where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

An outstanding challenge in the field of molecular biology has been to understand the process by which proteins fold into their characteristic three-dimensional structures. Here, we report the results of atomic-level molecular dynamics simulations, over periods ranging between 100 μs and 1 ms, that reveal a set of common principles underlying the folding of 12 structurally diverse proteins. In simulations conducted with a single physics-based energy function, the proteins, representing all three major structural classes, spontaneously and repeatedly fold to their experimentally determined native structures. Early in the folding process, the protein backbone adopts a nativelike topology while certain secondary structure elements and a small number of nonlocal contacts form. In most cases, folding follows a single dominant route in which elements of the native structure appear in an order highly correlated with their propensity to form in the unfolded state.

https://science.sciencemag.org/content/sci/334/6055/517.full.pdf

How Fast-Folding Proteins Fold

Stochastic differential equations and diffusion processes

The protein-folding problem was first posed about one half-century ago. The term refers to three broad questions: (i) What is the physical code by which an amino acid sequence dictates a protein's native structure? (ii) How can proteins fold so fast? (iii) Can we devise a computer algorithm to predict protein structures from their sequences? We review progress on these problems. In a few cases, computer simulations of the physical forces in chemically detailed models have now achieved the accurate folding of small proteins. We have learned that proteins fold rapidly because random thermal motions cause conformational changes leading energetically downhill toward the native structure, a principle that is captured in funnel-shaped energy landscapes. And thanks in part to the large Protein Data Bank of known structures, predicting protein structures is now far more successful than was thought possible in the early days. What began as three questions of basic science one half-century ago has now grown into the full-fledged research field of protein physical science.

http://science.sciencemag.org/content/sci/338/6110/1042.full.pdf

The Protein-Folding Problem, 50 Years On

http://nathan.instras.com/ResearchProposalDB/doc-108.pdf

Radiative decay engineering 5: metal-enhanced fluorescence and plasmon emission

http://hxiris.med.upenn.edu/publications/methods2004.pdf

Hydrogen exchange methods to study protein folding.

Equilibrium and kinetic hydrogen exchange experiments show that cytochrome c is composed of five foldon units that continually unfold and refold even under native conditions. Folding proceeds by the stepwise assembly of the foldon units rather than one amino acid at a time. The folding pathway is determined by a sequential stabilization process; previously formed foldons guide and stabilize subsequent foldons to progressively build the native protein. Four other proteins have been found to show similar behavior. These results support stepwise protein folding pathways through discrete intermediates.

https://www.pnas.org/content/pnas/102/13/4741.full.pdf

Protein folding: The stepwise assembly of foldon units

The fluorescence depolarization dynamics of organic fluorescent dye probes (nile red, cresyl violet, DODCI, rhodamine B, and rhodamine DPPE) were studied in cationic, anionic, and neutral micelles by picosecond time-resolved single-photon-counting technique. The fluorescence anisotropy decay of the dye intercalated inside the micelle is a two-exponential function. The anisotropy decay was interpreted by using a model of rotational (wobbling) and translational diffusion of the dye in the micelle coupled with the rotational motion of the micelle as a whole. The rotational and translational diffusion coefficients of the dye, the order parameter, and the semicone angle for the wobbling diffusion in the micelle were determined. The concept of “microviscosity” in the micelle was critically discussed in the light of the rotational and translational diffusion coefficients and their temperature dependence.

Fluorescence Dynamics of Dye Probes in Micelles

A model-free method is described for constructing time-resolved area-normalized emission spectra (TRANES) using luminescence decays at all emission wavelengths. An isoemissive point in TRANES indicates that the observed emission from the sample is due to two species only, irrespective of the origin of the two species or the excited-state kinetics. Proof for the existence of an isoemissive point in TRANES is given for various cases involving two emissive species. The isoemissive point in TRANES is qualitatively similar to the isosbestic point in time-resolved absorption spectra (TRAS) in kinetic spectrophotometry involving two species.

https://www.tifr.res.in/~koti/wp-content/uploads/2012/10/paper4.pdf

Time-Resolved Area-Normalized Emission Spectroscopy (TRANES): A Novel Method for Confirming Emission from Two Excited States

Two fundamentally different views of how proteins fold are now being debated. Do proteins fold through multiple unpredictable routes directed only by the energetically downhill nature of the folding landscape or do they fold through specific intermediates in a defined pathway that systematically puts predetermined pieces of the target native protein into place? It has now become possible to determine the structure of protein folding intermediates, evaluate their equilibrium and kinetic parameters, and establish their pathway relationships. Results obtained for many proteins have serendipitously revealed a new dimension of protein structure. Cooperative structural units of the native protein, called foldons, unfold and refold repeatedly even under native conditions. Much evidence obtained by hydrogen exchange and other methods now indicates that cooperative foldon units and not individual amino acids account for the unit steps in protein folding pathways. The formation of foldons and their ordered pathway assembly systematically puts native-like foldon building blocks into place, guided by a sequential stabilization mechanism in which prior native-like structure templates the formation of incoming foldons with complementary structure. Thus the same propensities and interactions that specify the final native state, encoded in the amino-acid sequence of every protein, determine the pathway for getting there. Experimental observations that have been interpreted differently, in terms of multiple independent pathways, appear to be due to chance misfolding errors that cause different population fractions to block at different pathway points, populate different pathway intermediates, and fold at different rates. This paper summarizes the experimental basis for these three determining principles and their consequences. Cooperative native-like foldon units and the sequential stabilization process together generate predetermined stepwise pathways. Optional misfolding errors are responsible for 3-state and heterogeneous kinetic folding.

M. M. G. Krishna

Papers

Hydrogen exchange methods to study protein folding.

Protein folding: The stepwise assembly of foldon units

Fluorescence Dynamics of Dye Probes in Micelles

Time-Resolved Area-Normalized Emission Spectroscopy (TRANES): A Novel Method for Confirming Emission from Two Excited States

Protein folding and misfolding: mechanism and principles