Towards the Design of Metamorphic Proteins using Ensemble-Based Energetic Information

Miralles, Enric; Tagliabue, BenedettaPrimer pla d'una part del Parc de Diagonal-Mar. Es pot veure el paisatge del parc, realitzat amb estructures d'acer i elements de trencadís ceràmic. Al fons, es veuen uns edificis de gran alçada

Investigating Homology between Proteins using Energetic Profiles

Accumulated experimental observations demonstrate that protein stability is often preserved upon conservative point mutation. In contrast, less is known about the effects of large sequence or structure changes on the stability of a particular fold. Almost completely unknown is the degree to which stability of different regions of a protein is generally preserved throughout evolution. In this work, these questions are addressed through thermodynamic analysis of a large representative sample of protein fold space based on remote, yet accepted, homology. More than 3,000 proteins were computationally analyzed using the structural-thermodynamic algorithm COREX/BEST. Estimated position-specific stability (i.e., local Gibbs free energy of folding) and its component enthalpy and entropy were quantitatively compared between all proteins in the sample according to all-vs.-all pairwise structural alignment. It was discovered that the local stabilities of homologous pairs were significantly more correlated than those of non-homologous pairs, indicating that local stability was indeed generally conserved throughout evolution. However, the position-specific enthalpy and entropy underlying stability were less correlated, suggesting that the overall regional stability of a protein was more important than the thermodynamic mechanism utilized to achieve that stability. Finally, two different types of statistically exceptional evolutionary structure-thermodynamic relationships were noted. First, many homologous proteins contained regions of similar thermodynamics despite localized structure change, suggesting a thermodynamic mechanism enabling evolutionary fold change. Second, some homologous proteins with extremely similar structures nonetheless exhibited different local stabilities, a phenomenon previously observed experimentally in this laboratory. These two observations, in conjunction with the principal conclusion that homologous proteins generally conserved local stability, may provide guidance for a future thermodynamically informed classification of protein homology

A horizontal alignment tool for numerical trend discovery in sequence data: application to protein hydropathy.

PMC3794901An algorithm is presented that returns the optimal pairwise gapped alignment of two sets of signed numerical sequence values. One distinguishing feature of this algorithm is a flexible comparison engine (based on both relative shape and absolute similarity measures) that does not rely on explicit gap penalties. Additionally, an empirical probability model is developed to estimate the significance of the returned alignment with respect to randomized data. The algorithm's utility for biological hypothesis formulation is demonstrated with test cases including database search and pairwise alignment of protein hydropathy. However, the algorithm and probability model could possibly be extended to accommodate other diverse types of protein or nucleic acid data, including positional thermodynamic stability and mRNA translation efficiency. The algorithm requires only numerical values as input and will readily compare data other than protein hydropathy. The tool is therefore expected to complement, rather than replace, existing sequence and structure based tools and may inform medical discovery, as exemplified by proposed similarity between a chlamydial ORFan protein and bacterial colicin pore-forming domain. The source code, documentation, and a basic web-server application are available.JH Libraries Open Access Fun

Overview of the Horizontal Protein Comparison Tool (<i>HePCaT</i>) algorithm.

<p>The hydropathy profiles of two hypothetical proteins, each of length <i>M</i> = <i>N</i> = 20 residues, are shown (Step 1). Intraprotein signed distances are computed within each protein according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003247#pcbi.1003247.e001" target="_blank">Equation 1</a> in the main text (Step 2). Positive distances, <i>e.g</i>. measured from a residue with a local minimum value to a residue with a local maximum value, are indicated in red, negative distances in blue. The signed distance matrices are therefore square and symmetrically reflected across the diagonal. Distances for protein 1 and protein 2 correspond to matrices <b><i>D₁</i></b> and <b><i>D₂</i></b>, respectively. The similarity matrix <b><i>S</i></b> that ultimately compares the two proteins is constructed from the average absolute distance differences of <i>W</i> = 5 residue blocks between <b><i>D₁</i></b> and <b><i>D₂</i></b>, according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003247#pcbi.1003247.e002" target="_blank">Equation 2</a> (Step 3). In <b><i>S</i></b>, light colored squares indicate blocks of <i>W</i> = 5 residues starting at residue <i>i</i> in protein 1 and residue <i>j</i> in protein 2 with similarly shaped hydropathy, dark squares indicate dissimilar shapes. (<b><i>S</i></b><i>_{i = 1,j = 1}</i> is the lower left corner in the figure.) As described in the text, <b><i>S</i></b> is exhaustively searched and all longest alignments with up to possibly <i>GapMax</i> gaps, whose squares (average path distance, <i>APD</i>) pass a user-defined average similarity cutoff <i>C</i>, are kept in a list (set of colored arrows). The alignment of this list with the closest absolute shape (lowest <i>RMSD</i>) is defined as the optimal match (Step 5). An Optimal Path Score (<i>OPS</i>), defined by <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003247#pcbi.1003247.e004" target="_blank">Equation 4</a>, is assigned to the alignment and its significance is computed with respect to the score distribution of random alignments of identical length (Step 6). Note that the example alignment, while a reasonable visual match, is only marginally significant with respect to random alignments of identical length, due to its short length of 10 residues.</p

Parameters used in Equations 6 and 7 to estimate length-dependent random protein data probability distributions based on the Inverse Chi-Squared Distribution.

<p>Parameters used in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003247#pcbi.1003247.e006" target="_blank">Equations 6</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003247#pcbi.1003247.e007" target="_blank">7</a> to estimate length-dependent random protein data probability distributions based on the Inverse Chi-Squared Distribution.</p