Protein folding mechanisms and the multidimensional folding funnel

An important idea that emerges from the energy landscape theory of protein folding is that subtle global features of the protein landscape can profoundly affect the apparent mechanism of folding. The relationship between various characteristic temperatures in the phase diagrams and landmarks in the folding funnel at fixed temperatures can be used to classify different folding behaviors. The one-dimensional picture of a folding funnel classifies folding kinetics into four basic scenarios, depending on the relative location of the thermodynamic barrier and the glass transition as a function of a single-order parameter. However, the folding mechanism may not always be quantitatively described by a single-order parameter. Several other order parameters, such as degree of secondary structure formation, collapse and topological order, are needed to establish the connection between minimalist models and proteins in the laboratory. In this article we describe a simple multidimensional funnel based on two-order parameters that measure the degree of collapse and topological order. The appearance of several different “mechanisms” is illustrated by analyzing lattice models with different potentials and sequences with different degrees of design. In most cases, the two-dimensional analysis leads to a classification of mechanisms totally in keeping with the one-dimensional scheme, but a topologically distinct scenario of fast folding with traps also emerges. The nature of traps depends on the relative location of the glass transition surface and the thermodynamic barrier in the multidimensional funnel. Proteins 32:136–158, 1998. © 1998 Wiley-Liss, Inc.     

Markovian and non-Markovian protein sequence evolution: aggregated Markov process models

Over the years, there have been claims that evolution proceeds according to systematically different processes over different timescales and that protein evolution behaves in a non-Markovian manner. On the other hand, Markov models are fundamental to many applications in evolutionary studies. Apparent non-Markovian or time-dependent behavior has been attributed to influence of the genetic code at short timescales and dominance of physicochemical properties of the amino acids at long timescales. However, any long time period is simply the accumulation of many short time periods, and it remains unclear why evolution should appear to act systematically differently across the range of timescales studied. We show that the observed time-dependent behavior can be explained qualitatively by modeling protein sequence evolution as an aggregated Markov process (AMP): a time-homogeneous Markovian substitution model observed only at the level of the amino acids encoded by the protein-coding DNA sequence. The study of AMPs sheds new light on the relationship between amino acid-level and codon-level models of sequence evolution, and our results suggest that protein evolution should be modeled at the codon level rather than using amino acid substitution models.     

An evolutionary model for protein-coding regions with conserved RNA structure

Here we present a model of nucleotide substitution in protein-coding regions that also encode the formation of conserved RNA structures. In such regions, apparent evolutionary context dependencies exist, both between nucleotides occupying the same codon and between nucleotides forming a base pair in the RNA structure. The overlap of these fundamental dependencies is sufficient to cause "contagious" context dependencies which cascade across many nucleotide sites. Such large-scale dependencies challenge the use of traditional phylogenetic models in evolutionary inference because they explicitly assume evolutionary independence between short nucleotide tuples. In our model we address this by replacing context dependencies within codons by annotation-specific heterogeneity in the substitution process. Through a general procedure, we fragment the alignment into sets of short nucleotide tuples based on both the protein coding and the structural annotation. These individual tuples are assumed to evolve independently, and the different tuple sets are assigned different annotation-specific substitution models shared between their members. This allows us to build a composite model of the substitution process from components of traditional phylogenetic models. We applied this to a data set of full-genome sequences from the hepatitis C virus where five RNA structures are mapped within the coding region. This allowed us to partition the effects of selection on different structural elements and to test various hypotheses concerning the relation of these effects. Of particular interest, we found evidence of a functional role of loop and bulge regions, as these were shown to evolve according to a different and more constrained selective regime than the nonpairing regions outside the RNA structures. Other potential applications of the model include comparative RNA structure prediction in coding regions and RNA virus phylogenetics.     

Testing for Spatial Clustering of Amino Acid Replacements Within Protein Tertiary Structure

Widely used models of protein evolution ignore protein structure. Therefore, these models do not predict spatial clustering of amino acid replacements with respect to tertiary structure. One formal and biologically implausible possibility is that there is no tendency for amino acid replacements to be spatially clustered during evolution. An alternative to this is that amino acid replacements are spatially clustered and this spatial clustering can be fully explained by a tendency for similar rates of amino acid replacement at sites that are nearby in protein tertiary structure. A third possibility is that the amount of clustering exceeds that which can be explained solely on the basis of independently evolving protein sites with spatially clustered replacement rates. We introduce two simple and not very parametric hypothesis tests that help distinguish these three possibilities. We then apply these tests to 273 homologous protein families. The null hypothesis of no spatial clustering is rejected for 102 of 273 families. The explanation of spatially clustered rates but independent change among sites is rejected for 43 families. These findings need to be reconciled with the common practice of basing evolutionary inferences on models that assume independent change among sites. [Reviewing Editior: Dr. David Pollock]     

Proteomic traces of speciation

Recent work has shown that the network of structural similarity between protein domains exhibits a power-law distribution of edges per node. The scale-free nature of this graph, termed the protein domain universe graph or PDUG, may be reproduced via a divergent model of structural evolution. The performance of this model, however, does not preclude the existence of a successful convergent model. To further resolve the issue of protein structural evolution, we explore the predictions of both convergent and divergent models directly. We show that when nodes from the PDUG are partitioned into subgraphs on the basis of their occurrence in the proteomes of particular organisms, these subgraphs exhibit a scale-free nature as well. We explore a simple convergent model of structural evolution and find that the implications of this model are inconsistent with features of these organismal subgraphs. Importantly, we find that biased convergent models are inconsistent with our data. We find that when speciation mechanisms are added to a simple divergent model, subgraphs similar to the organismal subgraphs are produced, demonstrating that dynamic models can easily explain the distributions of structural similarity that exist within proteomes. We show that speciation events must be included in a divergent model of structural evolution to account for the non-random overlap of structural proteomes. These findings have implications for the long-standing debate over convergent and divergent models of protein structural evolution, and for the study of the evolution of organisms as a whole.     

MtArt: a new model of amino acid replacement for Arthropoda

A statistical approach was applied to select those models that best fit each individual mitochondrial (mt) protein at different taxonomic levels of metazoans. The existing mitochondrial replacement matrices, MtREV and MtMam, were found to be the best-fit models for the mt-proteins of vertebrates, with the exception of Nd6, at different taxonomic levels. Remarkably, existing mitochondrial matrices generally failed to best-fit invertebrate mt-proteins. In an attempt to better model the evolution of invertebrate mt-proteins, a new replacement matrix, named MtArt, was constructed based on arthropod mt-proteomes. The new model was found to best fit almost all analyzed invertebrate mt-protein data sets. The observed pattern of model fit across the different data sets indicates that no single replacement matrix is able to describe the general evolutionary properties of mt-proteins but rather that taxonomical biases and/or the existence of different mt-genetic codes have great influence on which model is selected.     

Modelling repressor proteins docking to DNA

The docking of repressor proteins to DNA starting from the unbound protein and model-built DNA coordinates is modeled computationally. The approach was evaluated on eight repressor/DNA complexes that employed different modes for protein/ DNA recognition. The global search is based on a protein-protein docking algorithm that evaluates shape and electrostatic complementarity, which was modified to consider the importance of electrostatic features in DNA-protein recognition. Complexes were then ranked by an empirical score for the observed amino acid /nucleotide pairings (i.e., protein-DNA pair potentials) derived from a database of 20 protein/DNA complexes. A good prediction had at least 65% of the correct contacts modeled. This approach was able to identify a good solution at rank four or better for three out of the eight complexes. Predicted complexes were filtered by a distance constraint based on experimental data defining the DNA footprint. This improved coverage to four out of eight complexes having a good model at rank four or better. The additional use of amino acid mutagenesis and phylogenetic data defining residues on the repressor resulted in between 2 and 27 models that would have to be examined to find a good solution for seven of the eight test systems. This study shows that starting with unbound coordinates one can predict three-dimensional models for protein/DNA complexes that do not involve gross conformational changes on association. Proteins 33:535–549, 1998. © 1998 Wiley-Liss, Inc.     

Plenty more fish in the sea: comparative and functional genomics using teleost models.

Biology has collaborated with evolution to create an enormous repertoire of animal variation. This in turn has provided experimental biologists with models that can be used in the lab to simulate more complex systems. Amongst the organisms that have been used in this way are fish, where a large number of species have been utilised in a variety of different ways. Fish possess the smallest genomes of any vertebrate, making them ideal as models for genome analysis and gene discovery. Fish are also easy to maintain in a laboratory environment and can be bred easily. Fish often have well-defined physiology and respond well to many experimental procedures. Finally, fish are of great economic importance in their own right, as one of the world's largest sources of protein. In this review, the relationship between fish species is examined along with the role of different fish models in a wide range of biological disciplines.     

Design,construction, crystallization,and preliminary X-ray studies of a fine-tuning mutant (F133V) of module-substituted chimera hemoglobin

A chimera βα-subunit of human hemoglobin was crystallized into a carbonmonoxy form. The protein was assembled by substituting the structural portion of a β-subunit of hemoglobin (M4 module of the subunit) for its counterpart in the α-subunit. In order to overcome the inherent instability in the crystallization of the chimera subunit, a site-directed mutagenesis (F133V) technique was employed based on a computer model. The crystal was used for an X-ray diffraction study yielding a data set with a resolution of 2.5 Å. The crystal belongs to the monoclinic space group P2₁, with cell dimensions of a = 62.9, b = 81.3, c = 55.1 Å, and β = 91.0°. These dimensions are similar to the crystallographic parameters of the native β-subunit tetramers in three different ligand states, one of which is a cyanide form that was also crystallized in this study. Proteins 32:263–267, 1998. © 1998 Wiley-Liss, Inc.     

TIAMMAt: Leveraging Biodiversity to Revise Protein Domain Models,Evidence from Innate Immunity

Sequence annotation is fundamental for studying the evolution of protein families, particularly when working with nonmodel species. Given the rapid, ever-increasing number of species receiving high-quality genome sequencing, accurate domain modeling that is representative of species diversity is crucial for understanding protein family sequence evolution and their inferred function(s). Here, we describe a bioinformatic tool called Taxon-Informed Adjustment of Markov Model Attributes (TIAMMAt) which revises domain profile hidden Markov models (HMMs) by incorporating homologous domain sequences from underrepresented and nonmodel species. Using innate immunity pathways as a case study, we show that revising profile HMM parameters to directly account for variation in homologs among underrepresented species provides valuable insight into the evolution of protein families. Following adjustment by TIAMMAt, domain profile HMMs exhibit changes in their per-site amino acid state emission probabilities and insertion/deletion probabilities while maintaining the overall structure of the consensus sequence. Our results show that domain revision can heavily impact evolutionary interpretations for some families (i.e., NLR’s NACHT domain), whereas impact on other domains (e.g., rel homology domain and interferon regulatory factor domains) is minimal due to high levels of sequence conservation across the sampled phylogenetic depth (i.e., Metazoa). Importantly, TIAMMAt revises target domain models to reflect homologous sequence variation using the taxonomic distribution under consideration by the user. TIAMMAt’s flexibility to revise any subset of the Pfam database using a user-defined taxonomic pool will make it a valuable tool for future protein evolution studies, particularly when incorporating (or focusing) on nonmodel species.     

The Universal Trend of Amino Acid Gain–Loss is Caused by CpG Hypermutability

Understanding the cause of the changes in the amino acid composition of proteins is essential for understanding the evolution of protein functions. Since the early 1970s, it has been known that the frequency of some amino acids in protein sequences is increasing and that of others is decreasing. Recently, it was found that the trends of amino acid changes were similar in 15 taxa representing Bacteria, Archaea, and Eukaryota. However, the cause of this similarity in the trend of the gains and losses of amino acids continued to be debated. Here, we show that this trend of the gain and loss of amino acids can be simply explained by CpG hypermutability. We found that the frequency of amino acids coded by codons with TpG dinucleotides and those with CpA dinucleotides is increasing, while that of amino acids coded by codons with CpG dinucleotides is decreasing. We also found that organisms that lack DNA methyltransferase show different trends of the gain and loss of amino acids. DNA methyltransferase methylates CpG dinucleotides and induces CpG hypermutability. The incorporation of CpG hypermutability into models of protein evolution will improve studies on protein evolution in different organisms. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Exploring Potential Signals of Selection for Disordered Residues in Prokaryotic and Eukaryotic Proteins

Intrinsically disordered proteins (IDPs) are an important class of proteins in all domains of life for their functional importance. However, how nature has shaped the disorder potential of prokaryotic and eukaryotic proteins is still not clearly known. Randomly generated sequences are free of any selective constraints, thus these sequences are commonly used as null models. Considering different types of random protein models, here we seek to understand how the disorder potential of natural eukaryotic and prokaryotic proteins differs from random sequences. Comparing proteome-wide disorder content between real and random sequences of 12 model organisms, we noticed that eukaryotic proteins are enriched in disordered regions compared to random sequences, but in prokaryotes such regions are depleted. By analyzing the position-wise disorder profile, we show that there is a generally higher disorder near the N- and C-terminal regions of eukaryotic proteins as compared to the random models; however, either no or a weak such trend was found in prokaryotic proteins. Moreover, here we show that this preference is not caused by the amino acid or nucleotide composition at the respective sites. Instead, these regions were found to be endowed with a higher fraction of protein–protein binding sites, suggesting their functional importance. We discuss several possible explanations for this pattern, such as improving the efficiency of protein–protein interaction, ribosome movement during translation, and post-translational modification. However, further studies are needed to clearly understand the biophysical mechanisms causing the trend.     

Protein evolution with dependence among codons due to tertiary structure

Markovian models of protein evolution that relax the assumption of independent change among codons are considered. With this comparatively realistic framework, an evolutionary rate at a site can depend both on the state of the site and on the states of surrounding sites. By allowing a relatively general dependence structure among sites, models of evolution can reflect attributes of tertiary structure. To quantify the impact of protein structure on protein evolution, we analyze protein-coding DNA sequence pairs with an evolutionary model that incorporates effects of solvent accessibility and pairwise interactions among amino acid residues. By explicitly considering the relationship between nonsynonymous substitution rates and protein structure, this approach can lead to refined detection and characterization of positive selection. Analyses of simulated sequence pairs indicate that parameters in this evolutionary model can be well estimated. Analyses of lysozyme c and annexin V sequence pairs yield the biologically reasonable result that amino acid replacement rates are higher when the replacements lead to energetically favorable proteins than when they destabilize the proteins. Although the focus here is evolutionary dependence among codons that is associated with protein structure, the statistical approach is quite general and could be applied to diverse cases of evolutionary dependence where surrogates for sequence fitness can be measured or modeled.     

On Ohta's hypothesis: Most amino acid substitutions are deleterious

Ohta's hypothesis that most amino acid substitutions are deleterious grew out of a class of population-genetics models called shift models. Recently, shift models have been shown to be biologically unreasonable and have been replaced by a more plausible house-of-cards model. In this paper, the simplest form of the house-of-cards models is shown to be incompatible with most of the major features of protein evolution. Moreover, this model is shown to not be a model of exclusively deleterious-allele evolution, but rather to be a model with an equal mix of deleterious and advantageous substitutions.     

Interaction potentials for protein folding

We outline a general strategy for determining the effective coarse-grained interactions between the amino acids of a protein from the experimentally derived native-state structures. The method is, in principle, free from any adjustable or empirically determined parameters, and it is tested on simple models and compared with other existing approaches. Proteins 30:244–248, 1998. © 1998 Wiley-Liss, Inc.     

Variation in evolutionary processes at different codon positions

Evolutionary studies commonly model single nucleotide substitutions and assume that they occur as independent draws from a unique probability distribution across the sequence studied. This assumption is violated for protein-coding sequences, and we consider modeling approaches where codon positions (CPs) are treated as separate categories of sites because within each category the assumption is more reasonable. Such "codon-position" models have been shown to explain the evolution of codon data better than homogenous models in previous studies. This paper examines the ways in which codon-position models outperform homogeneous models and characterizes the differences in estimates of model parameters across CPs. Using the PANDIT database of multiple species DNA sequence alignments, we quantify the differences in the evolutionary processes at the 3 CPs in a systematic and comprehensive manner, characterizing previously undescribed features of protein evolution. We relate our findings to the functional constraints imposed by the genetic code, protein function, and the types of mutation that cause synonymous and nonsynonymous codon changes. The results increase our understanding of selective constraints and could be incorporated into phylogenetic analyses or gene-finding techniques in the future. The methods used are extended to an overlapping reading frame data set, and we discover that overlapping reading frames do not necessarily cause more stringent evolutionary constraints.     

Folding-unfolding energy change of a simple sphere model protein and an energy landscape of the folding process

We have calculated the free energy of a spherical model of a protein or part of a protein generated in the way of protein folding. Two spherical models are examined; one is a homogeneous model consisting of only one residue type—hydrophobic. The other is a heterogeneous model consisting of two residue types—strong hydrophobic and weak hydrophobic. Both models show a folding transition state, and the latter model reproduces the trend of the experimental folded-unfolded energy change. The heterogeneous model suggests that in the folding process of a protein of more than 70 residues, a specific region of the protein folds first to form a stable region, then the other residues follow the folding process. The energy landscape of folding of a small protein is approximately a funnel model, whereas a flatter energy landscape is suggested for larger proteins of more than 55–70 residues. Proteins 33:408–416, 1998. © 1998 Wiley-Liss, Inc.     

Structure prediction of a complex between the chromosomal protein HMG-D and DNA

Non-histone chromosomal proteins are an important part of nuclear structure and function due to their ability to interact with DNA to form and modulate chromatin structure and regulate gene expression. However, the understanding of the function of chromosomal proteins at the molecular level has been hampered by the lack of structures of chromosomal protein–DNA complexes. We have carried out a molecular dynamics modeling study to provide insight into the mode of DNA binding to the chromosomal HMG-domain protein, HMG-D. Three models of a complex of HMG-D bound to DNA were derived through docking the protein to two different DNA fragments of known structure. Molecular dynamics simulations of the complexes provided data indicating the most favorable model. This model was further refined by molecular dynamics simulation and extensively analyzed. The structure of the corresponding HMG-D-DNA complex exhibits many features seen in the NMR structures of the sequence-specific HMG-domain-DNA complexes, lymphoid enhancer factor 1 (LEF-1) and testis determining factor (SRY). The model reveals differences from these known structures that suggest how chromosomal proteins bind to many different DNA sequences with comparable affinity. Proteins 30:113–135, 1998. © 1998 Wiley-Liss, Inc.     

The evolution and evolutionary consequences of marginal thermostability in proteins

When we seek to explain the characteristics of living systems in their evolutionary context, we are often interested in understanding how and why certain properties arose through evolution, and how these properties then affected the continuing evolutionary process. This endeavor has been assisted by the use of simple computational models that have properties characteristic of natural living systems but allow simulations over evolutionary timescales with full transparency. We examine a model of the evolution of a gene under selective pressure to code for a protein that exists in a prespecified folded state at a given growth temperature. We observe the emergence of proteins with modest stabilities far below those possible with the model, with a denaturation temperature tracking the simulation temperature, despite the absence of selective pressure for such marginal stability. This demonstrates that neither observations of marginally stable proteins, nor even instances where increased stability interferes with function, provide evidence that marginal stability is an adaptation. Instead the marginal stability is the result of a balance between predominantly destabilizing mutations and selection that shifts depending on effective population size. Even if marginal stability is not an adaptation, the natural tendency of proteins toward marginal stability, and the range of stabilities that occur during evolution, may have significant effect on the evolutionary process.