Heat capacity of protein folding.

We construct a Hamiltonian for a single domain protein where the contact enthalpy and the chain entropy decrease linearly with the number of native contacts. The hydration effect upon protein unfolding is included by modeling water as ideal dipoles that are ordered around the unfolded surfaces, where the influence of these surfaces, covered with an "ice-like" shell of water, is represented by an effective field that directs the water dipoles. An intermolecular pair interaction between water molecules is also introduced. The heat capacity of the model exhibits, the common feature of small globular proteins, two peaks corresponding to cold and warm unfolding, respectively. By introducing ad hoc vibrational modes, we obtain quantitatively good accordance with experiments on myoglobin.     

Heat capacity effects in protein folding and ligand binding: a re-evaluation of the role of water in biomolecular thermodynamics

Large "anomalous" heat capacity (DeltaC(p)) effects are a common feature of the thermodynamics of biomolecular interactions in aqueous solution and, as a result of the improved facility for direct calorimetric measurements, there is a growing body of experimental data for such effects in protein folding, protein-protein and protein-ligand interactions. Conventionally such heat capacity effects have been ascribed to hydrophobic interactions, and there are some remarkably convincing demonstrations of the usefulness of this concept. Nonetheless, there is also increasing evidence that hydrophobic interactions are not the only possible source of such effects. Here we re-evaluate the possible contributions of other interactions to the heat capacity changes to be expected for cooperative biomolecular folding and binding processes, with particular reference to the role of hydrogen bonding and solvent water interactions. Simple models based on the hydrogen-bonding propensity of water as a function of temperature give quantitative estimates of DeltaC(p) that compare well with experimental observations for both protein folding and ligand binding. The thermodynamic contribution of bound waters in protein complexes is also estimated. The prediction from simple lattice models is that trapping of water in a complex should give more exothermic binding (DeltaDeltaH-6 to -12 kJ mol(-1)) with lower entropy (DeltaDeltaS(0) approximately -11 J mol(-1) K(-1)) and more negative DeltaC(p) (by about -75 J mol(-1) K(-1)) per water molecule. More generally, it is clear that significant DeltaC(p) effects are to be expected for any macromolecular process involving a multiplicity of cooperative weak interactions of whatever kind.     

Thermodynamics of protein folding: a microscopic view

Statistical thermodynamics provides a powerful theoretical framework for analyzing, understanding and predicting the conformational properties of biomolecules. The central quantity is the potential of mean force or effective energy as a function of conformation, which consists of the intramolecular energy and the solvation free energy. The intramolecular energy can be reasonably described by molecular mechanics-type functions. While the solvation free energy is more difficult to model, useful results can be obtained with simple approximations. Such functions have been used to estimate the intramolecular energy contribution to protein stability and obtain insights into the origin of thermodynamic functions of protein folding, such as the heat capacity. With reasonable decompositions of the various energy terms, one can obtain meaningful values for the contribution of one type of interaction or one chemical group to stability. Future developments will allow the thermodynamic characterization of ever more complex biological processes.     

Entropy capacity determines protein folding

Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Here, based on the known experimental data and using theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue-that is, an entropy capacity-for fast protein folding. Statistical analysis of conformational entropy and number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts (class alpha/beta has the largest number of contacts) and average conformational entropy per residue (class all-alpha has the largest number of rotatable angles phi, psi, and chi per residue). These class-specific features determine the folding rates: alpha proteins are the fastest folding proteins, then follow beta and alpha+beta proteins, and finally alpha/beta proteins are the slowest ones. Our result is in agreement with the experimental folding rates for 60 proteins. This suggests that structural and sequence properties are important determinants of protein folding rates.     

Mitotic mechanisms: an alternative view

The mechanisms that control spindle structure and move chromosomes remain as mysterious as ever. Using the diatom as a model spindle type, several interesting and counter-intuitive possibilities have emerged. For example, there may not be an anaphase motor and a primary energy-requiring (force-producing) mechanism may actually move chromosomes away from the pole. Force may be a primary factor controlling microtubule assembly disassembly.     

Genomic determinants of protein folding thermodynamics in prokaryotic organisms

Here we investigate how thermodynamic properties of orthologous proteins are influenced by the genomic environment in which they evolve. We performed a comparative computational study of 21 protein families in 73 prokaryotic species and obtained the following main results. (i) Protein stability with respect to the unfolded state and with respect to misfolding are anticorrelated. There appears to be a trade-off between these two properties, which cannot be optimized simultaneously. (ii) Folding thermodynamic parameters are strongly correlated with two genomic features, genome size and G+C composition. In particular, the normalized energy gap, an indicator of folding efficiency in statistical mechanical models of protein folding, is smaller in proteins of organisms with a small genome size and a compositional bias towards A+T. Such genomic features are characteristic for bacteria with an intracellular lifestyle. We interpret these correlations in light of mutation pressure and natural selection. A mutational bias toward A+T at the DNA level translates into a mutational bias toward more hydrophobic (and in general more interactive) proteins, a consequence of the structure of the genetic code. Increased hydrophobicity renders proteins more stable against unfolding but less stable against misfolding. Proteins with high hydrophobicity and low stability against misfolding occur in organisms with reduced genomes, like obligate intracellular bacteria. We argue that they are fixed because these organisms experience weaker purifying selection due to their small effective population sizes. This interpretation is supported by the observation of a high expression level of chaperones in these bacteria. Our results indicate that the mutational spectrum of a genome and the strength of selection significantly influence protein folding thermodynamics.     

Alpha-synuclein multistate folding thermodynamics: implications for protein misfolding and aggregation

Alpha-synuclein aggregation has been tightly linked with the pathogenesis of Parkinson's disease and other neurodegenerative disorders. Despite the protein's putative function in presynaptic vesicle regulation, the roles of lipid binding in modulating alpha-synuclein conformations and the aggregation process remain to be fully understood. This study focuses on a detailed thermodynamic characterization of monomeric alpha-synuclein folding in the presence of SDS, a well-studied lipid mimetic. Far-UV CD spectroscopy was employed for detection of conformational transitions induced by SDS, temperature, and pH. The data we present here clearly demonstrate the multistate nature of alpha-synuclein folding, which involves two predominantly alpha-helical partially folded thermodynamic intermediates that we designate as F (most folded) and I (intermediately folded) states. Likely structures of these alpha-synuclein conformational states are also discussed. These partially folded forms can exist in the presence of either monomeric or micellar forms of SDS, which suggests that alpha-synuclein has an intrinsic propensity for adopting multiple alpha-helical structures even in the absence of micelle or membrane binding, a feature that may have implications for its biological activity and toxicity. Additionally, we discuss the relation between alpha-synuclein three-state folding and its aggregation, within the context of isothermal titration calorimetry and transmission electron microscopy measurements of SDS-initiated oligomer formation.     

Confinement effects on the thermodynamics of protein folding: Monte Carlo simulations

The effects of chaperonin-like cage-induced confinement on protein stability have been studied for molecules of varying sizes and topologies. Minimalist models based on Gō-like interactions are employed for the proteins, and density-of-states-based Monte Carlo simulations are performed to accurately characterize the thermodynamic transitions. This method permits efficient sampling of conformational space and yields precise estimates of free energy and entropic changes associated with protein folding. We find that confinement-driven stabilization is not only dependent on protein size and cage radius, but also on the specific topology. The choice of the confining potential is also shown to have an effect on the observed stabilization and the scaling behavior of the stabilization with respect to the cage size.     

Heat capacity changes associated with nucleic acid folding

Whereas heat capacity changes (DeltaCPs) associated with folding transitions are commonplace in the literature of protein folding, they have long been considered a minor energetic contributor in nucleic acid folding. Recent advances in the understanding of nucleic acid folding and improved technology for measuring the energetics of folding transitions have allowed a greater experimental window for measuring these effects. We present in this review a survey of current literature that confronts the issue of DeltaCPs associated with nucleic acid folding transitions. This work helps to gather the molecular insights that can be gleaned from analysis of DeltaCPs and points toward the challenges that will need to be overcome if the energetic contribution of DeltaCP terms are to be put to use in improving free energy calculations for nucleic acid structure prediction.     

Heat capacity change for ribonuclease A folding.

The change in heat capacity deltaCp for the folding of ribonuclease A was determined using differential scanning calorimetry and thermal denaturation curves. The methods gave equivalent results, deltaCp = 1.15+/-0.08 kcal mol(-1) K(-1). Estimates of the conformational stability of ribonuclease A based on these results from thermal unfolding are in good agreement with estimates from urea unfolding analyzed using the linear extrapolation method.     

Plant intelligence: an alternative point of view

The concept of plant intelligence has been advanced by Trewavas as a potentially useful framework to guide those seeking to understand plant growth and development. In this short critique, the validity of this concept is critically assessed. Central to this critique is the proposition that the concept of the individual, to which intelligence and behaviour are intimately linked, cannot usefully be applied to plants. It is argued that the adaptive responses of plants are best appreciated if the importance of the autonomy of the individual organs is acknowledged. Although Trewavas does acknowledge the autonomy of organs by describing an individual plant as being 'a democratic confederation', that terminology implies a complexity to the interaction between organs which would demand a cogitative ability beyond that actually demonstrated in plants. It may be more appropriate to consider a plant as operating normally as a simple economic federation of many specialized economies (organs and cells). Occasionally, there can be a dramatic, and sometimes complex, reshaping of the economic balances, with the result that the fate of some or many of the individual cells will change. However, such major changes in growth and development are driven by a few simple events in an individual organ and cells. These driving events are more akin to small local revolutions in individual states than they are to democratic decisions in a sophisticated confederation.     

An alternative view of protein fold space

Comparing and subsequently classifying protein structures information has received significant attention concurrent with the increase in the number of experimentally derived 3-dimensional structures. Classification schemes have focused on biological function found within protein domains and on structure classification based on topology. Here an alternative view is presented that groups substructures. Substructures are long (50-150 residue) highly repetitive near-contiguous pieces of polypeptide chain that occur frequently in a set of proteins from the PDB defined as structurally non-redundant over the complete polypeptide chain. The substructure classification is based on a previously reported Combinatorial Extension (CE) algorithm that provides a significantly different set of structure alignments than those previously described, having, for example, only a 40% overlap with FSSP. Qualitatively the algorithm provides longer contiguous aligned segments at the price of a slightly higher root-mean-square deviation (rmsd). Clustering these alignments gives a discreet and highly repetitive set of substructures not detectable by sequence similarity alone. In some cases different substructures represent all or different parts of well known folds indicative of the Russian doll effect--the continuity of protein fold space. In other cases they fall into different structure and functional classifications. It is too early to determine whether these newly classified substructures represent new insights into the evolution of a structural framework important to many proteins. What is apparent from on-going work is that these substructures have the potential to be useful probes in finding remote sequence homology and in structure prediction studies. The characteristics of the complete all-by-all comparison of the polypeptide chains present in the PDB and details of the filtering procedure by pair-wise structure alignment that led to the emergent substructure gallery are discussed. Substructure classification, alignments, and tools to analyze them are available at http://cl.sdsc.edu/ce.html.     

Heat capacity of folding of proteins corrected for disulfide cross-links

The heat capacities (DeltaC(p,f)) for the temperature-induced folding of proteins: barnase, lysozyme T4, papain, trypsin, ribonuclease T1, chymotrypsin, lysozyme and ribonuclease A have been calculated from the change in solvent accessible surface area between the native state and extended polypeptide chain. To visualize the effect of disulfide cross-links on molar heat capacity, loops of varying number of alanine residues and extended alanine chains with terminal cystein are modeled. The difference in DeltaC(p) values between the extended state and the loop conformation of proteins is linearly related to the number of residues in the loop. Corrections to the heat capacity of folding (DeltaC(p,f)) are applied for proteins with cross-links based on this observation. There is good correlation between corrected values of DeltaC(p,f) and experimental values.     

The present view of the mechanism of protein folding

We can track the positions and movements of all the atoms in small proteins as they fold and unfold by combining experimental studies with atomic-resolution molecular dynamics simulations. General principles as to how such complex architectures form so rapidly are now emerging from in-depth studies of a few proteins.     

Sex-sorted sperm and fertility: an alternative view

Although contemporary methods of physically separating X from Y chromosome-bearing spermatozoa are now very efficient, overall fertility rates following the use of sex-sorted sperm are not as impressive, in spite of many attempts to improve them. At the same time, there are suggestions from evolutionary biology, and from sex allocation theory in particular, that there may need to be a modification to the chance theory of sex determination in mammals. This is because it now appears that the mammalian female could have some influence on the sex of her offspring, and furthermore, that this influence could be preconceptual. If so, this could go some way towards accounting for the putative inefficiencies in fertilization following insemination with sex-sorted sperm.     

The D-channel of cytochrome oxidase: an alternative view

The D-pathway in A-type cytochrome c oxidases conducts protons from a conserved aspartate on the negatively charged N-side of the membrane to a conserved glutamic acid at about the middle of the membrane dielectric. Extensive work in the past has indicated that all four protons pumped across the membrane on reduction of O(2) to water are transferred via the D-pathway, and that it is also responsible for transfer of two out of the four "chemical protons" from the N-side to the binuclear oxygen reduction site to form product water. The function of the D-pathway has been discussed in terms of an apparent pK(a) of the glutamic acid. After reacting fully reduced enzyme with O(2), the rate of formation of the F state of the binuclear heme-copper active site was found to be independent of pH up to pH~9, but to drop off at higher pH with an apparent pK(a) of 9.4, which was attributed to the glutamic acid. Here, we present an alternative view, according to which the pH-dependence is controlled by proton transfer into the aspartate residue at the N-side orifice of the D-pathway. We summarise experimental evidence that favours a proton pump mechanism in which the proton to be pumped is transferred from the glutamic acid to a proton-loading site prior to proton transfer for completion of oxygen reduction chemistry. The mechanism is discussed by which the proton-pumping activity is decoupled from electron transfer by structural alterations of the D-pathway. This article is part of a Special Issue entitled: Allosteric cooperativity in respiratory proteins.     

Animal exchange ratios: an alternative point of view

An alternative interpretation is provided of the concepts of carrying capacity and exchange ratios, particularly suitable for game animal species, based on management models for a given area of rangeland or pasture. It involves modelling animal population dynamics as discrete‐time logistic equations. Carrying capacity is then generated endogenously using rainfall as a proxy. The model interaction parameters, also generated endogenously, represent the animal exchange ratios. Because these two parameters are generated endogenously, this approach takes into account all the animals' habitat requirements (food, cover, water and space) simultaneously, unlike other approaches that tend to consider food requirements only. This makes the approach amenable to multi‐species situations. It also captures the ecological definition of population growth models where the realized rather than the theoretical carrying capacity is determined endogenously.     

Quality control of protein folding: an overview

Here a brief introduction to the series is given, which highlights concepts, recent findings and current challenges in understanding chaperone function and quality control of proteins.