Inferring the rate-length law of protein folding

Slowest-first protein translation scheme: Structural asymmetry and co-translational folding

Proteins are translated from the N to the C terminus, raising the basic question of how this innate directionality affects their evolution. To explore this question, we analyze 16,200 structures from the Protein Data Bank (PDB). We find remarkable enrichment of α helices at the C terminus and β strands at the N terminus. Furthermore, this α-β asymmetry correlates with sequence length and contact order, both determinants of folding rate, hinting at possible links to co-translational folding (CTF). Hence, we propose the "slowest-first" scheme, whereby protein sequences evolved structural asymmetry to accelerate CTF: the slowest of the cooperatively folding segments are positioned near the N terminus so they have more time to fold during translation. A phenomenological model predicts that CTF can be accelerated by asymmetry in folding rate, up to double the rate, when folding time is commensurate with translation time; analysis of the PDB predicts that structural asymmetry is indeed maximal in this regime. This correspondence is greater in prokaryotes, which generally require faster protein production. Altogether, this indicates that accelerating CTF is a substantial evolutionary force whose interplay with stability and functionality is encoded in secondary structure asymmetry.

How fast do mobile organisms respond to stimuli? Response times from bacteria to elephants and whales

Quick responses to fast changes in the environment are crucial in animal behaviour and survival, for example to seize prey, escape predators, or negotiate obstacles. Here, we study the 'simple response time' that is the time elapsed between receptor stimulation and motor activation as typically shown in escape responses, for mobile organisms of various taxa ranging from bacteria to large vertebrates. We show that 95% of these simple response times lie within one order of magnitude of the overall geometric mean of about 25 ms, which is similar to that of a well-studied sensory time scale, the inverse of the critical flicker fusion frequency in vision, also lying within close bounds for all the organisms studied. We find that this time scale is a few times smaller than the minimum time to move by one body length, which is known to lie also within a relatively narrow range for all moving organisms. The remarkably small 10²-fold range of the simple response time among so disparate life forms varying over 10²⁰-fold in body mass suggests that it is determined by basic physicochemical constraints, independently on the structure and scale of the organism. We thus propose first-principle estimates of the simple response and sensory time scales in terms of physical constants and a few basic biological properties common to mobile organisms and constraining their responses.

An Effective Cumulative Torsion Angles Model for Prediction of Protein Folding Rates

BACKGROUND

Protein folding rate is mainly determined by the size of the conformational space to search, which in turn is dictated by factors such as size, structure and amino-acid sequence in a protein. It is important to integrate these factors effectively to form a more precisely description of conformation space. But there is no general paradigm to answer this question except some intuitions and empirical rules. Therefore, at the present stage, predictions of the folding rate can be improved through finding new factors, and some insights are given to the above question.

OBJECTIVE

Its purpose is to propose a new parameter that can describe the size of the conformational space to improve the prediction accuracy of protein folding rate.

METHODS

Based on the optimal set of amino acids in a protein, an effective cumulative backbone torsion angles (CBTAeff) was proposed to describe the size of the conformational space. Linear regression model was used to predict protein folding rate with CBTAeff as a parameter. The degree of correlation was described by the coefficient of determination and the mean absolute error MAE between the predicted folding rates and experimental observations.

RESULTS

It achieved a high correlation (with the coefficient of determination of 0.70 and MAE of 1.88) between the logarithm of folding rates and the (CBTAeff)0.5 with experimental over 112 twoand multi-state folding proteins.

CONCLUSION

The remarkable performance of our simplistic model demonstrates that CBTA based on optimal set was the major determinants of the conformation space of natural proteins.

Cotranslational folding allows misfolding-prone proteins to circumvent deep kinetic traps

Many large proteins suffer from slow or inefficient folding in vitro. It has long been known that this problem can be alleviated in vivo if proteins start folding cotranslationally. However, the molecular mechanisms underlying this improvement have not been well established. To address this question, we use an all-atom simulation-based algorithm to compute the folding properties of various large protein domains as a function of nascent chain length. We find that for certain proteins, there exists a narrow window of lengths that confers both thermodynamic stability and fast folding kinetics. Beyond these lengths, folding is drastically slowed by nonnative interactions involving C-terminal residues. Thus, cotranslational folding is predicted to be beneficial because it allows proteins to take advantage of this optimal window of lengths and thus avoid kinetic traps. Interestingly, many of these proteins' sequences contain conserved rare codons that may slow down synthesis at this optimal window, suggesting that synthesis rates may be evolutionarily tuned to optimize folding. Using kinetic modeling, we show that under certain conditions, such a slowdown indeed improves cotranslational folding efficiency by giving these nascent chains more time to fold. In contrast, other proteins are predicted not to benefit from cotranslational folding due to a lack of significant nonnative interactions, and indeed these proteins' sequences lack conserved C-terminal rare codons. Together, these results shed light on the factors that promote proper protein folding in the cell and how biomolecular self-assembly may be optimized evolutionarily.

Applications of Molecular Dynamics Simulation in Structure Prediction of Peptides and Proteins

Compared with rapid accumulation of protein sequences from high-throughput DNA sequencing, obtaining experimental 3D structures of proteins is still much more difficult, making protein structure prediction (PSP) potentially very useful. Currently, a vast majority of PSP efforts are based on data mining of known sequences, structures and their relationships (informatics-based). However, if closely related template is not available, these methods are usually much less reliable than experiments. They may also be problematic in predicting the structures of naturally occurring or designed peptides. On the other hand, physics-based methods including molecular dynamics (MD) can utilize our understanding of detailed atomic interactions determining biomolecular structures. In this mini-review, we show that all-atom MD can predict structures of cyclic peptides and other peptide foldamers with accuracy similar to experiments. Then, some notable successes in reproducing experimental 3D structures of small proteins through MD simulations (some with replica-exchange) of the folding were summarized. We also describe advancements of MD-based refinement of structure models, and the integration of limited experimental or bioinformatics data into MD-based structure modeling.

Role of Proteome Physical Chemistry in Cell Behavior

We review how major cell behaviors, such as bacterial growth laws, are derived from the physical chemistry of the cell’s proteins. On one hand, cell actions depend on the individual biological functionalities of their many genes and proteins. On the other hand, the common physics among proteins can be as important as the unique biology that distinguishes them. For example, bacterial growth rates depend strongly on temperature. This dependence can be explained by the folding stabilities across a cell’s proteome. Such modeling explains how thermophilic and mesophilic organisms differ, and how oxidative damage of highly charged proteins can lead to unfolding and aggregation in aging cells. Cells have characteristic time scales. For example, E. coli can duplicate as fast as 2–3 times per hour. These time scales can be explained by protein dynamics (the rates of synthesis and degradation, folding, and diffusional transport). It rationalizes how bacterial growth is slowed down by added salt. In the same way that the behaviors of inanimate materials can be expressed in terms of the statistical distributions of atoms and molecules, some cell behaviors can be expressed in terms of distributions of protein properties, giving insights into the microscopic basis of growth laws in simple cells.

Protein unfolding rates correlate as strongly as folding rates with native structure

Although the folding rates of proteins have been studied extensively, both experimentally and theoretically, and many native state topological parameters have been proposed to correlate with or predict these rates, unfolding rates have received much less attention. Moreover, unfolding rates have generally been thought either to not relate to native topology in the same manner as folding rates, perhaps depending on different topological parameters, or to be more difficult to predict. Using a dataset of 108 proteins including two-state and multistate folders, we find that both unfolding and folding rates correlate strongly, and comparably well, with well-established measures of native topology, the absolute contact order and the long range order, with correlation coefficient values of 0.75 or higher. In addition, compared to folding rates, the absolute values of unfolding rates vary more strongly with native topology, have a larger range of values, and correlate better with thermodynamic stability. Similar trends are observed for subsets of different protein structural classes. Taken together, these results suggest that choosing a scaffold for protein engineering may require a compromise between a simple topology that will fold sufficiently quickly but also unfold quickly, and a complex topology that will unfold slowly and hence have kinetic stability, but fold slowly. These observations, together with the established role of kinetic stability in determining resistance to thermal and chemical denaturation as well as proteases, have important implications for understanding fundamental aspects of protein unfolding and folding and for protein engineering and design.

General mechanism of two-state protein folding kinetics

We describe here a general model of the kinetic mechanism of protein folding. In the Foldon Funnel Model, proteins fold in units of secondary structures, which form sequentially along the folding pathway, stabilized by tertiary interactions. The model predicts that the free energy landscape has a volcano shape, rather than a simple funnel, that folding is two-state (single-exponential) when secondary structures are intrinsically unstable, and that each structure along the folding path is a transition state for the previous structure. It shows how sequential pathways are consistent with multiple stochastic routes on funnel landscapes, and it gives good agreement with the 9 order of magnitude dependence of folding rates on protein size for a set of 93 proteins, at the same time it is consistent with the near independence of folding equilibrium constant on size. This model gives estimates of folding rates of proteomes, leading to a median folding time in Escherichia coli of about 5 s.