Mathematics, Thermodynamics, and Modeling to Address Ten Common Misconceptions about Protein Structure, Folding, and Stability

To fully understand the roles proteins play in cellular processes, students need to grasp complex ideas about protein structure, folding, and stability. Our current understanding of these topics is based on mathematical models and experimental data. However, protein structure, folding, and stability are often introduced as descriptive, qualitative phenomena in undergraduate classes. In the process of learning about these topics, students often form incorrect ideas. For example, by learning about protein folding in the context of protein synthesis, students may come to an incorrect conclusion that once synthesized on the ribosome, a protein spends its entire cellular life time in its fully folded native confirmation. This is clearly not true; proteins are dynamic structures that undergo both local fluctuations and global unfolding events. To prevent and address such misconceptions, basic concepts of protein science can be introduced in the context of simple mathematical models and hands-on explorations of publicly available data sets. Ten common misconceptions about proteins are presented, along with suggestions for using equations, models, sequence, structure, and thermodynamic data to help students gain a deeper understanding of basic concepts relating to protein structure, folding, and stability

Evolution favors protein mutational robustness in sufficiently large populations

BACKGROUND: An important question is whether evolution favors properties such as mutational robustness or evolvability that do not directly benefit any individual, but can influence the course of future evolution. Functionally similar proteins can differ substantially in their robustness to mutations and capacity to evolve new functions, but it has remained unclear whether any of these differences might be due to evolutionary selection for these properties. RESULTS: Here we use laboratory experiments to demonstrate that evolution favors protein mutational robustness if the evolving population is sufficiently large. We neutrally evolve cytochrome P450 proteins under identical selection pressures and mutation rates in populations of different sizes, and show that proteins from the larger and thus more polymorphic population tend towards higher mutational robustness. Proteins from the larger population also evolve greater stability, a biophysical property that is known to enhance both mutational robustness and evolvability. The excess mutational robustness and stability is well described by existing mathematical theories, and can be quantitatively related to the way that the proteins occupy their neutral network. CONCLUSIONS: Our work is the first experimental demonstration of the general tendency of evolution to favor mutational robustness and protein stability in highly polymorphic populations. We suggest that this phenomenon may contribute to the mutational robustness and evolvability of viruses and bacteria that exist in large populations

Inferring stabilizing mutations from protein phylogenies : application to influenza hemagglutinin

One selection pressure shaping sequence evolution is the requirement that a protein fold with sufficient stability to perform its biological functions. We present a conceptual framework that explains how this requirement causes the probability that a particular amino acid mutation is fixed during evolution to depend on its effect on protein stability. We mathematically formalize this framework to develop a Bayesian approach for inferring the stability effects of individual mutations from homologous protein sequences of known phylogeny. This approach is able to predict published experimentally measured mutational stability effects (ΔΔG values) with an accuracy that exceeds both a state-of-the-art physicochemical modeling program and the sequence-based consensus approach. As a further test, we use our phylogenetic inference approach to predict stabilizing mutations to influenza hemagglutinin. We introduce these mutations into a temperature-sensitive influenza virus with a defect in its hemagglutinin gene and experimentally demonstrate that some of the mutations allow the virus to grow at higher temperatures. Our work therefore describes a powerful new approach for predicting stabilizing mutations that can be successfully applied even to large, complex proteins such as hemagglutinin. This approach also makes a mathematical link between phylogenetics and experimentally measurable protein properties, potentially paving the way for more accurate analyses of molecular evolution

Defining an Essence of Structure Determining Residue Contacts in Proteins

The network of native non-covalent residue contacts determines the three-dimensional structure of a protein. However, not all contacts are of equal structural significance, and little knowledge exists about a minimal, yet sufficient, subset required to define the global features of a protein. Characterisation of this “structural essence” has remained elusive so far: no algorithmic strategy has been devised to-date that could outperform a random selection in terms of 3D reconstruction accuracy (measured as the Ca RMSD). It is not only of theoretical interest (i.e., for design of advanced statistical potentials) to identify the number and nature of essential native contacts—such a subset of spatial constraints is very useful in a number of novel experimental methods (like EPR) which rely heavily on constraint-based protein modelling. To derive accurate three-dimensional models from distance constraints, we implemented a reconstruction pipeline using distance geometry. We selected a test-set of 12 protein structures from the four major SCOP fold classes and performed our reconstruction analysis. As a reference set, series of random subsets (ranging from 10% to 90% of native contacts) are generated for each protein, and the reconstruction accuracy is computed for each subset. We have developed a rational strategy, termed “cone-peeling” that combines sequence features and network descriptors to select minimal subsets that outperform the reference sets. We present, for the first time, a rational strategy to derive a structural essence of residue contacts and provide an estimate of the size of this minimal subset. Our algorithm computes sparse subsets capable of determining the tertiary structure at approximately 4.8 Å Ca RMSD with as little as 8% of the native contacts (Ca-Ca and Cb-Cb). At the same time, a randomly chosen subset of native contacts needs about twice as many contacts to reach the same level of accuracy. This “structural essence” opens new avenues in the fields of structure prediction, empirical potentials and docking

How Protein Stability and New Functions Trade Off

Numerous studies have noted that the evolution of new enzymatic specificities is accompanied by loss of the protein's thermodynamic stability (ΔΔG), thus suggesting a tradeoff between the acquisition of new enzymatic functions and stability. However, since most mutations are destabilizing (ΔΔG>0), one should ask how destabilizing mutations that confer new or altered enzymatic functions relative to all other mutations are. We applied ΔΔG computations by FoldX to analyze the effects of 548 mutations that arose from the directed evolution of 22 different enzymes. The stability effects, location, and type of function-altering mutations were compared to ΔΔG changes arising from all possible point mutations in the same enzymes. We found that mutations that modulate enzymatic functions are mostly destabilizing (average ΔΔG = +0.9 kcal/mol), and are almost as destabilizing as the “average” mutation in these enzymes (+1.3 kcal/mol). Although their stability effects are not as dramatic as in key catalytic residues, mutations that modify the substrate binding pockets, and thus mediate new enzymatic specificities, place a larger stability burden than surface mutations that underline neutral, non-adaptive evolutionary changes. How are the destabilizing effects of functional mutations balanced to enable adaptation? Our analysis also indicated that many mutations that appear in directed evolution variants with no obvious role in the new function exert stabilizing effects that may compensate for the destabilizing effects of the crucial function-altering mutations. Thus, the evolution of new enzymatic activities, both in nature and in the laboratory, is dependent on the compensatory, stabilizing effect of apparently “silent” mutations in regions of the protein that are irrelevant to its function

An integrated platform for automatic design and screening of virtual mutants based on 3D-QSAR analysis

tAn innovative application of 3D-QSAR methodology to the rational design of enzymes is here reported.The introduction of amidase activity inside the scaffold of lipase B from Candida antarctica (CaLB) wasstudied and 3D-QSAR models were constructed to correlate the structures of a set of CaLB mutants withtheir experimentally measured activities. Properties, like hydrophilicity, hydrophobicity and hydrogenbonding capability of the enzyme active site were computed by means of the GRID method and theoutput was used as molecular descriptors. Correlations with experimental behavior of the catalysts werecalculated by means of partial least square regression (PLS). The analysis of the QSAR model fully exploitsfundamental knowledge while avoiding conceptual biases. Rationales for driving enzyme engineeringare disclosed and a priori evaluation of new virtual candidate mutants becomes feasible. On that respect,the whole procedure for production of virtual mutants and scoring of their activity was automated withina workflow constructed by means of the modeFRONTIER package. The method allows for the automatedconstruction and scoring of each mutant in 2 h on a normal workstation

Designability and Disease.

Structural designability is the number of ways it is possible to encode for structure. A protein’s designability has been equated with the size of sequence space encoding for the protein’s structure, a measure that reflects the structure’s robustness to mutation. Current evidence suggests that designability is fundamental to our understanding of the evolvability and distribution of structures in nature and is a significant factor associated with human disease. Here, we describe definitions and principles underlying the concept of designability and discuss its relation to disease