in terms of many-body systems?

(2) How does a given protein work? What is the mechanism of such biochemical 'nano-machine'?

New concepts to neglect irrelevant degrees of freedom as well as efficient and problem-oriented, parallel algorithms for molecular dynamics simulations, being indispensable tools in that area, are our methodological focus.

Both lines of questions phrased above are closely interlinked. Progress in the understanding of the physics of proteins, on the one hand, enables improved and more realistic simulation techniques, which allow to study a growing number of biochemical processes in great detail. Through analysis of well-understood mechanisms, on the other hand, one can learn to separate relevant aspects in protein dynamics from irrelevant ones - which is prerequisite for the construction of effective protein models. In short, we find a close interplay between theory development, algorithmic progress, and application.

Understanding protein function requires work in classical mechanics, electrostatics, statistical mechanics, quantum mechanics, and computer science. Up to now there is no unifying 'protein theory'; rather, there is a patch-work of methods and concepts describing different facets of these complex systems. Accordingly, success depends on the ability to work on, to apply, to combine and to implement many 'patches'. It is therefore typical to groups like this to offer a wide range of projects to students and, vice versa, our research requires the contributions of many motivated students. Below a few contributions of group members to these facets are sketched. This work by members of the group and others has been done in the groups of Klaus Schulten (UIUC, Urbana-Champaign, Illinois, U.S.A.), Paul Tavan (Institut für Medizinische Optik, Universität München, Germany), and Kurt Wüthrich, ETH Zürich, Swizzerland)

At room temperature, the motion of the several thousand atoms of a protein can to a good approximation be described classically, which is the basis for the success of molecular dynamics simulations. These are computationally demanding, however, and, therefore, development of efficient parallel algorithms is essential. At present the simulations are restricted to very short time scales (nanoseconds); most functional processes are much slower and, hence, currently are out of reach. Protein folding, for example, typically requires milliseconds to seconds to be completed, and thus protein structure prediction is one of the 'great challenges' for theoretical biophysics. We and many others strive for more and more efficient simulation techniques by using high performance parallel computers as well as by developing tricky algorithms for the time consuming calculation of electrostatic interactions between the many charged atoms in a protein. The generalized Verlet method, e.g., enabled to study a very large protein - the socalled 'photosynthetic reaction center' - as well as a 'patch' of lipid membrane (the native environment of many proteins).

A number of these new methods has been implemented within the parallel molecular dynamics program EGO, which thus allows very efficient simulations. Using EGO, we were able to study a prototypic ligand-receptor system for molecular recognition (streptavidin-biotin) to simulate the unbinding of this complex for the first time, and, by comparing the required 'rupture force' with single molecule atomic force microscopy experiments, to demonstrate the power of the molecular dynamics method.

Despite that progress conventional methods to compute the detailed motion of many thousand atoms are not efficient enough to describe structural rearrangements, which occur on a microsecond time scale, i.e., three orders of magnitude slower than the simulation time scale. These socalled 'conformational transitions' between 'conformational substates' are of central interest, though, since in many instances they represent the elementary steps of protein function; they are the `gears and wheels' which make many proteins work. Sophisticated experiments have contributed much to our knowledge on conformational transitions - much more than theory has up to now.

Aiming at an improved theoretical treatment, we and few others have begun to employ concepts of statistical mechanics to protein dynamics. Here, the most basic concept is the distinction between 'relevant' and 'irrelevant' degrees of freedom. For protein dynamics, it is obvious to assume that most details of the fast atomic vibrations are indeed irrelevant for the proper description of conformational transitions. Accordingly, the conformational dynamics of a given protein should be describable by (hopefully few) 'relevant' degrees of freedom without wasting time in computing the atomic motion to its finest details. Due to the highly irregular structure of proteins, that scenario of 'mesoscopic dynamics' bears a series of challenges. To name only the most fundamental one, already the question of how to identify the relevant degrees of freedom and how to separate them from the many irrelevant ones is not at all as easily solved as it is, e.g., for crystal vibrations (where phonons serve that purpose).

To that aim we have rigorously defined the notion of conformational substates as minima in a free energy landscape spanned by suitably chosen relevant degrees of freedom. This statistical approach led to develop a method ('conformational flooding') to predict the slow conformational transitions in proteins by means of computer simulations - a task which has not yet been solved otherwise. Here, the trick is to derive approximate analytical descriptions of the substates of interest and to use those descriptions to accelerate the conformational transitions in (modified) molecular dynamics simulations. In doing so, the slow conformational dynamics is shifted into the fast simulation time scale, and thereby many slow processes are made accessible to computer simulations.

In a first application of 'conformational flooding' the collective gating motion of an ion channel (gramicidin A), which can be observed using patch clamp techniques, bound be described correctly. Currently we are studying as examples of conformational motion a trypsin inhibitor and myoglobin as well as the pathogenic conformational transitions in prions, which have become well known trough Prusiner s' work, for which he recently received the Nobel Prize.

A very recent focus of interest concerns the study of chemical reactions in proteins, particularly enzymatic reactions. Since chemical reactions are intrinsically quantum mechanical, they cannot be described by molecular dynamics techniques, which treat the atomic motion classically. Recently density functional techniques for computation of electronic (ground) states have matured to the point where they can serve to describe those region of an enzyme quantum-mechanically, where the chemical reactions take place, while the remainder of the protein is described classically. Such hybrid-approach holds the promise to trade off the complexity and the size of a protein and the effort of a quantum-mechanical description. We intend to apply this method to the study of the enzymatic mechanism of acetylcholinesterase, one of the fastest enzymes known.

We are convinced that the close interplay between methodological developments and applications, sketched above, will continue to be fruitful. With applications to an increasing number of biochemical systems we continuously seek to sharpen our computational tools, to check newly developed concepts and methods against experiment, to demonstrate their feasibility, and to extend our knowledge on proteins.