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Double-mutant cycles: new directions and applications
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ScienceDirect Double-mutant cycles: new directions and applications Amnon Horovitz, Rachel C Fleisher and Tridib Mondal Double-mutant cycle (DMC) analysis is a powerful approach for detecting and quantifying the energetics of both direct and long-range interactions in proteins and other chemical systems. It can also be used to unravel higher-order interactions (e.g. three-body effects) that lead to cooperativity in protein folding and function. In this review, we describe new applications of DMC analysis based on advances in native mass spectrometry and high-throughput methods such as next generation sequencing and protein complementation assays. These developments have facilitated carrying out highthroughput DMC analysis, which can be used to characterize increasingly higher-order interactions and very large interaction networks in proteins. Such studies have provided insights into the extent of cooperativity (epistasis) in protein structures. High-throughput DMC studies have also been used to validate correlated mutation analysis and can provide restraints for protein docking. Address Department of Structural Biology, Weizmann Institute of Science, Rehovot 7610001, Israel Corresponding author: Horovitz, Amnon ([email protected])
Current Opinion in Structural Biology 2019, 58:10–17 This review comes from a themed issue on Biophysical and computational methods
larger or smaller, respectively, than the effect of the double mutation. The DMC approach has also been extended for measuring higher-order coupling between N residues by constructing the appropriate N-dimensional mutant construct that comprises all the 2N possible combinations of mutations [3]. Despite the apparent simplicity of the DMC method, several complications can be encountered when it is employed. Owing to free energy conservation in thermodynamic cycles, lack of coupling (i.e. independence) is indicated by additive free energy changes (or product of binding constants), but it is not necessarily obvious what the criterion for independence should be when, for example, growth rates or melting temperatures are measured. Another potential pitfall is that the measured free energies do not actually correspond to the process of interest because of the existence of off-pathway or onpathway intermediates as pointed out, for example, in DMC analyses of channel activation [4]. Finally, it is also not always obvious what should be the choice of mutations. In general, mutations to alanine have been employed in DMC analysis so that perturbations are local and specific interactions are removed without new ones being introduced. However, it was recently suggested that averaging over the effects of all possible types of mutations at a pair of positions provides a better measure of their coupling [5].
Edited by Laura Itzhaki
https://doi.org/10.1016/j.sbi.2019.03.025 0959-440X/ã 2018 Elsevier Ltd. All rights reserved.
Introduction In double-mutant cycle (DMC) analysis [1,2], two residues are mutated separately and in combination and the effects of the mutations on the free energy of some process (e.g. folding, binding or catalysis) are measured. The difference between the effect of the double mutation, and the sum of effects of the two single mutations provides a measure of the energetic coupling between the two residues. Such energetic coupling may reflect direct interactions between residues in contact or indirect longrange interactions. Non-additive effects are also often referred to as epistasis, which can be positive or negative when the sum of effects of the two single mutations is Current Opinion in Structural Biology 2019, 58:10–17
The DMC method was first used to detect energetic coupling between residues in the active site of tyrosyl–tRNA synthetase [6]. It has since then been used to (i) quantify the strength of intra-protein and inter-protein pairwise interactions; (ii) provide restraints for structure determination (e.g. in docking [7]) much like NOEs in NMR or cross-linking mass spectrometry data; and (iii) unravel higher-order coupling in proteins and protein complexes. The DMC strategy has also been used to detect and quantify interactions in nonprotein systems such as RNA [8] and synthetic compounds [9]. Recent applications of DMCs for studying the energetics of protein complex formation include dissecting pairwise interactions across the interface between the transcription factor TEAD and its intrinsically disordered co-activator protein, YAP [10]. A recent example for analysis of intraprotein pairwise interactions by DMCs is provided by a study that showed the presence of non-native interactions in the denatured state of the KIX protein, which is part of another co-activator complex called CBP [11]. Higher-order cooperativity was revealed, for example, in a recent DMC analysis of the interaction of heparin with three coupled hotspot residues in anti-thrombin [12]. Finally, recent examples for DMC-assisted docking include studies that www.sciencedirect.com
Double-mutant cycles Horovitz, Fleisher and Mondal 11
identified the binding sites of the TRPV1 ion channel for capsaicin [13] and the odorant-gated ion channel from the malaria vector, Anopheles gambiae, for various inhibitors [14]. Here, we will not provide an exhaustive review of the many studies involving DMC analysis. Instead, we will focus on new methodological and conceptual developments associated with this technique, which have not been reviewed before [1,2]. These include combining DMC with native mass spectrometry (MS), next-generation sequencing and correlated mutation analysis.
Native MS and DMC analysis Native MS is a method that facilitates the transfer of protein complexes to the gas phase without disrupting them [15–17]. The increasingly high resolution of this technique provides a way to measure the relative concentrations of co-existing species with small differences in mass between them (e.g. due to mutation or ligand binding) from their intensities. Native MS is, therefore, a unique and invaluable tool in biophysical chemistry since the values of multiple equilibrium constants can be determined from a single spectrum of one sample. One important application of this approach has, therefore, been the determination of the values of successive
ligand binding constants of allosteric proteins [18]. More recently, it was shown that it is possible to combine native MS with DMC analysis to detect inter-protein pairwise interactions and measure their energetics [19]. In this application of DMC analysis, residues i in protein X and j in protein Y are mutated (often to alanine), thereby creating a cycle that comprises the four possible complexes that can be formed by the two wild-type proteins, Xi and Yj, and the two mutant proteins, X0 and Y0 (Figure 1). The coupling energy between residues i and j, DDGint, is given by the difference in the changes in free energy of complex formation upon mutation of residue i when residue j is present, DG (ij ! 0j), and when residue j is also mutated, DG (i0 ! 00). In terms of binding constants, the coupling energy can be expressed as follows: DDGint = RTln (KijK00/Ki0K0j), where Kij = [XiYj]/[Xi][Yj] and all the other binding constants are defined accordingly. The coupling energy can, therefore, be expressed as a function only of the concentrations of the four complexes, as follows: DDGint = RTln([XiYj][X0Y0]/([XiY0][X0Yj]) since the concentrations of all the free species cancel out. Hence, by mixing the two wild-type proteins and their corresponding single mutants and then measuring the
Figure 1
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Double-mutant cycle for measuring coupling between two residues involved in a protein–protein interaction. X and Y stand for two proteins such as colicin E9 endonuclease (black) and the bacterial immunity protein Im2 (gray) that form a 1:1 complex (PDB ID: 2WPT). Two residues, i and j (cyan), in these respective proteins are mutated individually and in combination to some other residue (e.g. alanine in pink) designated by ‘0’. The free energy changes upon the mutations are indicated in the scheme. The coupling energy can be calculated from the areas of the peaks in the mass spectrum that correspond to the four respective complexes (see main text) as indicated by the color code. www.sciencedirect.com
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intensities of the four possible co-existing complexes from a single spectrum one can obtain a direct estimate of DDGint that does not depend on knowing the concentrations of the free species. This approach, which was applied to study interactions between colicin E9 endonuclease and the Im2 immunity protein [19], circumvents the need for generating binding isotherms (which are sensitive to errors in concentrations). It can also be carried out using crude Escherichia coli cell extracts,
thereby obviating the need for protein purification [20]. This approach requires, however, that the response factor, that is the relationship between concentration and peak area, is the same for all the complexes. In principle, it should be possible to generate n and m single mutants of two interacting proteins, respectively, thereby generating n m DMCs that can yield n m potential restraints for docking the two proteins from a single MS spectrum (Figure 2).
Figure 2
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Current Opinion in Structural Biology
Double-mutant cycles can provide restraints for docking. Identifying the correct structure of a protein complex (shown at the bottom) out of an ensemble of potential structures (shown at the top) can be achieved using DMC-derived restraints. Creating n and m single mutants of two interacting proteins, respectively, yields n m DMCs that can provide n m potential restraints for docking the two proteins from a single MS spectrum. In the example shown here, constructing four mutations in each protein resulted in 16 cycles two of which yielded significant coupling energies that are likely to reflect contacts between the residues highlighted in yellow. The 16 coupling energies are shown in the 4 4 matrix and the heat map indicates their respective strengths. Current Opinion in Structural Biology 2019, 58:10–17
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Double-mutant cycles Horovitz, Fleisher and Mondal 13
Distance-dependence of coupling energies DMC-assisted structure prediction (e.g. docking) relies on the assumption that significant non-zero coupling energies reflect direct pairwise interactions. It has been found, however, that residues separated by 20–25 A˚ can still be coupled although the extent of energetic coupling between two positions in a protein decays exponentially as a function of the distance between them [21]. In agreement with these findings, a graph theory-based analysis of T4 phage lysozyme showed that coupled residues tend to belong to the same 3-clique (i.e. a subset of three residues in which every pair of residues is directly connected) [22]. Our thinking about protein behavior tends to be native-centric and long-range coupling is, therefore, usually attributed to propagation of an allosteric signal through the protein structure (although longrange coupling can also be observed in the absence of a change in 3D structure). For example, long-range epistasis in the effects of the mutations H192P and A282P in E. coli transketolase, which are separated by 33 A˚, was found to be associated with strong anti-correlated dynamics at these sites [23]. Long-range coupling was also observed recently between respective residues in the effector binding and dimerization surfaces of the E. coli biotin repressor, BirA [24]. Indirect coupling can, however, also reflect interactions between residues that are in contact only in the non-native states of a protein. This idea was explored by combining DMC analysis with 2D and 3D lattice models [25,26] for which it was possible to calculate the coupling energies for all possible pairs of positions. The coupling energies for pairs in contact were found [25] to be mostly but not exclusively negative (stabilizing). By contrast, the coupling energies for pairs not in contact were found to be mostly positive and smaller in absolute value. The number of residue pairs not in contact far exceeds, however, the number in contact and their overall contribution to stability is, therefore, substantial. The coupling energies for pairs in contact and not in contact reflect positive and negative design of native state stability, respectively. Correlated
mutations at positions not in contact, although reported to be relatively infrequent [27], may reflect such negative design. In a more recent work, DMC analysis and lattice models were combined to study the role of epistasis in evolution [28]. In agreement with a previous work on correlated mutations in lattice models selected for stability [29], this study showed that the extent of epistasis depends on the properties of the ensemble, for example, on the number of states in which an interaction is present. This study also showed that epistasis results in the unpredictability of evolutionary pathways.
High-throughput DMC analysis Experimental DMC studies have usually focused on specific pairwise interactions in systems of interest. Given their relatively small-scale nature and inherent bias in choice of mutations, they have been unable to shed light on more global features of proteins such as allosteric networks and statistical tendencies for positive and negative epistasis, that is the prevalence and nature of coupling of residue pairs in different proteins. Consequently, there has been a need for studies in which the effects of very large numbers of mutations on some thermodynamic or kinetic property of a protein are measured quantitatively (Figure 3). In an early such study, 2048 variants of l repressor were generated in which the 11 residues comprising the helix-turn-helix motif of its N-terminal domain were mutated to alanine with a singlesite probability of 0.5 [30]. Comparing the frequencies of pairwise substitutions with the product of the corresponding single-site substitution frequencies in active variants revealed that most of the mutational effects are additive (the Boltzmann distribution relates frequencies to free energies). Recently, all possible DMCs were constructed for the 9 residue a2 helix of five different PDZ domains [5], thereby generating 13 168 variants (1 wild-type, 9 19 single mutants and 36 19 19 double mutants) per domain. A bacterial two-hybrid assay was then used to determine the binding free energies of the PDZ variants for their respective peptide ligands. The values of the
Figure 3
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High-throughput double-mutant cycle analysis. Methods developed in recent years such as protein complementation [34] and bacterial two-hybrid [5] assays facilitate high-throughput DMC analysis, which can yield coupling energies for >105 pairs of residues in a system of interest. Such studies can provide insights into patterns of epistasis, higher-order coupling and communication networks in proteins (in which case sequences one and two are the same as in a contact map) or between proteins. www.sciencedirect.com
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coupling energies for most pairs of positions in all the homologs were found to have unimodal distributions centered close to zero, thereby indicating widespread additive effects as reported before [30]. It remains to be established, however, whether the average of the coupling energies for all possible 19 19 combinations of mutations at a pair of positions used in this study provides a better estimate of the pairwise coupling energy in the wild-type protein than a value derived from the effects of judiciously chosen mutations (e.g. to alanine). The bimodal distributions observed were interpreted to reflect the existence of equilibrium between two distinct conformational states of the PDZ domains. Interestingly, the different PDZ domains display some variation in their couplings but they also have a set of conserved couplings that may reflect common functional constraints. It should be noted that coupling energies for intra-protein interactions determined by measuring binding free energies have a different physical origin than those determined by measuring folding free energies [31]. Massive DMC analysis of protein–protein interactions has also been carried out for protein G domain B1 (GB1) binding to the FC domain of IgG (IgGFC) [32] and the formation of the AP-1 transcription factor complex by the products of the FOS and JUN protooncogenes [33]. In the latter case, all possible substitutions were introduced at 32 positions in each of the proteins, thereby creating 369 664 (19 19 32 32) inter-protein DMCs. Data were obtained for 107 625 of these cycles using a protein complementation assay in which the two proteins of interest, JUN and FOS, were fused to two respective fragments of methotrexateresistant DHFR [34]. Binding of the proteins to each other brings the two fragments together and allows growth, in the presence of methotrexate, that reflects the strength of the protein–protein interaction (PPI). Large-scale additivity was observed also in this study, that is the effects of double mutations on the PPI scores were well predicted by the product of effects of the corresponding single mutations. Given, however, that the PPI score is not a well-defined thermodynamic property, additivity was also demonstrated by using a model that relates the PPI score to binding free energy in a rigorous manner. In agreement with the study on the GB1–IgGFC interaction [32], negative epistasis was found to be more frequent than positive epistasis and was observed for 15 and 11% of the pairs tested, respectively. Negative epistasis was usually found to be observed when the two single mutations reduced the PPI strength in a moderate fashion whereas positive epistasis when the two single mutations greatly weakened the interaction or had opposing effects [33]. A more dramatic difference between the frequencies of negative and positive epistasis was found in a study on a 9-residue substrate-binding motif of yeast hsp90 [35]. There, about 46 and 2% of the studied pairs were found to display Current Opinion in Structural Biology 2019, 58:10–17
negative and positive epistasis, respectively, when it was assessed by comparing the growth of the double mutant with the product of the growth rates of the corresponding single mutants.
Higher-order coupling Higher-order interactions, which are prevalent in proteins and other macromolecules such as tRNA [36], can be analyzed by the appropriate multi-dimensional mutant cycle [3]. Three-way interactions, for example, are dissected using triple-mutant cubes as described in recent studies [12,37,38]. Owing to the amount of work involved and error propagation, there have been fewer studies using multi-dimensional mutant cycles of four-way and five-way interactions. Examples for studies of higherorder coupling include three-dimensional and fourdimensional mutant cycle analysis of the hydrophobic core of staphylococcal nuclease [39], a four-dimensional mutant cycle analysis of voltage-dependent gating in the Kv channel [40] and a combinatorically incomplete (28/25) analysis of a five-way interaction in an alkaline phosphatase active site [41]. More recently, five-way coupling between four residues and a Mg2+ ion was investigated in the Bacillus stearothermophilus tryptophanyl-tRNA synthetase [42]. Surprisingly, the highest-order term, that is the five-way coupling, was found to be by far the most dominant contribution to catalytic efficiency (kcat/Km) although the magnitude of higher-order terms is usually expected to diminish in factorial decomposition as has also been observed experimentally [43]. Higher-order coupling is also less expected from evolutionary considerations [41] and must, therefore, confer some selective advantage. In the case of the B. stearothermophilus tryptophanyl-tRNA synthetase, it was suggested that this advantage arises from the coordinated motions of the coupled residues, which lead to transition-state stabilization, although the role of dynamics in catalysis is controversial [44]. The physical origin of higher-order coupling is often entropic. In a three-way interaction, for example, the entropic price due to immobilizing residue A when it interacts with residue B is not paid again when residue A interacts also with residue C. Consequently, the A–C interaction becomes more favorable in the presence of the A–B interaction. Regardless of its physical origins, higher-order coupling can also arise owing to the presence of multiple co-existing and energetically distinct states of the protein [28]. In the case of a 100-residue protein, for example, there are about 1.6 105, 3.9 106 and 75 107 possible three-way, four-way and five-way couplings. It is still unknown, however, how many of them are energetically significant.
Correlated mutation analysis Predictions of protein three-dimensional structures [45] and protein–protein interactions [46] have improved www.sciencedirect.com
Double-mutant cycles Horovitz, Fleisher and Mondal 15
dramatically in recent years owing to developments in computational methods for detecting correlated mutations in proteins (and RNA). These methods work because co-evolving positions tend to be close in space [27]. In principle, however, co-evolving positions can also reflect common ancestry or indirect interactions, that is long-range allosteric coupling or interactions in non-native states. Distinguishing between co-variation that reflects energetic coupling (either short-range or long-range) and co-variation that has no physical basis (e.g. due to common ancestry) can be achieved by employing DMC analysis [47]. Computational analysis of co-evolving residues in the Mre11–Rad50 protein complex, for example, revealed correlations, which were confirmed by DMC analysis, between a tyrosine residue located near the active site of Mre11 and several Rad50 residues located more than 40 A˚ away [48]. It was suggested that this long-range coupling is involved in the reciprocal regulation of the ATPase (Rad50) and nuclease (Mre11) activities of the complex. In another study, correlated mutations at positions 7–30 A˚ apart in the motor domain of kinesin were shown by DMC analysis to reflect thermodynamic coupling [49]. Interestingly, co-evolving positions were identified in both studies [48,49] using statistical coupling analysis [5]. This method is relatively weak in comparison to other methods such as direct coupling analysis (e.g. Ref. [27]) in predicting direct structural contacts but appears to be superior in identifying long-range functional couplings that can be verified by DMC analysis [5].
DMC analysis [e.g. Ref. 11] will remain the key approach for determining their structures. Finally, it remains to be whether combining single-molecule established approaches with DMC analysis can lead to new insights into protein structure and function. Such a combination could, for example, facilitate resolving the strength of a pairwise interaction in different co-existing conformational (allosteric) states whereas conventional DMC analysis yields only a single ensemble-averaged value.
Conflict of interest statement Nothing declared.
Acknowledgements This work was supported by grant 2015170 of the United States-Israel Binational Science Foundation and the Minerva Foundation with funding from the Federal German Ministry for Education and Research. AH is an incumbent of the Carl and Dorothy Bennett Professorial Chair in Biochemistry.
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Concluding remarks Studies based on DMC analysis and carried out during the past three decades have led to an inventory of the strengths of different pairwise interactions (e.g. saltbridges, aromatic-aromatic interactions, hydrogen bonds etc.) in proteins and other molecules. Knowing the strength of various pairwise interactions is important for understanding and design of protein stability [50]. However, other aspects of protein behavior such as cooperativity in folding and allostery are due to interaction networks, that is higher-order coupling, and not just the sum of contributions of pairwise interactions. Analysis of higher-order coupling requires employing multi-dimensional mutant cycle analysis, which is labor-intensive. Hence, relatively few such studies have been carried out to date [e.g. Refs. 12,36–40,41] especially when considering the vast dimensions of protein sequence space. It is likely, however, that newly developed methods that facilitate high-throughput DMC analysis will lead to more studies in the future that focus on higherorder coupling. High-throughput DMC analysis may also be employed in the future to determine structures of proteins or protein complexes that are difficult to determine by conventional approaches such as X-ray crystallography. In cases of transient states (e.g. transition states in particular), combining kinetic measurements with www.sciencedirect.com
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48. Gao Y, Meyer JR, Nelson SW: A network of allosterically coupled residues in the bacteriophage T4 Mre11-Rad50 complex. Protein Sci 2016, 25:2054-2065. 49. Richard J, Kim ED, Nguyen H, Kim CD, Kim S: Allostery wiring map for kinesin energy transduction and its evolution. J Biol Chem 2016, 291:20932-20945. 50. Goldenzweig A, Fleishman SJ: Principles of protein stability and their application in computational design. Annu Rev Biochem 2018, 87:105-129.
Current Opinion in Structural Biology 2019, 58:10–17
ScienceDirect Double-mutant cycles: new directions and applications Amnon Horovitz, Rachel C Fleisher and Tridib Mondal Double-mutant cycle (DMC) analysis is a powerful approach for detecting and quantifying the energetics of both direct and long-range interactions in proteins and other chemical systems. It can also be used to unravel higher-order interactions (e.g. three-body effects) that lead to cooperativity in protein folding and function. In this review, we describe new applications of DMC analysis based on advances in native mass spectrometry and high-throughput methods such as next generation sequencing and protein complementation assays. These developments have facilitated carrying out highthroughput DMC analysis, which can be used to characterize increasingly higher-order interactions and very large interaction networks in proteins. Such studies have provided insights into the extent of cooperativity (epistasis) in protein structures. High-throughput DMC studies have also been used to validate correlated mutation analysis and can provide restraints for protein docking. Address Department of Structural Biology, Weizmann Institute of Science, Rehovot 7610001, Israel Corresponding author: Horovitz, Amnon ([email protected])
Current Opinion in Structural Biology 2019, 58:10–17 This review comes from a themed issue on Biophysical and computational methods
larger or smaller, respectively, than the effect of the double mutation. The DMC approach has also been extended for measuring higher-order coupling between N residues by constructing the appropriate N-dimensional mutant construct that comprises all the 2N possible combinations of mutations [3]. Despite the apparent simplicity of the DMC method, several complications can be encountered when it is employed. Owing to free energy conservation in thermodynamic cycles, lack of coupling (i.e. independence) is indicated by additive free energy changes (or product of binding constants), but it is not necessarily obvious what the criterion for independence should be when, for example, growth rates or melting temperatures are measured. Another potential pitfall is that the measured free energies do not actually correspond to the process of interest because of the existence of off-pathway or onpathway intermediates as pointed out, for example, in DMC analyses of channel activation [4]. Finally, it is also not always obvious what should be the choice of mutations. In general, mutations to alanine have been employed in DMC analysis so that perturbations are local and specific interactions are removed without new ones being introduced. However, it was recently suggested that averaging over the effects of all possible types of mutations at a pair of positions provides a better measure of their coupling [5].
Edited by Laura Itzhaki
https://doi.org/10.1016/j.sbi.2019.03.025 0959-440X/ã 2018 Elsevier Ltd. All rights reserved.
Introduction In double-mutant cycle (DMC) analysis [1,2], two residues are mutated separately and in combination and the effects of the mutations on the free energy of some process (e.g. folding, binding or catalysis) are measured. The difference between the effect of the double mutation, and the sum of effects of the two single mutations provides a measure of the energetic coupling between the two residues. Such energetic coupling may reflect direct interactions between residues in contact or indirect longrange interactions. Non-additive effects are also often referred to as epistasis, which can be positive or negative when the sum of effects of the two single mutations is Current Opinion in Structural Biology 2019, 58:10–17
The DMC method was first used to detect energetic coupling between residues in the active site of tyrosyl–tRNA synthetase [6]. It has since then been used to (i) quantify the strength of intra-protein and inter-protein pairwise interactions; (ii) provide restraints for structure determination (e.g. in docking [7]) much like NOEs in NMR or cross-linking mass spectrometry data; and (iii) unravel higher-order coupling in proteins and protein complexes. The DMC strategy has also been used to detect and quantify interactions in nonprotein systems such as RNA [8] and synthetic compounds [9]. Recent applications of DMCs for studying the energetics of protein complex formation include dissecting pairwise interactions across the interface between the transcription factor TEAD and its intrinsically disordered co-activator protein, YAP [10]. A recent example for analysis of intraprotein pairwise interactions by DMCs is provided by a study that showed the presence of non-native interactions in the denatured state of the KIX protein, which is part of another co-activator complex called CBP [11]. Higher-order cooperativity was revealed, for example, in a recent DMC analysis of the interaction of heparin with three coupled hotspot residues in anti-thrombin [12]. Finally, recent examples for DMC-assisted docking include studies that www.sciencedirect.com
Double-mutant cycles Horovitz, Fleisher and Mondal 11
identified the binding sites of the TRPV1 ion channel for capsaicin [13] and the odorant-gated ion channel from the malaria vector, Anopheles gambiae, for various inhibitors [14]. Here, we will not provide an exhaustive review of the many studies involving DMC analysis. Instead, we will focus on new methodological and conceptual developments associated with this technique, which have not been reviewed before [1,2]. These include combining DMC with native mass spectrometry (MS), next-generation sequencing and correlated mutation analysis.
Native MS and DMC analysis Native MS is a method that facilitates the transfer of protein complexes to the gas phase without disrupting them [15–17]. The increasingly high resolution of this technique provides a way to measure the relative concentrations of co-existing species with small differences in mass between them (e.g. due to mutation or ligand binding) from their intensities. Native MS is, therefore, a unique and invaluable tool in biophysical chemistry since the values of multiple equilibrium constants can be determined from a single spectrum of one sample. One important application of this approach has, therefore, been the determination of the values of successive
ligand binding constants of allosteric proteins [18]. More recently, it was shown that it is possible to combine native MS with DMC analysis to detect inter-protein pairwise interactions and measure their energetics [19]. In this application of DMC analysis, residues i in protein X and j in protein Y are mutated (often to alanine), thereby creating a cycle that comprises the four possible complexes that can be formed by the two wild-type proteins, Xi and Yj, and the two mutant proteins, X0 and Y0 (Figure 1). The coupling energy between residues i and j, DDGint, is given by the difference in the changes in free energy of complex formation upon mutation of residue i when residue j is present, DG (ij ! 0j), and when residue j is also mutated, DG (i0 ! 00). In terms of binding constants, the coupling energy can be expressed as follows: DDGint = RTln (KijK00/Ki0K0j), where Kij = [XiYj]/[Xi][Yj] and all the other binding constants are defined accordingly. The coupling energy can, therefore, be expressed as a function only of the concentrations of the four complexes, as follows: DDGint = RTln([XiYj][X0Y0]/([XiY0][X0Yj]) since the concentrations of all the free species cancel out. Hence, by mixing the two wild-type proteins and their corresponding single mutants and then measuring the
Figure 1
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Double-mutant cycle for measuring coupling between two residues involved in a protein–protein interaction. X and Y stand for two proteins such as colicin E9 endonuclease (black) and the bacterial immunity protein Im2 (gray) that form a 1:1 complex (PDB ID: 2WPT). Two residues, i and j (cyan), in these respective proteins are mutated individually and in combination to some other residue (e.g. alanine in pink) designated by ‘0’. The free energy changes upon the mutations are indicated in the scheme. The coupling energy can be calculated from the areas of the peaks in the mass spectrum that correspond to the four respective complexes (see main text) as indicated by the color code. www.sciencedirect.com
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intensities of the four possible co-existing complexes from a single spectrum one can obtain a direct estimate of DDGint that does not depend on knowing the concentrations of the free species. This approach, which was applied to study interactions between colicin E9 endonuclease and the Im2 immunity protein [19], circumvents the need for generating binding isotherms (which are sensitive to errors in concentrations). It can also be carried out using crude Escherichia coli cell extracts,
thereby obviating the need for protein purification [20]. This approach requires, however, that the response factor, that is the relationship between concentration and peak area, is the same for all the complexes. In principle, it should be possible to generate n and m single mutants of two interacting proteins, respectively, thereby generating n m DMCs that can yield n m potential restraints for docking the two proteins from a single MS spectrum (Figure 2).
Figure 2
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Current Opinion in Structural Biology
Double-mutant cycles can provide restraints for docking. Identifying the correct structure of a protein complex (shown at the bottom) out of an ensemble of potential structures (shown at the top) can be achieved using DMC-derived restraints. Creating n and m single mutants of two interacting proteins, respectively, yields n m DMCs that can provide n m potential restraints for docking the two proteins from a single MS spectrum. In the example shown here, constructing four mutations in each protein resulted in 16 cycles two of which yielded significant coupling energies that are likely to reflect contacts between the residues highlighted in yellow. The 16 coupling energies are shown in the 4 4 matrix and the heat map indicates their respective strengths. Current Opinion in Structural Biology 2019, 58:10–17
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Double-mutant cycles Horovitz, Fleisher and Mondal 13
Distance-dependence of coupling energies DMC-assisted structure prediction (e.g. docking) relies on the assumption that significant non-zero coupling energies reflect direct pairwise interactions. It has been found, however, that residues separated by 20–25 A˚ can still be coupled although the extent of energetic coupling between two positions in a protein decays exponentially as a function of the distance between them [21]. In agreement with these findings, a graph theory-based analysis of T4 phage lysozyme showed that coupled residues tend to belong to the same 3-clique (i.e. a subset of three residues in which every pair of residues is directly connected) [22]. Our thinking about protein behavior tends to be native-centric and long-range coupling is, therefore, usually attributed to propagation of an allosteric signal through the protein structure (although longrange coupling can also be observed in the absence of a change in 3D structure). For example, long-range epistasis in the effects of the mutations H192P and A282P in E. coli transketolase, which are separated by 33 A˚, was found to be associated with strong anti-correlated dynamics at these sites [23]. Long-range coupling was also observed recently between respective residues in the effector binding and dimerization surfaces of the E. coli biotin repressor, BirA [24]. Indirect coupling can, however, also reflect interactions between residues that are in contact only in the non-native states of a protein. This idea was explored by combining DMC analysis with 2D and 3D lattice models [25,26] for which it was possible to calculate the coupling energies for all possible pairs of positions. The coupling energies for pairs in contact were found [25] to be mostly but not exclusively negative (stabilizing). By contrast, the coupling energies for pairs not in contact were found to be mostly positive and smaller in absolute value. The number of residue pairs not in contact far exceeds, however, the number in contact and their overall contribution to stability is, therefore, substantial. The coupling energies for pairs in contact and not in contact reflect positive and negative design of native state stability, respectively. Correlated
mutations at positions not in contact, although reported to be relatively infrequent [27], may reflect such negative design. In a more recent work, DMC analysis and lattice models were combined to study the role of epistasis in evolution [28]. In agreement with a previous work on correlated mutations in lattice models selected for stability [29], this study showed that the extent of epistasis depends on the properties of the ensemble, for example, on the number of states in which an interaction is present. This study also showed that epistasis results in the unpredictability of evolutionary pathways.
High-throughput DMC analysis Experimental DMC studies have usually focused on specific pairwise interactions in systems of interest. Given their relatively small-scale nature and inherent bias in choice of mutations, they have been unable to shed light on more global features of proteins such as allosteric networks and statistical tendencies for positive and negative epistasis, that is the prevalence and nature of coupling of residue pairs in different proteins. Consequently, there has been a need for studies in which the effects of very large numbers of mutations on some thermodynamic or kinetic property of a protein are measured quantitatively (Figure 3). In an early such study, 2048 variants of l repressor were generated in which the 11 residues comprising the helix-turn-helix motif of its N-terminal domain were mutated to alanine with a singlesite probability of 0.5 [30]. Comparing the frequencies of pairwise substitutions with the product of the corresponding single-site substitution frequencies in active variants revealed that most of the mutational effects are additive (the Boltzmann distribution relates frequencies to free energies). Recently, all possible DMCs were constructed for the 9 residue a2 helix of five different PDZ domains [5], thereby generating 13 168 variants (1 wild-type, 9 19 single mutants and 36 19 19 double mutants) per domain. A bacterial two-hybrid assay was then used to determine the binding free energies of the PDZ variants for their respective peptide ligands. The values of the
Figure 3
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High-throughput double-mutant cycle analysis. Methods developed in recent years such as protein complementation [34] and bacterial two-hybrid [5] assays facilitate high-throughput DMC analysis, which can yield coupling energies for >105 pairs of residues in a system of interest. Such studies can provide insights into patterns of epistasis, higher-order coupling and communication networks in proteins (in which case sequences one and two are the same as in a contact map) or between proteins. www.sciencedirect.com
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coupling energies for most pairs of positions in all the homologs were found to have unimodal distributions centered close to zero, thereby indicating widespread additive effects as reported before [30]. It remains to be established, however, whether the average of the coupling energies for all possible 19 19 combinations of mutations at a pair of positions used in this study provides a better estimate of the pairwise coupling energy in the wild-type protein than a value derived from the effects of judiciously chosen mutations (e.g. to alanine). The bimodal distributions observed were interpreted to reflect the existence of equilibrium between two distinct conformational states of the PDZ domains. Interestingly, the different PDZ domains display some variation in their couplings but they also have a set of conserved couplings that may reflect common functional constraints. It should be noted that coupling energies for intra-protein interactions determined by measuring binding free energies have a different physical origin than those determined by measuring folding free energies [31]. Massive DMC analysis of protein–protein interactions has also been carried out for protein G domain B1 (GB1) binding to the FC domain of IgG (IgGFC) [32] and the formation of the AP-1 transcription factor complex by the products of the FOS and JUN protooncogenes [33]. In the latter case, all possible substitutions were introduced at 32 positions in each of the proteins, thereby creating 369 664 (19 19 32 32) inter-protein DMCs. Data were obtained for 107 625 of these cycles using a protein complementation assay in which the two proteins of interest, JUN and FOS, were fused to two respective fragments of methotrexateresistant DHFR [34]. Binding of the proteins to each other brings the two fragments together and allows growth, in the presence of methotrexate, that reflects the strength of the protein–protein interaction (PPI). Large-scale additivity was observed also in this study, that is the effects of double mutations on the PPI scores were well predicted by the product of effects of the corresponding single mutations. Given, however, that the PPI score is not a well-defined thermodynamic property, additivity was also demonstrated by using a model that relates the PPI score to binding free energy in a rigorous manner. In agreement with the study on the GB1–IgGFC interaction [32], negative epistasis was found to be more frequent than positive epistasis and was observed for 15 and 11% of the pairs tested, respectively. Negative epistasis was usually found to be observed when the two single mutations reduced the PPI strength in a moderate fashion whereas positive epistasis when the two single mutations greatly weakened the interaction or had opposing effects [33]. A more dramatic difference between the frequencies of negative and positive epistasis was found in a study on a 9-residue substrate-binding motif of yeast hsp90 [35]. There, about 46 and 2% of the studied pairs were found to display Current Opinion in Structural Biology 2019, 58:10–17
negative and positive epistasis, respectively, when it was assessed by comparing the growth of the double mutant with the product of the growth rates of the corresponding single mutants.
Higher-order coupling Higher-order interactions, which are prevalent in proteins and other macromolecules such as tRNA [36], can be analyzed by the appropriate multi-dimensional mutant cycle [3]. Three-way interactions, for example, are dissected using triple-mutant cubes as described in recent studies [12,37,38]. Owing to the amount of work involved and error propagation, there have been fewer studies using multi-dimensional mutant cycles of four-way and five-way interactions. Examples for studies of higherorder coupling include three-dimensional and fourdimensional mutant cycle analysis of the hydrophobic core of staphylococcal nuclease [39], a four-dimensional mutant cycle analysis of voltage-dependent gating in the Kv channel [40] and a combinatorically incomplete (28/25) analysis of a five-way interaction in an alkaline phosphatase active site [41]. More recently, five-way coupling between four residues and a Mg2+ ion was investigated in the Bacillus stearothermophilus tryptophanyl-tRNA synthetase [42]. Surprisingly, the highest-order term, that is the five-way coupling, was found to be by far the most dominant contribution to catalytic efficiency (kcat/Km) although the magnitude of higher-order terms is usually expected to diminish in factorial decomposition as has also been observed experimentally [43]. Higher-order coupling is also less expected from evolutionary considerations [41] and must, therefore, confer some selective advantage. In the case of the B. stearothermophilus tryptophanyl-tRNA synthetase, it was suggested that this advantage arises from the coordinated motions of the coupled residues, which lead to transition-state stabilization, although the role of dynamics in catalysis is controversial [44]. The physical origin of higher-order coupling is often entropic. In a three-way interaction, for example, the entropic price due to immobilizing residue A when it interacts with residue B is not paid again when residue A interacts also with residue C. Consequently, the A–C interaction becomes more favorable in the presence of the A–B interaction. Regardless of its physical origins, higher-order coupling can also arise owing to the presence of multiple co-existing and energetically distinct states of the protein [28]. In the case of a 100-residue protein, for example, there are about 1.6 105, 3.9 106 and 75 107 possible three-way, four-way and five-way couplings. It is still unknown, however, how many of them are energetically significant.
Correlated mutation analysis Predictions of protein three-dimensional structures [45] and protein–protein interactions [46] have improved www.sciencedirect.com
Double-mutant cycles Horovitz, Fleisher and Mondal 15
dramatically in recent years owing to developments in computational methods for detecting correlated mutations in proteins (and RNA). These methods work because co-evolving positions tend to be close in space [27]. In principle, however, co-evolving positions can also reflect common ancestry or indirect interactions, that is long-range allosteric coupling or interactions in non-native states. Distinguishing between co-variation that reflects energetic coupling (either short-range or long-range) and co-variation that has no physical basis (e.g. due to common ancestry) can be achieved by employing DMC analysis [47]. Computational analysis of co-evolving residues in the Mre11–Rad50 protein complex, for example, revealed correlations, which were confirmed by DMC analysis, between a tyrosine residue located near the active site of Mre11 and several Rad50 residues located more than 40 A˚ away [48]. It was suggested that this long-range coupling is involved in the reciprocal regulation of the ATPase (Rad50) and nuclease (Mre11) activities of the complex. In another study, correlated mutations at positions 7–30 A˚ apart in the motor domain of kinesin were shown by DMC analysis to reflect thermodynamic coupling [49]. Interestingly, co-evolving positions were identified in both studies [48,49] using statistical coupling analysis [5]. This method is relatively weak in comparison to other methods such as direct coupling analysis (e.g. Ref. [27]) in predicting direct structural contacts but appears to be superior in identifying long-range functional couplings that can be verified by DMC analysis [5].
DMC analysis [e.g. Ref. 11] will remain the key approach for determining their structures. Finally, it remains to be whether combining single-molecule established approaches with DMC analysis can lead to new insights into protein structure and function. Such a combination could, for example, facilitate resolving the strength of a pairwise interaction in different co-existing conformational (allosteric) states whereas conventional DMC analysis yields only a single ensemble-averaged value.
Conflict of interest statement Nothing declared.
Acknowledgements This work was supported by grant 2015170 of the United States-Israel Binational Science Foundation and the Minerva Foundation with funding from the Federal German Ministry for Education and Research. AH is an incumbent of the Carl and Dorothy Bennett Professorial Chair in Biochemistry.
References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as: of special interest 1.
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Concluding remarks Studies based on DMC analysis and carried out during the past three decades have led to an inventory of the strengths of different pairwise interactions (e.g. saltbridges, aromatic-aromatic interactions, hydrogen bonds etc.) in proteins and other molecules. Knowing the strength of various pairwise interactions is important for understanding and design of protein stability [50]. However, other aspects of protein behavior such as cooperativity in folding and allostery are due to interaction networks, that is higher-order coupling, and not just the sum of contributions of pairwise interactions. Analysis of higher-order coupling requires employing multi-dimensional mutant cycle analysis, which is labor-intensive. Hence, relatively few such studies have been carried out to date [e.g. Refs. 12,36–40,41] especially when considering the vast dimensions of protein sequence space. It is likely, however, that newly developed methods that facilitate high-throughput DMC analysis will lead to more studies in the future that focus on higherorder coupling. High-throughput DMC analysis may also be employed in the future to determine structures of proteins or protein complexes that are difficult to determine by conventional approaches such as X-ray crystallography. In cases of transient states (e.g. transition states in particular), combining kinetic measurements with www.sciencedirect.com
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16 Biophysical and computational methods
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Double-mutant cycles Horovitz, Fleisher and Mondal 17
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