Surface residues and non-additive interactions stabilize a consensus homeodomain protein

Thermodynamic Coupling in a Consensus-Designed Spectrin Repeat Protein

Cooperativity is a central feature to protein folding and is important for protein design. Repeat proteins are good systems for quantifying the thermodynamic basis of cooperativity. Analysis of repeat proteins composed of identical consensus repeats show that repeats strongly drive the folding of their neighbors through extensive tertiary contacts. Here, we use the consensus approach to quantify the cooperativity of folding of spectrin repeat arrays. Spectrin repeats are unique among tandem repeat proteins in that they share an elongated α-helix that spans neighboring repeats. We generate a consensus spectrin repeat sequence and show that this sequence is structured by CD and NMR spectroscopy, and is considerably more stable than extant spectrin repeats. By generating pairs of consensus spectrin repeats, we find tandem repeats to be further stabilized, demonstrating cooperative stabilization by neighboring repeats. Using an Ising model to analyze single- and tandem spectrin repeat unfolding, we find that the consensus stability increase results from intrinsic but not interfacial stabilization. By introducing mutations and insertions at the boundary between consensus repeats, we find that cooperativity is driven primarily by helical propagation; to a lesser extent, helix propagation also stabilizes partly folded states where one of two repeats is unfolded.

High-Accuracy Prediction of Stabilizing Surface Mutations to the Three-Helix Bundle, UBA(1), with EmCAST

The accurate modeling of energetic contributions to protein structure is a fundamental challenge in computational approaches to protein analysis and design. We describe a general computational method, EmCAST (empirical Cα stabilization), to score and optimize the sequence to the structure in proteins. The method relies on an empirical potential derived from the database of the Cα dihedral angle preferences for all possible four-residue sequences, using the data available in the Protein Data Bank. Our method produces stability predictions that naturally correlate one-to-one with the experimental results for solvent-exposed mutation sites. EmCAST predicted four mutations that increased the stability of a three-helix bundle, UBA(1), from 2.4 to 4.8 kcal/mol by optimizing residues in both helices and turns. For a set of eight variants, the predicted and experimental stabilizations correlate very well (R2 = 0.97) with a slope near 1 and with a 0.16 kcal/mol standard error for EmCAST predictions. Tests against literature data for the stability effects of surface-exposed mutations show that EmCAST outperforms the existing stability prediction methods. UBA(1) variants were crystallized to verify and analyze their structures at an atomic resolution. Thermodynamic and kinetic folding experiments were performed to determine the magnitude and mechanism of stabilization. Our method has the potential to enable the rapid, rational optimization of natural proteins, expand the analysis of the sequence/structure relationship, and supplement the existing protein design strategies.

Singular value decomposition of protein sequences as a method to visualize sequence and residue space

Singular value decomposition (SVD) of multiple sequence alignments (MSAs) is an important and rigorous method to identify subgroups of sequences within the MSA, and to extract consensus and covariance sequence features that define the alignment and distinguish the subgroups. This information can be correlated to structure, function, stability, and taxonomy. However, the mathematics of SVD is unfamiliar to many in the field of protein science. Here, we attempt to present an intuitive yet comprehensive description of SVD analysis of MSAs. We begin by describing the underlying mathematics of SVD in a way that is both rigorous and accessible. Next, we use SVD to analyze sequences generated with a simplified model in which the extent of sequence conservation and covariance between different positions is controlled, to show how conservation and covariance produce features in the decomposed coordinate system. We then use SVD to analyze alignments of two protein families, the homeodomain and the Ras superfamilies. Both families show clear evidence of sequence clustering when projected into singular value space. We use k-means clustering to group MSA sequences into specific clusters, show how the residues that distinguish these clusters can be identified, and show how these clusters can be related to taxonomy and function. We end by providing a description a set of Python scripts that can be used for SVD analysis of MSAs, displaying results, and identifying and analyzing sequence clusters. These scripts are freely available on GitHub.