Unified perspective on proteins A physics approach

Unified perspective on proteins: A physics approach

The revolution in molecular biology [1] sparked by the discovery [2] of the structure of the DNA molecule 50 years ago has led to a breathtakingly beautiful description of life. Life employs well-tailored chain molecules to store and replicate information, to carry out a dizzying array of functionalities, and to provide a molecular basis for natural selection. The complementary base pairing mechanism in DNA combined with its double-helix structure serves as a repository of information and provides a pretty mechanism for replication [2]. The replication is prone to errors or mutations and these errors, which are the basis of evolution, are in turn copied in future generations [3]. Using the RNA molecule as an inter-mediary, the information contained in the DNA genes is translated into proteins, which are linear chains of amino acids. Unlike the DNA molecule, which adopts a limited number of related structures, protein molecules [4-6] fold into thousands of native state structures under physiological conditions. For proteins, form determines functionality and the rich variety of observed forms underscores the versatility of proteins. There then follows a complex orchestrated dance in which proteins catalyze reactions, interact with each other, and finally feed back into the gene to regulate the synthesis of other proteins [1].

A protein molecule is large and has many atoms. In addi-tion, the water molecules surrounding the protein play a cru-cial role in its behavior. At the microscopic level, the laws of quantum mechanics can be used to deduce the interactions but the number of degrees of freedom is far too many for the system to be studied in all its detail. When one attempts to look at the problem in a coarse-grained manner [7] with what one hopes are the essential degrees of freedom, it is very hard to determine what the effective potential energies of interaction are. This situation makes the protein problem particularly daunting and no solution has yet been found. Over many decades, much experimental data has been accumulated yet theoretical progress has been somewhat limited. The problem is highly interdisciplinary and touches on biology, chemistry, and physics and it is often hard to distill the essential features of each of the multiple aspects of the problem. The great successes of quantum chemistry in the determination of the structure of the DNA molecule [2] and in the spectacular prediction that helices and sheets [8-10] are the building blocks of protein structures have spurred much work using detailed chemistry on understanding the protein problem. Such work has been very insightful in pro-viding useful hints on how proteins behave at the atomic scale in performing their tasks. The missing feature, of course, in such a theoretical approach is that it treats each protein as a special entity with all the attendant details of the sequence of amino acids, their intricate side chain atoms, and the water molecules. Such an approach, while quite valuable, neither has as a goal nor can lend itself to a unified way of understanding seemingly disparate phenomena pertaining to proteins. Reinforcing this, experiments, which are very chal-lenging, are carried out on one protein at a time and cry out for an understanding of the behavior of an individual class of protein.

The lessons we have learned from physics are of a different nature. The history of physics is replete with examples of the elucidation of connections between what seem to be distinct phenomena and the development of a unifying frame-work, which, in turn, leads to new observable consequences [11,12]. There have been many attempts at using physics-based approaches for understanding proteins. These have provided valuable insights on how one might think about the problem and have served as a means of understanding experimental data. Yet no simple unification has been achieved in a deeper understanding of the key principles at work in proteins.

We restrict ourselves to globular proteins which display the rich variety of native state structures. There are other interesting and important classes of proteins [13] such as membrane proteins and fibrous proteins which we do not consider here. Our goal here is to present a different ap-proach to understanding proteins—our focus is on under-standing the origin of protein structures and how they form the basis for both functionality and natural selection. Our work points to a unification of the various aspects of allproteins: symmetry and geometry determine the limited menu of folded conformations that a protein can choose from for its native state structure; these structures are in a margin-ally compact phase in the vicinity of a phase transition and are therefore eminently suited for biological function; these structures are the molecular target for the powerful forces of evolution; proteins are well-designed sequences of amino ac-ids which fit well into one of these predetermined folds; and proteins are prone to misfolding and aggregation leading to the formation of amyloids, which are implicated in debilitating human diseases [14,15] such as Alzheimer’s, light-chain amyloidosis, and spongiform encephalopathies. We present a discussion of the nature of the denatured state (which can loosely be thought of as the collection of unfolded conformations) and its possible key role in the pro-tein folding problem. We also show how disordered proteins could fit into our unified framework.

The problem of how life was created is a fascinating one. Our focus is on looking at life on earth and asking how it works. The lessons we learn provide hints to the answers of deep and fundamental questions that have been pondered by our ancients: Was life on earth inevitable? Then there is the question posed by Henderson [16] about whether the nature of our physical world is biocentric. Is there a need for fine-tuning in biochemistry to provide for the fitness of life in the cosmos or even less ambitiously for life here on earth? Surprisingly, as we will show, a physics approach turns out to be valuable for thinking about these questions.

The main text of the paper contains the principal ideas and details of the calculations are relegated to the Appen-dixes. In Sec. II, we introduce the description of a protein as a thick polymer chain and highlight the differences in its phase diagram with respect to the usual string and bead model. In Sec. III, we make a comparison of the predictions obtained from the simple tube model against experimental data available on protein native state structures. In Sec. IV, we introduce a more refined model in which the tube picture is reinforced with the geometrical constraints that arise in the formation of hydrogen bonds and discuss the resulting phase diagram for an isolated peptide chain. In Sec. V, we discuss several consequences of our model including the nature of the free energy landscape, the innate propensity of proteins to aggregate into amyloidlike forms, and the role played by proteins as the targets of natural selection in molecular evo-lution. In Sec. VI, we discuss the nature of the denatured state of proteins and its possible role in protein folding. In the final Sec. VII, we conclude with a summary.

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