Predicting the melting point of human C-type lysozyme mutants

Abstract

A complete understanding of the relationships between protein structure and stability remains an open problem. Much of our insight comes from laborious experimental analyses that perturb structure via directed mutation. The glycolytic enzyme lysozyme is among the most well characterized proteins under this paradigm, due to its abundance and ease of manipulation. To speed up such analyses, efficient computational models that can accurately predict mutation effects are needed. We employ a minimal Distance Constraint Model (mDCM) to predict the stability of a series of lysozyme mutants (specifically, human wild-type C-type lysozyme and 14 point mutations). With three phenomenological parameters that characterize microscopic interactions, the mDCM parameters are determined by obtaining the least squares error between predicted and experimental heat capacity curves. The mutants are chemically and structurally diverse, but have been experimentally characterized under nearly identical thermodynamic conditions (pH, ionic strength, etc.). The parameters found from best fits to heat capacity curves for one or more lysozyme structures are subsequently used to predict the heat capacity on the remaining. We simulate a typical experimental situation, where prediction of relative stabilities in an untested mutated structure is based on known results as they accumulate. From the statistical significance of these simulations, we establish that the mDCM is a viable predictor for relative stability of protein mutants. Remarkably, using parameters from any single fitting yields an average percent error of 4.3%. Across the dataset, the mDCM reproduces experimental trends sufficiently well (R = 0.64) to be of practical value to experimentalists when making decisions about which mutations to invest time and funds for characterization.

Fig. (1)

The wild-type human C-type lysozyme structure. The CB atoms of the 14 mutated positions are highlighted and color-coded by highly (white), medium (light grey) and least (dark grey) solvent accessible.

Fig. (2)

Kernel density functions for each of the three model parameters generated from the m = 20 best wild-type lysozyme parameter sets. The percent variation for each parameter {δ_nat, v_nat, u_sol} is 15.9, 2.0 and 24.2 percent, respectively. The density functions and percent variation values for the lysozyme mutants are similar (cf, Table 3). The kernel density plots were generated using the R statistical package.

Fig. (3)

The m = 1 absolute best-fits to the experimental heat capacity data for the human C-type lysozyme and the 14 different point mutations considered here. Experimental data points are shown by dots, whereas the mDCM predicted curves are shown in solid line. To facilitate comparisons, the coordinate ranges in all 15 examples are equal.

Fig. (4)

Histogram plotting the accuracy of the mDCM T_m predictions when only a single parameter set is used.

Fig. (5)

The average T_m value for each structure using each of the other 14 parameter sets is plotted (error bars equal ± one standard deviation). In all but three cases, the experimental T_m falls within the range defined by the error bars.

Fig. (6)

(A) The ΔT_m values (T_m,mut − T_m,wt) for each of the 14 × 13 = 182 cases is plotted against the experimental equivalent. The Pearson correlation coefficient is R = 0.64. (B) Average ΔT_m’ values (T_m,mut(pred) − T_m,wt(exp)) versus the experimental ΔT_m values. The Pearson correlation coefficient is R = 0.60.

Fig. (7)

Cross-sections of the n × m landscape for four different lysozyme mutant examples (columns). In each case, average prediction accuracy is reported over all values of n for a given value of m. Five different values of m (rows) are shown. In all cases, our results surprisingly demonstrate that increasing the amount of parameter diversity does not improve the average difference between the experimental and predicted T_m values. The results from ten different simulations are shown superimposed on each other to show that our results are robust. Across the ten simulations, the average behavior is largely conserved, and in each case the average ΔT_m values are within the error bars of the other nine.