Investigating the linkage between disease-causing amino acid variants and their effect on protein stability and binding

Abstract

Single amino acid variations (SAV) occurring in human population result in natural differences between individuals or cause diseases. It is well understood that the molecular effect of SAV can be manifested as changes of the wild type characteristics of the corresponding protein, among which are the protein stability and protein interactions. Typically the effect of SAV on protein stability and interactions is assessed via the changes of the wild type folding and binding free energies. However, in terms of SAV affecting protein functionally and disease susceptibility, one wants to know to what extend the wild type function is perturbed by the SAV. Here we demonstrate that relative, rather than the absolute, change of the folding and binding free energy serves as a good indicator for SAV association with disease. Using HumVar as a source for disease-causing SAV and experimentally determined free energy changes from ProTherm and SKEMPI databases, we achieved correlation coefficients (CC) between the disease index (P_d) and relative folding ( $P_p^{r,f}$ and binding ( $P_p^{r,b}$) probability indexes, respectively. The obtained CCs demonstrate the applicability of the proposed approach and serves as good indicators for SAV association with disease.

1. Introduction

Human genetic variations result in natural differences among the humans or may cause diseases[1]. Genetic variations originate from subtle differences in DNA and it is well know that humans share 99.5% of DNA code and only the rest 0.5% results in the uniqueness of individuals. However, despite of low occurrence, common genetic variations may contribute significantly to human’s susceptibility to common diseases[2–4]. Thus, understanding common human genetic variations and associated functional impact is a very important part of any genetic study and shows great potential for direct clinical applications[5, 6].

Genetic differences can be manifested at different levels as a Single Nucleotide Polymorphism (SNPs), which is a genetic change of single nucleotide or as non-synonymous SNP (nsSNP), which results in amino acid change in the corresponding transcribed product. In this work we focus on substitutions of single amino acid in the corresponding protein and following the literature such a change is termed single amino acid variation (SAV) [4, 7–9]. The SAV can affect the corresponding protein’s function and thus may be associated with human diseases[10–13]. Predicting disease associated SAV’s effect and discriminating disease-causing and harmless SAV is of crucial importance for the early diagnostics and medicine [5, 14–17]. However, predicting the effect of disease-associated SAV is not a trivial problem[18, 19], prompting many researchers to develop predictive algorithms and tools[6, 18–23].

Disease-causing SAV can alter the function of the corresponding protein resulting in dysfunctional macromolecule[13, 18, 24–26]. Some disease-causing SAVs affect protein stability, resulting in the loss of the protein function[11, 25, 27, 28]. Other disease-causing SAVs that occur in protein interaction interface may disrupt the protein interaction network by altering the affinity of interacting partners[24, 29, 30]. The effects on protein folding and binding can be accessed via the changes of folding free energy (ΔΔG) and binding free energy (ΔΔΔG). Many computational and experimental efforts were carried out to determine the changes of folding and binding free energies due to SAVs and a large number of experimental measurements are collected in databases[31, 32]. However, in terms of SAV affecting protein functionally and disease susceptibility, it is also important to know to what extend the wild type property is perturbed by SAV. In this work, we investigate two quantities, the relative change of the folding (f_f ) and binding (f_b ) free energies. It is shown that relative, rather than the absolute, change of the folding and binding free energy serves as a good indicator for SAV association with disease. The original work of Casadio and colleagues demonstrated that disease index (P_d ) and folding probability index ( P_p ) are linearly correlated, although the obtained correlation coefficient (CC) was not impressive[14]. Following their work[14] and our own investigation[26], we show that higher CC can be achieved between the and changes of the folding and binding, if one takes the relative folding $P_p^f$ and binding $P_p^b$ probability index instead of the absolute changes.

2. Materials and Methods

ProTherm and SKEMPI Databases

In this study, the ProTherm [32] and the SKEMPI [31] databases are used to collect the experimentally measured changes of folding and binding free energies. The ProTherm is a database providing thermodynamic parameters, structural information, measuring methods, experimental conditions and literature information of 25820 entries from 740 different proteins. In ProTherm, 12561 single amino acid mutations are available and linked to entries in Protein Data Bank (PDB)[33]. The SKEMPI database collects data of the changes in thermodynamic parameters and kinetic rate constants for 3047 protein-protein mutants. In SKEMPI, structures of the complex are available in the PDB and mutations’ corresponding structural regions in proteins are also provided. Since protein’s folding energy is affected by many factors including PH, temperature etc., we downloaded the cases satisfying the experimental conditions that 6<pH<8 and 20 °C <T<40°C. Thus, 1925 cases of singe amino acid mutations in ProTherm and 2286 cases of singe amino acid mutations in SKEMPI are downloaded for the statistical study in this work.

Relative change of folding and binding free energies (f_k)

SAV’s effect on protein stability and binding can be quantified by the changes of folding and binding free energies[20, 34]. It can be expected that larger change of the free folding or binding energies should have higher probability to be linked to disease. However, the magnitude of absolute folding free energy (ΔG) or the absolute binding free energy (ΔΔG) of wild type (WT) is very different among proteins, varying from several to tens kcal/mol. The same magnitude of change of folding free energy (ΔΔG) may affect the protein stability quite differently if the corresponding proteins have very different WT folding free energies. For example, several kcal/mol folding free energy change may be devastating for a protein with WT folding free energy of the same magnitude, but could have little effect on stability of very stable protein with folding free energy above tens of kcal/mol. The same arguments can be extended to protein-protein interactions. Strong binder’s functionality may not be affected by small changes of the binding free energy, while the recognition of weak binders may completely abolished by SAV causing change of the binding free energy of order of a kcal/mol. Such considerations prompted us to consider the relative change of the folding and binding free energies as an indicator for disease association. Thus, we define the relative folding or binding free energy change as:

$$f_k=\frac{\mathrm{\Delta }\mathrm{\Delta }{G}_k(\mathrm{X},\mathrm{Y})}{\mathrm{\Delta }{G}_{k,w}},$$ (1)

where k stands for k=f (folding) and k=b (binding) free energy, ΔΔG_k(X,Y) is the change of the folding or binding free energy caused by SAV X→Y and ΔG_k,w is the wild type folding (k=f) or binding (k=b) free energy.

The relative probability index of protein folding ( $P_p^{r,\mathrm{f}}$) and binding ( $P_p^{r,\mathrm{b}}$) free energies

The absolute probability index (P_p ) was introduced by Casadio and colleagues [14] to quantify SAV’s probability to increase or decrease protein’s folding stability by 1kcal/mol:

$$P_p=\frac{\text{Number}\text{of}\mathrm{X}\text{to}\mathrm{Y}\text{SAV}\text{with}|\mathrm{\Delta }\mathrm{\Delta }G>1\mathit{kcal}/\mathit{mol}|\text{in}\text{the}\text{dataset}}{\text{Total}\text{number}\text{of}\mathrm{X}\text{to}\mathrm{Y}\text{SAV}\text{in}\text{the}\text{dataset}}$$ (2)

In the lights of above considerations, instead of using absolute change of binding and folding free energy, we calculate the relative free energy change caused by SAVs and use it as an indicator for disease association. Thus, we define the relative perturbation index ( $P_p^{r,k}$) to evaluate the SAV’s probability to affect the protein’s function and to result in disease:

$$P_p^{r,k}=\frac{\text{Number}\text{of}\mathrm{X}\text{to}\mathrm{Y}\text{SAV}\text{with}|f_k>f_{\mathit{threshold}}|\text{in}\text{the}\text{dataset}}{\text{Total}\text{number}\text{of}\mathrm{X}\text{to}\mathrm{Y}\text{SAV}\text{in}\text{the}\text{dataset}},$$ (3)

where f_k is the threshold value determining the relative free energy change to be considered disease-causing. It varies from 0 (none of the mutations is disease-causing) to 1 (all mutations are disease-causing). The f_threshold is the threshold which shows to what extend the wild type stability or binding is perturbed by SAV. The same equation is applied for the relative changes of the folding (k=f) and binding (k=b) energies.

3. Results

The primary goal of our investigation is to find a quantities related to the changes of the folding and binding free energies caused by SAV and the corresponding probability of the same mutations to be disease causing. The probability of a given type of SAV to be disease-causing is estimated via the disease index P_d (degree of harmfulness) [14, 26] and tested quantities are the relative perturbation indexes, $P_p^{r,\mathrm{f}}$ and $P_p^{r,\mathrm{b}}$.

Disease index

In our previous work[26], we used the HumVar dataset[21] to obtain the disease index (P_d)[14], or the degree of harmfulness, for every possible amino acid mutation by taking all 380 different combinations of 20 natural amino acids. HumVar dataset is released on 2014 and contains 69,240 entries, out of which 37,935 termed polymorphism, 24,685 disease and 6,578 unclassified. Among 380 possible amino mutations, 108 were not observed and 123 were observed less than 10 times in the HumVar dataset. It is well known that the sample size is an important feature of statics study and larger sample sizes generally lead to increased precision when estimating unknown parameters. In our case, each SAV has different sample sizes and some SAVs are rarely observed in the database. To ensure that the corresponding P_d is not calculated for very limited number of cases, we only take mutations which are observed more than ten times in the HumVar database. The results for sixty most harmful SAVs are shown in Table 1.

Table 1.

Lists of sixty most harmful SAVs. The degree of harmfulness P_d and frequencies are shown as well.

SAVs	Frequency(%)	Disease index (Pd)	SAVs	Frequency(%)	Disease index (Pd)
cf	0.33	0.74	cs	0.47	0.52
ws	0.12	0.70	fs	0.54	0.52
cg	0.26	0.67	ni	0.19	0.52
cy	0.96	0.67	hp	0.25	0.52
ik	0.05	0.67	rc	2.52	0.52
mr	0.18	0.66	fv	0.19	0.51
wc	0.30	0.65	dv	0.40	0.51
gc	0.40	0.65	wl	0.11	0.51
cw	0.23	0.64	gw	0.16	0.50
cr	0.93	0.63	dy	0.49	0.50
rp	0.74	0.63	ki	0.06	0.49
lp	2.06	0.63	ve	0.26	0.49
wg	0.13	0.62	if	0.25	0.49
gv	0.95	0.61	lq	0.23	0.48
lr	0.65	0.60	ad	0.47	0.48
in	0.29	0.60	rl	0.65	0.48
yc	1.13	0.59	tr	0.27	0.48
vd	0.21	0.59	qp	0.34	0.47
gr	2.39	0.59	ap	0.77	0.47
ir	0.05	0.58	ys	0.19	0.45
mk	0.16	0.58	fi	0.15	0.43
is	0.18	0.57	vg	0.41	0.42
gd	1.27	0.57	gs	1.66	0.42
fc	0.22	0.57	ny	0.15	0.42
wr	0.56	0.56	dg	0.75	0.42
yn	0.13	0.55	ae	0.33	0.41
sw	0.08	0.54	pr	0.66	0.41
ge	1.04	0.53	lh	0.16	0.41
rw	2.18	0.53	ek	2.26	0.40
vf	0.32	0.53	sf	0.78	0.40

The relative binding and folding probability indexes and determining the selected ratio of disease-causing and harmless free energy changes

Previous studies showed that P_d and P_p are linearly correlated indicating that disease mechanism is associated with changes of protein stability or protein binding[14, 26, 35]. Here we apply $P_p^{r,k}$ to further explore such a linkage. However, it should be clarified that both indexes, $P_p^{r,f}$ and $P_p^{r,b}$, depend on the threshold value chosen to classify the free energy changes as disease-causing or not. In previous works[14, 26, 35], absolute value of the free energy change was used, typically 1kcal/mol. Here we explore different approach by requiring that the threshold value of the relative free energy change to be a parameter. Thus, in our approach, there is no specific threshold value for the free energy changes, rather the cases with sorted free energy changes are dynamically selected to result in selected ratio of disease-causing and harmless mutations for each particular SAV type.

The $P_p^{r,f}$ and $P_p^{r,b}$ probability indexes are calculated with the dynamically selected threshold value using the databases. Similar to the previous disease index calculation, each SAV shows different sample size and rarely observed SAVs tend to have $P_p^{r,k}$ very sensitive to the sample size. Thus, to reduce the effect from the relative rarely observed SAV, we take only the SAVs, which are observed no less than 5 times and 10 times in the database to obtain the $P_p^{r,k}$. In the SKEMPI database, there are 64 different SAV type observed for at least five times and 20 different SAV types observed for at least 10 times. Also, 50 different mutations are observed for at least five times and 29 different mutations are observed for at least 10 times in the ProTherm database. These truncated datasets are comprised of proteins with different WT properties. Thus, the wild type folding free energy varies from −17.2 to −1.2 kcal/mol within 63 different proteins and the wild type binding free energy varies from −20.87 to −4.28 kcal/mol taken within 62 different protein complexes.

Investigating the correlation between P_d and $P_p^{r,k}$ as a function of cut-off parameter value (f_threshold )

As it was outlined above, the f_threshold determines what relative change (f_k) of the folding or binding free energy is considered to be disease-causing. Since the optimal value is unknown, we carried out an analysis to determine its optimal value. It was done by calculating the Pearson product-moment CC between P_d and $P_p^{r,k}$ systematically altering the f_threshold. Figure 1(a) shows the CC of P_d and $P_p^{r,b}$ using different threshold values. It can be observed that CC increases with f_threshold at the beginning and then starts to decrease when f_threshold is more than 0.18. This behavior of CC demonstrates that there is an optimal f_threshold that provides the best correlation between P_d and $P_p^{r,f}$. The CC is larger when N >10, perhaps, due to better statistics. Therefore, f_threshold =0.18 is selected as the optimal $P_p^{r,b}$ in our study. Similarly, the CC of P_d and $P_p^{r,f}$ using different f_threshold is shown in figure 1(b). It can be seen that CC increases with f_threshold at the beginning and reaches the maximum at f_threshold =0.3 for N>5. However, for N>10, CC continues to increase above f_threshold of 0.3, but the number of cases lowers resulting in small $P_p^{r,f}$ (this causes artificial overestimation of CC). Because of that, we select f_threshold =0.3 as the optimal $P_p^{r,f}$ in our study.

Figure 1.

(a) Pearson correlation coefficient (CC) between P_d and $P_p^{r,b}$ with dynamically selected f_threshold. (b) Pearson correlation coefficient (CC) between P_d and $P_p^{r,f}$ with dynamically selected f_threshold. N>5 and N>10 means only the SAVs, which are observed at least five or ten times in the datasets, were used for CC calculation.

To bridge current investigation with previously reported approaches, which used the absolute value of the free energy change, typically 1kcal/mol, to classify the free energy changes as disease-causing or not, here we carry similar analysis varying the absolute threshold value (ΔΔG_threshold ). This results in different ratio of disease-causing and harmless mutations, and we perform the absolute probability index calculation with dynamically selected ΔΔG_threshold and then calculate the CC of P_d and $P_p^k$ to study its change with ΔΔG_threshold value. Figure 2(a) shows the CC of P_d and $P_p^b$. The results show that CC reaches the maximum when ΔΔG_threshold =2kcal/mol for N>5. However, for N>10 situation, the max value can’t be determined since CC keeps increasing artificially with the increase of ΔΔG_threshold. Similarly, figure 2(b) shows the CC of P_d and $P_p^f$. For both N>5 and >10 cases, the maximum of CC is achieved at ΔΔG_threshold =1.5kcal/mol. Overall, the results show that 2kcal/mol and 1.5kcal/mol are the most optimal threshold value for absolute binding and folding P_p.

Figure 2.

(a) Pearson correlation coefficient (CC) between P_d and $P_p^b$ with dynamically selected ΔΔG_threshold. (b) Pearson correlation coefficient (CC) between P_d and $P_p^f$ with dynamically selected ΔΔG_threshold. N>5 and N>10 means only the SAVs, which are observed at least five or ten times in the datasets, were used for CC calculation.

The square of residuals (SR)

The above analysis was done with respect to the CC of the linear fitting of either $P_p^{r,k}$ or $P_p^k$ and P_d. However, the fitting procedure depends of the magnitude of the quantities being considered. Alternatively, here we investigate the square of residuals (SR) between either $P_p^{r,k}$ or $P_p^k$ and P_d using different threshold value. Linear relation between P_d and the corresponding $P_p^{r,k}$ or $P_p^k$ is considered as:

$$P_p^{r,k}=a{P}_d$$ (4)

$$P_p^k=b{P}_d,$$ (5)

where a and b are free coefficients which will be varied and k stands for k=f (folding) and k=b (binding) free energy

Then we can calculate the square of residual (SR) as:

$$\text{Square}\text{of}\text{residuals}(\text{relative}\text{probability}\text{index})=\sum _{X,Y}{(P_p^{r,k}-a{P}_d)}^2$$ (6)

$$\text{Square}\text{of}\text{residuals}(\text{absolute}\text{probability}\text{index})=\sum _{X,Y}{(P_p^k-b{P}_d)}^2,$$ (7)

where the summations runs over all X→Y pairs in corresponding dataset. k stands for k=f (folding) and k=b (binding) free energy The goals is to find optimal a and b coefficients resulting in smallest SR value.

Firstly, we perform the SR calculation between P_d and $P_p^k$ using 1kcal/mol as threshold or $P_p^{r,k}$ using above determined optimal thresholds (for relative indexes f_threshold =0.18 for binding and f_threshold =0.3 for folding). The slopes, “a” and “b” parameters, are free coefficients which are varied as parameters and the results are shown in Figure 3. It is shown that the relation between SR values and slope parameter is a parabolic function and the corresponding fitting equation is labeled in each graph. The SR value between P_d and $P_p^{r,k}$ is much smaller than that of the $P_p^k$ using 1kcal/mol, which indicates that the $P_p^{r,k}$ is better indicator for Pd.

Figure 3.

(a) The SR calculation of $P_p^{r,f}$ (using optimal f_threshold value) and $P_p^f$ (using 1kcal/mol threshold) when taking N>5. (b) The SR calculation of $P_p^{r,f}$ (using optimal f_threshold value) and $P_p^f$ (using 1kcal/mol threshold) when taking N>10. (c) The SR calculation of $P_p^{r,b}$ (using optimal f_threshold value) and $P_p^b$ (using 1kcal/mol threshold) when taking N>5. (d) The SR calculation of $P_p^{r,b}$ (using optimal f_threshold value) and $P_p^b$ (using 1kcal/mol threshold) when taking N>10. N>5 and N>10 means only the SAVs, which are observed at least five or ten times in the datasets, will be used for SR calculation.

Furthermore, we perform the SR calculation between P_d and $P_p^k$ or $P_p^{r,k}$ using above determined optimal thresholds (for relative indexes: f_threshold =0.18 for binding and f_threshold =0.3 for folding; and for absolute indexes: ΔΔG_threshold =2kcal/mol for binding and ΔΔG_threshold =1.5 kcal/mol for folding). The slopes “a” and “b” are also variable parameters and the goal is to further compare the performance of two quantities $P_p^{r,k}$ and $P_p^k$. The results about binding and folding are shown in figure 4. It can be observed that the SR of $P_p^{r,k}$ (with determined optimal thresholds) is still smaller comparing with absolute P_p (with determined optimal thresholds).

Figure 4.

(a) The SR calculation of $P_p^{r,f}$ (using optimal f_threshold value) and $P_p^f$ (using optimal ΔΔG_threshold value) when taking N>5. (b) The SR calculation of $P_p^{r,f}$ (using optimal f_threshold value) and $P_p^f$ (using optimal ΔΔG_threshold value) when taking N>10. (c) The SR calculation of $P_p^{r,b}$ (using optimal f_threshold value) and $P_p^b$ (using optimal ΔΔG_threshold value) when taking N>5. (d) The SR calculation of ${\mathrm{P}}_p^{r,b}$ (using optimal f_threshold value) and $P_p^b$ (using optimal ΔΔG_threshold value) when taking N>10. N>5 and N>10 means only the SAV, which are observed at least five or ten times in the datasets, will be used for SR calculation.

Using the fitting equation in each graph, we can determine the minimal SR values and the related slope values in each calculation and the results are shown in Table 2. It can be observed that $P_p^{r,k}$ always establishes smaller minimal SR values and the optimal slope values for the binding and folding linear model are approximately $P_d=0.96P_p^{r,f},P_d=0.84P_p^{r,b},P_d=1.25P_p^f$, and $P_d=0.98P_p^b$.

Table 2.

The minimal SR value and the corresponding slope. In each bracket, the first value is the minimal SR value in different category and the second values is the corresponding slope. N>5 and N>10 means that only the SAVs, which are observed at least five or ten times in the datasets, will be used for SR calculation

	$P_p^{r,k}$ (N>5)	$P_p^{r,k}$ (N>10)	$P_p^k$ (1kcal/mol, N>5)	$P_p^k$ (1kcal/mol, N>10)	$P_p^k$ (Optimal threshold, N>5)	$P_p^k$ (Optimal threshold, N>10)
SR (folding)	(1.66, 0.96)	(0.78, 1.04)	(2.79, 1.64)	(1.63, 1.85)	(2.1, 1.25)	(1.14, 1.37)
SR (binding)	(2.71, 0.84)	(0.13, 0.75)	(3.91, 1.45)	(0.86, 1.43)	(2.84, 0.98)	(0.24, 0.82)

Multiple Linear Regression (MLR)

Previous study has proved that disease-causing SAV can affect protein binding stability, folding stability and other effects such as protein structure and dynamics [36–39]. Human disease index P_d shows the probability of a given type of SAV to be disease-causing and here we ask the question if it can be correlated with three components including folding probability index, binding probability index and other effects represented by a variable C. This correlation between P_d and $P_p^{r,k}$ or $P_p^k$ can be described by the following equations, for relative and absolute probability indexes, respectively:

$$P_d=a{P}_p^{k,f}+b{P}_p^{k,b}+C$$ (8)

$$P_d=d{P}_p^f+e{P}_p^b+C,$$ (9)

where a, b, d, and e are coefficients to be determined. k stands for k=f (folding) and k=b (binding) free energy.

To study the disease-causing mutations’ association with both binding and folding free energy change, we perform the multiple linear regression (MLR) between P_d and $P_p^{r,k}$ or $P_p^k$ and calculate the corresponding CC. We take 30 SAV types, which are observed for at least five times in both SKEMPI database and ProTherm database, to establish the MLR. Firstly, the $P_p^{r,f}$ and $P_p^{r,b}$ or $P_p^f$ and $P_p^b$ as treated as independent variables and used to fit a linear equation to P_d data. We perform the MLR between P_d and $P_p^{r,k}$ (using above determined optimal thresholds), between P_d and $P_p^k$ (using 1kcal/mol as threshold) and between P_d and $P_p^k$ (using above determined optimal thresholds). The results for CC are shown in Table 3 and the MLR between P_d and $P_p^{r,k}$ establishes highest 0.61 CC value.

Table 3.

The results of the correlation coefficients (CCs) from the multiple linear regressions.

	Relative probability index (optimal threshold)	Absolute probability index (threshod:1kcal/mol)	Absolute probability index (optimal threshold)
CC of using independent $P_p^f$ and $P_p^b$	0.61	0.44	0.54
CC of using larger value between $P_p^f$ and $P_p^b$	0.59	0.40	0.49

It is known that many mutations have profound effects and can affect both protein folding and binding stability. Therefore, $P_p^{r,f}$ and $P_p^{r,b}$ or $P_p^f$ and $P_p^b$ are not completely independent and considering them as independent variables in MLR will probably bring in artificial errors. Since, the dependence between $P_p^{r,f}$ and $P_p^{r,b}$ or $P_p^f$ and $P_p^b$ is unknown and is hard to be quantified, we simply used the larger values between $P_p^f$ and $P_p^b$ for each type of SAV to represent the effects of both folding and binding stability changes. Therefore, in the MLR, the larger values among $P_p^f$ and $P_p^b$ for each type of SAV will be kept to represent both folding and binding effects and the smaller values for this SAV will be counted as 0. The corresponding CC calculations results are also shown in Table 3 and MLR between P_d and $P_p^{r,k}$ reaches 0.59 CC value, which is also higher than CC value obtained using $P_p^k$.

4. Discussion

The analysis indicates that the relative folding and binding free energy changes serve as better indicator for disease association as compared with the absolute energy changes. This is demonstrated by better CC and smaller square residual as benchmarked against disease indexes delivered from HumVar database. Such an observation is consistent with the expectation that weak binders and not very stable proteins will be affected more by alterations of the binding and folding free energy (as compared with strong binders and very stable proteins) and thus their functionality will be affected in greater manner. As result, they may become dysfunctional and the corresponding mutations could be disease-causing. The reported approach can be used in conjunction with other fags and characteristics to assist developing methods for predicting disease-causing SAVs.