Building blocks of protein structures: Physics meets biology

II. Geometrical framework for thinking about globular proteins: The power of poking

Recently, we presented a framework for understanding protein structure based on the idea that simple constructs of holding hands or touching of objects can be used to rationalize the common characteristics of globular proteins. We developed a consistent approach for understanding the formation of the two key common building blocks of helices and sheets as well as the compatible assembly of secondary structures into the tertiary structure through the notion of poking pairwise interactions. Here we benchmark our predictions with a detailed analysis of structural data of over 4000 proteins from the Protein Data Bank. We also present the results of detailed computer simulations of a simplified model demonstrating a pre-sculpted free energy landscape, determined by geometry and symmetry, comprising numerous minima corresponding to putative native state structures. We explore the consequences of our model. Our results suggest that symmetry and geometry are a powerful guide to capture the simplicity underlying protein complexity.

A geometrical framework for thinking about proteins

We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity.

III. Geometrical framework for thinking about globular proteins: Turns in proteins

We have shown recently that the notion of poking pairwise interactions along a chain provides a unifying framework for understanding the formation of both secondary and the tertiary protein structure based on symmetry and geometry. α-helices and β-sheets are found to be special geometries that have systematic poking contacts in a repetitive manner with the contacts being local along the α-helix and non-local along a pair of adjacent strands within a β-sheet. Pairwise poking interactions also govern tertiary structure formation, but they are weaker and there are no special geometrical constraints as in secondary structure formation. Here we demonstrate that protein turns, the most prevalent non-repetitive structural element in proteins, are instances of local (as in α-helices) and isolated (non-repetitive) poking pairwise contacts for which the geometrical constraints are partially relaxed. This simple and purely geometrical definition of protein turns (also sometimes known as reverse turns, β-turns, β-bends, hairpin bends, 310 bends, kinks, widgets, etc.) provides a simple framework for unifying them. We present the results of a systematic analysis and identify their structural classes as well as their respective amino acid preferences.

Solvent quality and nonbiological oligomer folding: revisiting conventional paradigms

We report on extensive molecular dynamics atomistic simulations of a meta-substituted poly-phenylacetylene (pPA) foldamer dispersed in three solvents, water H2O, cyclohexane cC6H12, and n-hexane nC6H14, and for three oligomer lengths 12mer, 16mer and 20mer. At room temperature, we find a tendency of the pPA foldamer to collapse into a helical structure in all three solvents but with rather different stability character, stable in water, marginally stable in n-hexane, unstable in cyclohexane. In the case of water, the initial and final number of hydrogen bonds of the foldamer with water molecules is found to be unchanged, with no formation of intrachain hydrogen bonding, thus indicating that hydrogen bonding plays no role in the folding process. In all three solvents, the folding is found to be mainly driven by electrostatics, nearly identical in the three cases, and largely dominant compared to van der Waals interactions that are different in the three cases. This scenario is also supported by the analysis of distribution of the bond and dihedral angles and by a direct calculation of the solvation and transfer free energies via thermodynamic integration. The different stability in the case of cyclohexane and n-hexane notwithstanding their rather similar chemical composition can be traced back to the different entropy-enthalpy compensation that is found similar for water and n-hexane, and very different for cyclohexane. A comparison with the same properties for poly-phenylalanine oligomers underscores the crucial differences between pPA and peptides. To highlight how these findings can hardly be interpreted in terms of a simple "good" and "poor" solvent picture, a molecular dynamics study of a bead-spring polymer chain in a Lennard-Jones fluid is also included.

Reframing the Protein Folding Problem: Entropy as Organizer

It has been a long-standing conviction that a protein's native fold is selected from a vast number of conformers by the optimal constellation of enthalpically favorable interactions. In marked contrast, this Perspective introduces a different mechanism, one that emphasizes conformational entropy as the principal organizer in protein folding while proposing that the conventional view is incomplete. This mechanism stems from the realization that hydrogen bond satisfaction is a thermodynamic necessity. In particular, a backbone hydrogen bond may add little to the stability of the native state, but a completely unsatisfied backbone hydrogen bond would be dramatically destabilizing, shifting the U(nfolded) ⇌ N(ative) equilibrium far to the left. If even a single backbone polar group is satisfied by solvent when unfolded but buried and unsatisfied when folded, that energy penalty alone, approximately +5 kcal/mol, would rival almost the entire free energy of protein stabilization, typically between -5 and -15 kcal/mol under physiological conditions. Consequently, upon folding, buried backbone polar groups must form hydrogen bonds, and they do so by assembling scaffolds of α-helices and/or strands of β-sheet, the only conformers in which, with rare exception, hydrogen bond donors and acceptors are exactly balanced. In addition, only a few thousand viable scaffold topologies are possible for a typical protein domain. This thermodynamic imperative winnows the folding population by culling conformers with unsatisfied hydrogen bonds, thereby reducing the entropy cost of folding. Importantly, conformational restrictions imposed by backbone···backbone hydrogen bonding in the scaffold are sequence-independent, enabling mutation─and thus evolution─without sacrificing the structure.

Marginally compact phase and ordered ground states in a model polymer with side spheres

We present the results of a quantitative study of the phase behavior of a model polymer chain with side spheres using two independent computer simulation techniques. We find that the mere addition of side spheres results in key modifications of standard polymer behavior. One obtains a marginally compact phase at low temperatures; the structures in this phase are reduced in dimensionality and are ordered, they include strands assembled into sheets and a variety of helices, and at least one of the transitions on lowering the temperature to access these ordered states is found to be first order. Our model serves to partially bridge conventional polymer phases with biomolecular phases.