Establishing the entatic state in folding metallated Pseudomonas aeruginosa azurin

Understanding how the folding of proteins establishes their functional characteristics at the molecular level challenges both theorists and experimentalists. The simplest test beds for confronting this issue are provided by electron transfer proteins. The environment provided by the folded protein to the cofactor tunes the metal's electron transport capabilities as envisioned in the entatic hypothesis. To see how the entatic state is achieved one must study how the folding landscape affects and in turn is affected by the metal. Here, we develop a coarse-grained functional to explicitly model how the coordination of the metal (which results in a so-called entatic or rack-induced state) modifies the folding of the metallated Pseudomonas aeruginosa azurin. Our free-energy functional-based approach directly yields the proper nonlinear extra-thermodynamic free energy relationships for the kinetics of folding the wild type and several point-mutated variants of the metallated protein. The results agree quite well with corresponding laboratory experiments. Moreover, our modified free-energy functional provides a sufficient level of detail to explicitly model how the geometric entatic state of the metal modifies the dynamic folding nucleus of azurin

Detection of a Light Echo from the Otherwise Normal SN 2007af

We present the discovery of a light echo from SN 2007af, a normal Type Ia supernova (SN Ia) in NGC 5584. Hubble Space Telescope (HST) images taken three years post explosion reveal two separate echoes; an outer echo and extended central region, which we propose as an unresolved inner echo. Multiple images were obtained in the F160W, F350LP, F555W, and F814W using the Wide Field Camera 3. If the outer echo is produced by an interstellar dust sheet perpendicular to the line of sight, it is located ~800 pc in front of the SN. The dust for the inner echo is 0.45 pc < d < 90 pc away from the SN. The inner echo color is consistent with typical interstellar dust wavelength-dependent scattering cross-sections, while the outer echo color does not match the predictions. Both dust sheets, if in the foreground, are optically thin for scattering, with the outer echo sheet thickness consistent with the inferred extinction from peak brightness. Whether the inner echo is from interstellar or circumstellar dust is ambiguous. Overall, the echo characteristics are quite similar to previously observed SN Ia echoes.Comment: 15 pages, 6 figures, 7 table

Simple models of protein folding and of non--conventional drug design

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the three--dimensional, biologically active, native conformation of a protein whose sequence is known. Using insight obtained from simple model simulations of the folding of proteins, in particular of the fact that this phenomenon is essentially controlled by conserved (native) contacts among (few) strongly interacting ("hot"), as a rule hydrophobic, amino acids, which also stabilize local elementary structures (LES, hidden, incipient secondary structures like $\alpha$--helices and $\beta$--sheets) formed early in the folding process and leading to the postcritical folding nucleus (i.e., the minimum set of native contacts which bring the system pass beyond the highest free--energy barrier found in the whole folding process) it is possible to work out a succesful strategy for reading the native structure of designed proteins from the knowledge of only their amino acid sequence and of the contact energies among the amino acids. Because LES have undergone millions of years of evolution to selectively dock to their complementary structures, small peptides made out of the same amino acids as the LES are expected to selectively attach to the newly expressed (unfolded) protein and inhibit its folding, or to the native (fluctuating) native conformation and denaturate it. These peptides, or their mimetic molecules, can thus be used as effective non--conventional drugs to those already existing (and directed at neutralizing the active site of enzymes), displaying the advantage of not suffering from the uprise of resistance

Role of Secondary Motifs in Fast Folding Polymers: A Dynamical Variational Principle

A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from chemical propensity to simple geometrical reasoning have been invoked to rationalize the existence of such secondary structures. We formulate a dynamical variational principle for selection in conformation space based on the requirement that the backbone of the native state of biologically viable polymers be rapidly accessible from the denatured state. The variational principle is shown to result in the emergence of helical order in compact structures.Comment: 4 pages, RevTex, 4 eps figure

Folding, Design and Determination of Interaction Potentials Using Off-Lattice Dynamics of Model Heteropolymers

We present the results of a self-consistent, unified molecular dynamics study of simple model heteropolymers in the continuum with emphasis on folding, sequence design and the determination of the interaction parameters of the effective potential between the amino acids from the knowledge of the native states of the designed sequences.Comment: 8 pages, 3 Postscript figures, uses RevTeX. Submitted to Physical Review Letter

An Analytical Approach to the Protein Designability Problem

We present an analytical method for determining the designability of protein structures. We apply our method to the case of two-dimensional lattice structures, and give a systematic solution for the spectrum of any structure. Using this spectrum, the designability of a structure can be estimated. We outline a heirarchy of structures, from most to least designable, and show that this heirarchy depends on the potential that is used.Comment: 16 pages 4 figure

Finite size effects on thermal denaturation of globular proteins

Finite size effects on the cooperative thermal denaturation of proteins are considered. A dimensionless measure of cooperativity, Omega, scales as N^zeta, where N is the number of amino acids. Surprisingly, we find that zeta is universal with zeta = 1 + gamma, where the exponent gamma characterizes the divergence of the susceptibility for a self-avoiding walk. Our lattice model simulations and experimental data are consistent with the theory. Our finding rationalizes the marginal stability of proteins and substantiates the earlier predictions that the efficient folding of two-state proteins requires the folding transition temperature to be close to the collapse temperature.Comment: 3 figures. Physical Review Letters (in press

Protein structures and optimal folding emerging from a geometrical variational principle

Novel numerical techniques, validated by an analysis of barnase and chymotrypsin inhibitor, are used to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the correct native state. It is found that, irrespective of the sequence, the native state of a protein has exceedingly large number of conformations with a given amount of structural overlap compared to other compact artificial backbones; moreover the conformational entropies of unrelated proteins of the same length are nearly equal at any given stage of folding. These results are suggestive of an extremality principle underlying protein evolution, which, in turn, is shown to be associated with the emergence of secondary structures.Comment: Revtex, 5 pages, 5 postscript figure

Viscosity Dependence of the Folding Rates of Proteins

The viscosity dependence of the folding rates for four sequences (the native state of three sequences is a beta-sheet, while the fourth forms an alpha-helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation we show that the folding rates increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and have a maximum at intermediate values. The Kramers theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn \alpha-helix topology is about 500 nanoseconds, whereas the time scale for forming a beta-sheet topology is about 10 microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical Review Letter

Deriving amino acid contact potentials from their frequencies of occurence in proteins: a lattice model study

The possibility of deriving the contact potentials between amino acids from their frequencies of occurence in proteins is discussed in evolutionary terms. This approach allows the use of traditional thermodynamics to describe such frequencies and, consequently, to develop a strategy to include in the calculations correlations due to the spatial proximity of the amino acids and to their overall tendency of being conserved in proteins. Making use of a lattice model to describe protein chains and defining a "true" potential, we test these strategies by selecting a database of folding model sequences, deriving the contact potentials from such sequences and comparing them with the "true" potential. Taking into account correlations allows for a markedly better prediction of the interaction potentials