To Students Contemplating Research in Theoretical Biophysics

Klaus Schulten

The Theoretical Biophysics Group is aware that there are differences as well as similarities in the quests towards physical and biological theory. The most important difference in the pursuit of biological theory is that the latter is about advancing biology and not about advancing physics or other fields. One must also realize that theory is not as welcome by experimentalists in biology as it is in physics, since successes of theory in biology have been few, the field of evolutionary and hereditary biology being the notable exception. Recently, though, the standing of theory in biology has dramatically improved, both due to challenges in the biological sciences which beg for theoretical approaches as well as due to the increasing and extremely supportive role of computation, e.g., for sequence analysis and structure determination.

Many challenges for theoretical work exist. Most pressing are needs for concepts and algorithms to handle and analyze the rapidly increasing genetic data bases. The complete genomes of many biological species have recently become available and many more will become available soon. For many proteins, variants for numerous biological species are known with rich and still unearthed information underlying the conservation and variability of amino acids. The problem of predicting the structure of proteins from genetic sequences, the so-called protein folding problem, begs a solution with immeasurable opportunities once a solution is at hand. A further challenge is the structure--function relationship of proteins, a problem with extremely wide scope and characterized both through universality and diversity. It is fair to say that nearly half a decade after the first discovery of the atomic structure of a protein scientist have not yet unveiled the mechanisms by which proteins achieve their many functions: to catalyze reactions, to receive and generate signals, to endow cells with shape and elasticity, to move cells and their internal cargo, and to control genetic expression. The complexity of proteins demands still utmost respect from theoretical scientists.

Much of the research in the Theoretical Biophysics Group at Beckman Institute focuses on proteins. Theoretical studies of proteins proliferated with the advent of sufficiently powerful computers to simulate large particle systems and with the explosive increase of atomic resolution structures of proteins. The latter structures, though necessary prerequisites, in themselves are not sufficient for any physical theory of protein function; the motions in a protein play an equal role. On the methodological side the field is concerned with providing accurate, yet simple, force fields which govern the atomic motion of proteins. Ultimately, force fields will be determined in combined classical (for the nuclear motion)/quantum chemical (for the valence electrons) calculations.

Researchers are investing currently strong efforts in developing efficient computational methods for classical dynamics of proteins involving tens to hundred thousands of atoms; a serious hurdle, for example, is the calculation of Coulomb forces since they need to be evaluated for all pairs of atoms for all time steps of the classical motion. Suitable integration schemes can economize the costly update of forces, in particular the Coulomb forces, with a resulting boost in computational efficiency. At present a practitioner of the theory of proteins needs to be extremely competent in scientific computing with an understanding of massively parallel computing holding a particular promise for further success.

On the conceptual side an entry to protein dynamics is provided by studying normal modes. Since the classical Hamiltonian describing atomic motion is significantly non-harmonic and also extremely heterogeneous, conventional normal mode analysis as applied, e.g., for crystals, is not suitable. A quasi-harmonic description derives normal modes from a principal component analysis, i.e., from a diagonalization of the covariance matrix of all atomic positions, averaged over time. However, a gliding average with a, say, 100~ps window, reveals that modes derived in such way vary in time due to significant conformational transitions and disorder in proteins. Protein motion needs to be characterized also on spatial scales involving multi-atom segments of proteins. In fact, many proteins exhibit conformational changes which can be described as rotations of segments around hinges or as motions of flaps formed by secondary structure elements, e.g., alpha-helices or loops between alpha-helices. Finally, the structure of proteins can undergo melting-type transitions when the environment changes, e.g., through binding of a charged substrate, a feature that is exploited by proteins involved in cellular signaling.

The abstraction of functional properties from molecular dynamics simulations still remains an important challenge. Following established approaches one can identify correlation functions and susceptibilities that provide essential characteristics of protein dynamics and can be related to observation and function. Examples are the following: a correlation function called the dynamic structure function is the Fourier transform of the motion of a protein's constituents and is observable through neutron diffraction or Moessbauer spectroscopy; the correlation function of the energy difference between two quantum states with diagonal coupling to the protein matrix accounts for the transition rate between the two states, e.g.,for the rate of electron transfer; the dielectric susceptibility and thermal susceptibility, determined through monitoring dipolar or energy fluctuations account for dielectric properties and the degree of order of water associated with proteins.

The theory of proteins, as a relatively young field, can benefit tremendously from related and already established fields. The closest relative is the theory of liquids since solvent molecules, though not connected into a polymer and much more homogeneous in structure, are subject to similar forces and to similar disorder phenomena. On larger length and longer time scales, molecular hydrodynamics can provide much guidance to gain understanding of low frequency motion of protein segments encompassing many atoms. Condensed matter theory of disordered materials likewise deals with systems, e.g., glasses, of great conceptual similarity. Condensed matter theory can also serve as a reminder that the primary role of theory is not quantitative description, but rather qualitative understanding; anybody suspecting that not much useful can come of such a role should have a close look at the triumphs of condensed matter theory.

The beauty of theoretical protein science stems from its rapidly increasing treasure of new structures and functions; one could hardly imagine a science with more relevance to the existence and well-being of humans, and with greater riches in new discoveries and, consequently, new challenges.

The greatest such challenge considers the interplay of many proteins in biological cells. This interplay is the core attribute of living systems, one may even say that it answers the question of the origin of life. Living systems are all made of many molecular components that self-assemble, control each other and self-replicate, and dealing with such systems has been a problem for scientists who were good at taking the molecular machines in living cells apart and learnt what they are made of. But how are these machines assembled? How can it be that proteins, describable by the laws of physics, assemble themselves into cellular machines and structures, these into complete living cells, and the latter into whole organisms that require a whole new language for their description, that of biology.

Where in this hierarchy of assemblies does the step from inorganic matter to living systems occur? Certainly single cells must be considered alive, and half a cell does not remain alive. What is the simplest living cell made of?

But is the cell the lowest organization that typifies living systems or can one glance the key characteristics of living systems already from its constituents. Would such attempt run counter to understanding life or could it provide a more gradual route to develop such understanding on the basis of what we know well. The answer cannot be known beforehand, but going this path scientists need to guide their search and analysis by keeping in mind the eventual goal of understanding how life comes about through the self-organization of innate matter.

Are we aware of principles that govern such self-organization? We definitely can state three principles.

One is that the sustenance of the order of systems in living cells requires a constant consumption of energy. Living systems cannot be static and in keeping alive consume resources. Important is that this principle holds down to any level of order in cells.

Second, self-organization is based on interactions of many components. Mathematically, this is reflected by the fact that nonlinear dynamical systems that account for interactions of components exhibit emergent properties in developing order from homogeneous initial conditions. Biologically, this is reflected in the many control components found in living cells: genes are controlled often through numerous other genes and molecules; the cell has developed also many signaling loops for the control of its metabolism and movement.

Lastly, one needs to account for the empirical fact that living systems are robust against minor perturbations such that they seek to employ networks of interactions that allow operation under perturbations as opposed to using network types that function only in a narrow range of physical parameters.

The principles of self-organization have been established during the past decades, but the real being of cells is molecular and there is still a wide gap in our knowledge. We need to build bridges between the molecular level of cells and higher organizational forms. To see where such bridges can be built is the most difficult part in this endeavor.

The Theoretical Biophysics Group at Beckman has developed a research program that assumes that suitable bridges have been identified. For example, the group investigates a cellular membrane in archaebacteria (purple membrane) that absorbs light and converts its energy into a membrane potential. Likewise, the group investigates an apparatus, called the photosynthetic unit, that exists in the cell membrane of certain photosynthetic bacteria and is more complex than the purple membrane. This apparatus contains six types of multi-protein complexes: the photosynthetic reaction center, the light harvesting complex 1, the light harvesting complex 2, a cytochrome, a bc1 complex, and an ATPase. All proteins are structurally quite well known so that explanations can be based on molecular level information.

The website of the Theoretical Biophysics Group provides further examples of our recent work that reflect the research opportunities available to students who choose a career in Theoretical Biophysics. Students with good backgrounds in physics, mathematics, and computing, with a strong motivation to discover the molecular organization of life, and the interest to work in a team of physicists, chemists, biologists and computer scientists are welcome to join us.

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