Enzymes are biological catalysts that speed up the reactions that are essential for life. As such, enzymes convert ‘reactant’ molecules into other molecules. Reactant molecules bind to part of the enzyme called the active site. Some of the amino acids that make up the active site must directly interact with these molecules to catalyze the reaction.

Mutating individual active site amino acids often greatly reduces or destroys the ability of the enzyme to increase reaction rates. These amino acids are known as ‘catalytic residues’. However, catalytic residues do not work in isolation: instead, they interact with other residues in the enzyme to carry out their function. Therefore, the effects of these interactions need to be characterized in order to fully understand how enzymes work.

Sunden et al. explored the interactions within a network of five residues found at the active site of an enzyme, called alkaline phosphatase, which was taken from the bacterial species E. coli. Nearly all of the possible combinations of these five residues were examined. The results of these experiments indicated that even though all five residues are structurally linked, only a subset of the residues affected one another functionally, even though all of them are structurally connected. In particular, three groups—or functional units—of residues were found in the enzyme structure. The residues within each functional unit directly or indirectly cooperate to increase different aspects of the enzyme's catalytic activity. Sunden et al. used this information to develop models that describe how the functional units work together, and suggest that the likelihood of the active site evolving so that its residues are not fully cooperative is high.

It remains to be seen whether similar cooperative networks exist in the active sites of other enzymes and how residues further away affect those in and around the active site. Understanding how the residues in the active site work together and being able to model their interactions could help efforts to develop more efficient enzymes for use in biotechnology in the future.

Scientists have long marveled at the enormous rate enhancements and exquisite specificities of enzymes. Remarkable progress has been made since catalysis was viewed as a ‘life force’ just over a century ago (Buchner, 1897; Hein, 1961; Barnett, 2003). Now, the chemical moieties involved in enzymatic transformations can be identified by a combination of structural and functional approaches. The positions of functional groups in X-ray structures can typically be combined with chemical intuition to derive mechanisms for enzymatic reactions (Benkovic and Bruice, 1966; Walsh, 1979; Sinnott, 1998; Silverman, 2002). Such mechanisms are routinely supported by site-directed mutagenesis experiments in which large deleterious rate effects are observed when putative catalytic residues are mutated.

While there remain a subset of reactions that are less understood and whose important and fascinating reaction details are still being worked out (e.g., Das et al., 2011; Weeks et al., 2012), we can write reasonable chemical mechanisms for the vast majority of enzymes (Benkovic and Bruice, 1966; Walsh, 1979; Sinnott, 1998; Silverman, 2002). In contrast, our understanding of the energetics that underlie enzymatic catalysis is far less developed. Such understanding is critical for elucidating the pathways that have been followed in molecular evolution and for designing new, highly efficient enzymes.

The current dominant mechanistic tools, X-ray crystallography and removal of catalytic residues via site-directed mutagenesis, while powerful, have fundamental limitations. Structures reveal the positions of functional groups in active sites, but these static pictures do not allow reaction probabilities to be determined. Specifically, although energies derived from a given structure can, in principle, reveal potential energies, full sampling of the ensemble states of the enzyme, substrates, and surrounding solvent is needed to obtain free energies. It is difficult to combine such sampling with high-level energy functions and to make nontrivial predictions required for independent assessment of such energetic models.

Site-directed mutagenesis has two fundamental limitations. First, site-directed mutagenesis reads out the difference in free energy of the reaction (ΔΔG) for the mutant enzyme relative to the wild type (WT), and so does not report an absolute energetic contribution to catalysis (Kraut et al., 2003; Herschlag and Natarajan, 2013). As an example, the vastly different assignments of the catalytic contributions of residues in the Ketosteroid Isomerase oxyanion hole, dependent on the type and extent of mutation, provide a particularly clear demonstration of this limitation and underscore the need to clearly and explicitly define the comparison states (Kraut et al., 2010; Schwans et al., 2011).

The second limitation of site-directed mutagenesis is that enzymatic residues do not act in isolation (Narlikar and Herschlag, 1998; Kraut et al., 2003). The apparent contribution of one residue is also a function of the surrounding residues and the overall structure, as demonstrated by energetic coupling in double mutant cycles and more dramatically by the fact that a denatured protein still contains its catalytic residues but these so-called catalytic residues no longer provide catalysis (see Kraut et al., 2003 for discussion) (Carter et al., 1984; Horovitz, 1996).

One seemingly important aspect of the interconnectivity of enzymatic residues is highlighted in X-ray structures, which typically reveal or suggest active site hydrogen bond networks and imply a functional connection between the identified catalytic residues and these more extensive ‘network residues’. Indeed, prior investigations have identified networks of energetically coupled residues in enzymes that contribute synergistically to catalysis. These studies include incisive double mutant cycle analysis demonstrating functional and energetic connections between residues (Hermes et al., 1990; Dion et al., 1993; Horovitz et al., 1994; Rajagopalan et al., 2002; Masterson et al., 2008; Singh et al., 2014). Larger scale coupled networks have been observed through statistical analysis of co-evolution and characterization of individual residue's relaxation timescales by NMR (e.g., Lockless and Ranganathan, 1999; Eisenmesser et al., 2002, 2005; McElheny et al., 2005; Freedman et al., 2009; Halabi et al., 2009; Doucet et al., 2011).

A remaining challenge, undertaken in this study, is to link mutant cycle analysis to extended networks. Currently, we lack the ability to ascertain the energetic properties of network residues from structural inspection, first principles, or empirical models. For example, do these networks act as fully cooperative units where disruption of any connection would dissipate the advantage from all of the residues in the network? In the other extreme, do certain side chains act independently from their network neighbors, positioned for function by their backbone placement and/or packing interactions with other portions of the side chain?

Although either extreme might be presumed unlikely, such expectations are not grounded in data given the current absence of quantitative assessments of these extended networks. We have therefore investigated the functional behaviors of an interaction network hypothesized from available structural data in the Escherichia coli alkaline phosphatase (AP) active site (Figure 1). Our experiments reveal and quantitatively delineate the energetic interconnectivity within this highly proficient active site, the type of active site that will be necessary to create if we are to engineer enzymes that rival the catalytic power of natural enzymes.

Figure 1

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Figure 1A shows the three-dimensional structure of E. coli AP; for simplicity, a single monomer of the homodimeric active enzyme is presented. Figure 1B,C shows a close-up and a schematic depiction of the network of residues in the active site, respectively, and Figure 1D depicts the reaction catalyzed by AP. As expected based on structural data, the presence of the Zn²⁺ ions and the active site nucleophile, S102, are required for measureable activity (Plocke et al., 1962; O'Brien and Herschlag, 2001; Andrews et al., 2013), and prior work has revealed functional effects from mutation of some of the Zn²⁺ ligands (Xu and Kantrowitz, 1992; Tibbits et al., 1994, 1996; Ma et al., 1995).

Here, we focus on the other residues in the active site and determine their functional and energetic connectivity (Figure 1C). The energetic effects we refer to here and in the remainder of this study are related to free energy differences. Prior work identified E322, which is required for Mg²⁺ binding, and R166 as catalytic residues, with mutations of these leading to 88,000 and 6300-fold decreases in the rate of catalytic activity, respectively (Zalatan et al., 2008; O'Brien et al., 2008). Nevertheless, these residues are part of an extensive hydrogen-bonded and Mg²⁺-coordinating network that also involves D101, D153, K328, the Mg²⁺ ion liganded by E322, and two water molecules (Figure 1C).

As described in the following sections, we determined the effects of removing each of the five side chains of this apparent network individually and in combination. To determine if a residue's contribution is independent of or dependent on the other side chains, we determined the activity of a minimal form of the AP active site with all five residues mutated, herein referred to as AP minimal (D101A/D153A/R166S/E322Y/K328A), and we also restored each side chain individually to this minimal enzyme. As described below, the results indicated a strong interdependence of the residues, prompting us to explore these interconnections by making nearly all possible combinations of these five mutants (28 out of 32; 2ⁿ, where n = 5, the number of positions mutated). Our results identified three interconnected functional units, each with distinct underlying energetic properties, and allowed us to develop a quantitative model that reproduces the observed rate constants and predicts the rate constants of the remaining four mutants not tested herein. For ease of reference, all of the measured and calculated rate constants are listed in Table 1 and shown graphically in Figure 2A and Figure 2B.

Figure 2

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Testing catalytic residues for independence vs interdependence

Figure 3A shows the effects from mutating each of the five active site residues depicted in Figure 1C. Each residue has a significant effect ranging from 64 to 88,000-fold, with the largest effects coming from R166 mutation and Mg²⁺ ion removal (E322Y). Previous studies have shown that replacing the E322 side chain with a tyrosine leads to loss of Mg²⁺ from the active site (Zalatan et al., 2008). We confirmed this result and showed that the E322Y mutant reaction is not activated by the presence of Mg²⁺ (‘Materials and methods’). The absence of Mg²⁺ binding and activation is consistent with the finding that other members of the AP superfamily that lack Mg²⁺ have a tyrosine at this position (Zalatan et al., 2008). Indeed, we chose the E322Y mutation for our studies because it gives the same functional effect as E322A while also creating this steric block to Mg²⁺ binding (Zalatan et al., 2008). While we did not test all possible mutations, several different mutations were tested at each position and shown to give very similar effects, providing no indication of idiosyncratic effects from any of the subtractive mutations made in this study (Appendix 1 Table 1).

Figure 3

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We next determined the degree to which these residues were dependent on one another in two simple ways. First, we removed all five residues simultaneously; if independent, the effects of removal would be multiplicative—that is, energetically additive (Equation 1). However, the cumulative effect assuming additivity gives a predicted activity that is 10⁶-fold lower than the observed activity of the minimal construct (Equation 1), indicating substantial energetic interdependence between these residues (Figure 3A);

${\text{ΔΔG}}^{‡}=\left[-\text{RT}\ln \left({\left(k_{cat}/K_{\text{M}}\right)}_{\mathbf{obsd}}/{\left(k_{cat}/K_{\text{M}}\right)}_{\mathbf{predicted}}\right)\right]=8.3\text{\hspace{0.17em}kcal}/\text{mol},$

(1) $k_{rel,}^{predicted}=k_{rel,\text{ D}101} \times k_{rel,\text{ R}166} \times k_{rel,\text{ D}153 }\times k_{rel,\text{ K}328}\times k_{rel, {\text{Mg}}^{2+}}.$

We next added each residue back in isolation to the minimal AP construct lacking all five residues, and we compared the rate effect from the added residue to the corresponding rate decrease from removing that residue from WT AP (Figure 3A,B). In each case, there was a larger deleterious effect from removing the residue than the rate enhancement afforded by adding it back. The differential effects ranged from 2.6 to >1900-fold, corresponding to differential energetic effects of up to at least 4.5 kcal/mol. Indeed, D153 added back in isolation is deleterious by at least 10-fold (Figure 3B) but beneficial by 230-fold when added in the otherwise WT background (Figure 3A). Further, the small 2.6-fold (0.57 kcal/mol) differential between restoring D101 to AP minimal and removing it from WT AP likely arises coincidentally from different mechanistic contributions (see below). Thus, each of the five residues has some energetic connection to at least one residue in this network. Overall, the contribution from adding all five residues back is 580-fold greater than predicted from assuming energetically additive effects from addition of each residue individually (Equation 1).

An empirical or theoretical framework to explain this energetic behavior is lacking. In particular, there is no way to discern from structural inspection of an active site whether all neighbors have substantial energetic interactions, the scale and form of these energetic connections, or whether and how far beyond nearest neighbors functional effects extend. Therefore, we proceeded to define the interconnections between active site residues for this model enzyme system.

Deep mutagenesis to uncover the interrelationships between active site residues: interconnected catalytic units

Figure 2A depicts the set of all 32 possible combinations of mutations of the five catalytic residues, using the color-coding from Figure 1 to represent the presence (colored) or absence (white) of each residue. In the following sections, we describe the energetic properties and interconnections of these residues.

The D101/R166/D153 functional unit

R166 was previously identified as a catalytic residue in the AP active site and hypothesized to stabilize the transition state via hydrogen bonds to the non-bridging oxygens (Figure 1C) (O'Brien and Herschlag, 1999; O'Brien et al., 2008). Mutation of R166 to serine or alanine has a similar energetic effect (O'Brien et al., 2008), and given the energetic similarity of R166S and R166A and the practical limits on the number of mutants that could be investigated, we used R166S in all subsequent experiments.

The effects of the other residues on R166 were determined by comparing the effect of mutation of this residue (R166S) in 13 different mutant backgrounds. We first determined the effects of D153 and D101, which are both within hydrogen bonding distance of R166. In the extremes, if the function of R166 was fully dependent on the neighboring aspartate residues then there would be little or no effect from adding back the R166 side chain in the absence of both D101 and D153. Alternatively, if R166 was independent of its neighbors, its full catalytic effect would be restored regardless of the presence of the aspartate residues.

Relative to the full effect of 6300-fold from addition of the R166 side chain with all other residues present, addition of this side chain in the absence of both aspartate side chains gives a much smaller rate increase of only ∼10-fold (Figure 4, left black bar). The presence of either aspartate residue increases the catalytic effectiveness of R166, such that reintroduction of the arginine side chain contributes 170 or 220-fold with D153 or D101 present, respectively, more than the increase from R166 addition with neither aspartate residue present. However, this is still considerably less than the 6300-fold increase with both aspartate residues present (Figure 4, black bars).

Figure 4

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These results indicate that the function of R166 is interconnected with and enhanced by its neighbors, D101 and D153. The simplest model to account for these effects is that each aspartate residue helps to position the arginine side chain for interaction with the non-bridging phosphoryl oxygen atoms (Figure 1C and see below).

We next asked whether the other network side chains are needed for full R166 function and enhance its function through either or both aspartate residues. The gray bars in Figure 4 compare the effects from reintroduction of the arginine side chain with or without the neighboring aspartate residues as in the black bars from this figure described above, but now comparing the effects in the presence or absence of K328 and the active site Mg²⁺. The effect of arginine add-back is nearly the same with and without K328 and the Mg²⁺ ion (cf. the pairs of black and gray bars in Figure 4). Hence, R166, D101, and D153 form a functional unit, independent of the Mg²⁺ ion and K328.

Structural effects of D101 and D153

Based on the functional effects shown in Figure 4, we expected mutation of D101 and D153 to result in a misaligned or less-ordered R166. This expectation is supported by prior X-ray structures of single mutants of D101 (Chen et al., 1992) or D153 (PDB 1AJC, 1AJD) and by a structure of the D101A/D153A double mutant collected as part of this investigation.

R166 adopts the same position in structures of WT AP, regardless of the presence of P_i in the active site (PDB 1ED9, 3TG0). Independent structures of apo D153G AP (PDB 1AJC, 1AJD) show displacement of R166 relative to its WT position. In one of these structures, the guanidinium group of R166 is rotated by ∼19°, which would distort the hydrogen bond angles with the non-bridging oxygen atoms of a phosphate bound as it is in WT AP (Figure 5—figure supplement 1). In the second structure of D153G AP, the R166 side chain is flipped away from the active site. The crystal structure of apo D101S similarly shows displacement of R166 (Chen et al., 1992). In contrast, E322Y AP, which lacks the bound Mg²⁺ ion that is not part of the R166 functional unit, does not influence the position of R166 (Zalatan et al., 2008; Figure 5—figure supplement 2).

To further explore the effects of the aspartate residues on the R166 functional unit, we solved the crystal structure of D101A/D153A AP (Table 2). In one subunit of the AP homodimer, the guanidinium group is flipped away from the active site and adopts a catalytically unproductive conformation that is similar to the conformation observed in one structure of D153G, but more displaced than in the other structure of D153G and D101S AP (Figure 5A). In the other monomer, R166 was observed to populate two rotameric positions, one of which is similarly flipped away from the active site while the other is pointed towards the active site. (Figure 5B). Although this structure lacks a bound Mg²⁺ ion in the active site, the functional and structural data presented above suggest that this loss will not influence the position of R166. In both active sites of D101A/D153A AP, the bound P_i is not well positioned, populating multiple conformations that are each distinct from its position in WT AP, which likely closely mimics the reactive phosphoryl conformation (Appendix 2 and Appendix 2 Figure 1) (Holtz et al., 1999; O'Brien et al., 2008). These structural comparisons provide evidence that the aspartate residues that flank R166 help to correctly position the reactive phosphoryl group and provide a self-consistent picture of the functional effects of the D101/R166/D153 functional unit. Nevertheless, a future challenge will be to quantitatively link structural rearrangements and resulting structural ensembles to functional effects (Frederick et al., 2007).

Table 2

Data collection
Space group	P6322
Unit cell axes
a, b, c (Å)	161.4, 161.4, 140.1
α, β, γ (ο)	90.0, 90.0, 120.0
Resolution range (Å)	52.89–2.24 (2.31–2.24)*,†
Rmerge (%)	43.0 (305.9)
Rpim (%)‡	9.6 (71.9)
<I>/<σI>	7.8 (1.4)
Completeness (%)	100.0 (100.0)
Multiplicity	21.6 (19.7)
CC1/2	0.996 (0.582)
Refinement
Resolution range (Å)	52.89–2.24†
No. unique reflections	51,819 (5086)
Rwork/Rfree (%)	21.7/25.9
Number of atoms	6794
Average B-factors (Å2)
protein	37.8
water	30.2
ligands	41.2
R.m.s. deviation from ideality
Bond length (Å)	0.006
Bond angles (ο)	1.10
Ramachandran statistics
Favored regions (%)	98.4
Allowed regions (%)	1.6
Outliers (%)	0
PDB code	4YR1

1. *

   Values in parenthesis are for the highest resolution shell.

2. †

   The high resolution cut-off applied during scaling and refinement was decided based on CC_1/2 and completeness (Diederichs and Karplus, 2013; Evans and Murshudov, 2013).

3. ‡

   R_pim is reported in addition to R_merge due to the high multiplicity of the data set.

Figure 5 with 2 supplements see all

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Possible roles of groups beyond the D101/R166/D153 functional unit in R166 positioning

Single hydrogen bonds between the aspartate residues and R166 might be expected to precisely position the arginine residue only if other interactions position the aspartate residues themselves. We have determined that the remaining groups of the apparent active site network, K328 and the Mg²⁺ ion, are not required, so positioning of the aspartate side chains must arise from distinct interactions.

The D101 carboxylate group accepts a hydrogen bond from a backbone amide and therefore could be directed by that interaction (Figure 1C). In contrast, the D153 carboxylate group does not appear to accept a hydrogen bond from residues beyond the five probed herein; however, its methylene group packs against the side chains of nearby residues.

Testing the role of the backbone amide in positioning D101 to, in turn, position R166 will be difficult, but the model for D153 is readily testable: mutation of the nearby side chains is predicted to eliminate the ability of D153 to stimulate R166 function. It will also be of interest to determine if, in the absence of the side chains that putatively pack around and position D153, the hydrogen bond network that comprises K328, the Mg²⁺ ion, and their associated water molecules is now needed to position D153 and, in turn, position the R166 side chain.

The D153/Mg²⁺(E322)/K328 functional unit

The Mg²⁺ ion in the AP active site had previously been identified as important for catalysis, decreasing activity ∼10⁵-fold when removed by replacing one of the metal ligands, E322, with a tyrosine or alanine, an effect even larger than that from removal of R166 (Zalatan et al., 2008). We assessed possible functional connections to the Mg²⁺ ion analogously to the approach taken above for R166.

Figure 6 shows the effect from addition of the bound Mg²⁺ ion (via restoration of E322; Zalatan et al., 2008 and ‘Materials and methods’) in eight different mutant backgrounds. These comparisons test the energetic interconnectivity of the Mg²⁺ ion with all residues other than D101, and we address D101 and the Mg²⁺ ion in the following section (‘The D101/Mg²⁺(E322) Functional Unit’). There is a substantial rate increase of 820-fold from Mg²⁺ ion addition in the absence of any of the other three residues (Figure 6, far left). This effect is ∼100-fold less than the maximal effect of 88,000-fold from Mg²⁺ ion addition in the otherwise WT context (Figure 6, far right).

Figure 6

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Consistent with the results presented above for R166, the presence of R166 has virtually no effect on the rate advantage from adding Mg²⁺ back to the active site, regardless of which other residues are present or absent (Figure 6, mutant sets −/+R166). Also, when either D153 or K328 is present, the effect from Mg²⁺ add-back remains the same. Only when both D153 and K328 are present is the full 88,000 effect observed (Figure 6, far right). The ∼100-fold differential effect with or without D153 and K328 indicates that the Mg²⁺ ion, D153, and K328 form a unit that is functionally separate from the catalytic contributions of the D101/R166/D153 unit.

Nevertheless, the two functional units are interconnected as they have D153 in common. From a functional perspective, given the close quarters within an active site, even if fully independent functional units were readily obtainable, interconnected units might still be preferable to allow a compact active site that can accommodate the density of groups needed to provide multiple interactions with centrally located substrates and thus optimal catalysis. From an evolutionary perspective, parsimony in natural selection might be expected to lead to multiple uses of the same residue, such that one residue could serve in two functional units, and one functional unit might serve as a foundation or scaffold from which to build other functional units, thereby leading to interconnected functional units. This idea is related to a proposal of Hanson and Rose that natural selection favors the use of the minimal number of acidic and basic residues in active sites, so that such residues tend to be reused when mechanistically reasonable (Hanson and Rose, 1975).

Whereas AP in its fully evolved form has functionally distinct D101/R166/D153 and D153/Mg²⁺/K328 units (i.e., these functional units do not provide an additional advantage to one another), mutations that disrupt the surrounding AP scaffold could alter these energetics and possibly render these units energetically interdependent (Narlikar and Herschlag, 1998; Kraut et al., 2003). Such mutations may have been present during the early evolution of the AP active site, when its scaffold may have been less precisely arranged.

The D101/Mg²⁺(E322) functional unit

Given the absence of direct connections between the active site Mg²⁺ or K328 and D101 and the above findings of circumscribed functional units, we initially expected that there would be no interactions between D101 and these groups. Data analogous to that of Figures 4, 6 probing the dependence of the K328 contribution with or without D101 confirmed this expectation for K328 (Figure 8—figure supplement 1). However, a connection was observed between D101 and the Mg²⁺ ion. Addition of D101 when the Mg²⁺ ion is not present leads to a ∼20-fold rate increase (Figure 7A); in contrast, there is no increase when Mg²⁺ is present (Figure 7B). Figure 7A,B shows only cases in which R166 is not present because D101 enhances the potency of R166 as part of the D101/R166/D153 functional unit (Figure 4); nevertheless, the interconnection of D101 with R166 and the Mg²⁺ ion are distinct, as the enhancement by D101 of the R166 contribution is the same with and without the Mg²⁺ ion present (Figure 4). Together, these results indicate that D101 has a stimulatory effect independent of R166, but only when the Mg²⁺ ion is not present.

Figure 7

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To further explore coupling between D101 and the Mg²⁺ ion, we plotted the effect of adding the Mg²⁺ ion with or without D101 present (Figure 8). The effect from the added Mg²⁺ ion varies depending on whether D153 and K328 are present, as described in the preceding section, but in each case the effect is diminished if D101 is present. Mirroring the larger effect from D101 addition in the absence of Mg²⁺, addition of the Mg²⁺ ion had a 30-fold larger effect in the absence of D101.

Figure 8 with 1 supplement see all

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Thus, D101 and the Mg²⁺ ion form a third functional unit, with energetic behavior distinct from the other two units. In the D101/R166/D153 functional unit, R166 has close to energetically additive effects from the neighboring aspartate residues, and the Mg²⁺ functional unit (D153/Mg²⁺/K328) exhibits cooperative energetic effects from K328 and D153. In contrast, the Mg²⁺ ion and D101 are energetically anti-cooperative, with a 20–30-fold contribution from each occurring only when the other group is absent.

These observations raise two questions addressed immediately below: (1) how are D101 and the Mg²⁺ ion functionally linked, and (2) what is the origin of their anti-cooperative energetics?

How are D101 and the Mg²⁺ ion functionally linked?

Consideration of the AP active site structural network reveals potential linkages between D101 and the Mg²⁺ ion. They are linked via R166 and D153 (Figure 1C), but these residues have no effect on the energetic coupling between D101 and the Mg²⁺ ion, so models involving these residues and this connection are ruled out. A second structural connection between D101 and the Mg²⁺ ion can be traced as follows: D51 is a ligand of both the Mg²⁺ ion and the Zn²⁺ ion that coordinates the nucleophilic oxyanion of S102 ($Z{n}_2^{2+}$), and D101 is directly upstream of S102, with its side chain anchored to the backbone amide of S102 (Figure 1C).

What is the origin of their anti-cooperative energetics?

Given this connection, why are these energetically anti-cooperative—that is, how is a favorable effect from each residue prevented or obviated by the presence of the other residue? A model that D101 and the Mg²⁺ ion can each make a catalytic interaction alone that is prevented by a steric block or conformational rearrangement upon addition of the other residue would require fortuitous catalytic interactions present in mutant enzyme forms that are not maintained in WT and is therefore unlikely. A more appealing model is the one in which the two residues have a redundant effect, such that either residue can alone provide a rate advantage through the same mechanism. Given that D51 is a ligand of both the Mg²⁺ ion and the Zn²⁺ ion that coordinates the nucleophilic oxyanion of S102 ($Z{n}_2^{2+}$, Figure 1B,C), the Mg²⁺ ion could help position the serine oxyanion with respect to the rest of the catalytic apparatus (Figure 1C). D101 is directly upstream of S102 with its side chain anchored to the backbone amide of the S102. Thus, it is possible that either D101 or Mg²⁺ interactions can facilitate proper positioning of the S102 oxyanion for nucleophilic attack and that, once either of the two interactions is made, positioning is optimized such that no further functional enhancement occurs upon addition of the second (Figure 1C).

Active site redundancy

As described above, our energetic data indicate that there is a redundant effect of the Mg²⁺ ion and D101. Redundancy is often observed in functional studies from the molecular to the cellular to the organismal level (Peracchi et al., 1998; Naor et al., 2005), but its origins are less clear. It is sometimes suggested that more ‘important’ pathways or functions evolve redundancy, but more complex mechanisms are required to maintain redundancy, otherwise it would simply be lost over evolution (Cookea et al., 1997). One intriguing idea is that redundancy is built to aid evolvability, and evolvability itself is a property that has been selected for over evolution (Maynard Smith, 1978; Conrad, 1979; Joyce, 1997). It is also possible that many reported cases of redundancy have individual functional effects that are too small to be detected in laboratory assays or have favorable functional effects that manifest only under natural growth conditions.

We propose a distinct origin of the D101/Mg²⁺ redundancy, arising from the high degree of connectivity within the AP active site. D101 and the Mg²⁺ ion are each involved in other functional networks and are embedded in an extensively interwoven active site. These interconnections presumably position functional groups to make optimal catalytic interactions. As noted above, the functional networks overlap with one another that is, have shared residues (Figure 9), and these overlaps may have arisen as evolution co-opted residues within active sites as anchor points for positioning new residues. Given the high density of functional groups within active sites and the presumed need for multiple interconnections to provide optimal positioning of functional groups for transition state interactions, residues that evolved for different functional purposes may end up structurally linked and with the ability to position the same group or groups.

Figure 9

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Evolutionary pathways and probabilities

The evolution of a fully cooperative network would be exceedingly improbable and more difficult the larger the number of constituent residues, as all of the residues would need to arise through random drift with a selective advantage accruing only once the entire network was in place. A probability model in which each of five residues would arise with a one in twenty probability (i.e., one active residue out of the total 20 amino acids) and all are needed for a selective advantage (i.e., full cooperativity) has a probability of 1/(6.8 × 10⁵) (Figure 10A, bottom pathway and Appendix 3). This probability arises because there are five steps (or positions) each with 20 possible residues, and there are five chances of ‘choosing’ a WT residue, starting with AP minimal with all five WT residues missing, four chances of choosing the next residue, etc.

Figure 10

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Conversely, evolution of a hypothetical enzyme in which each active site residue provides an independent rate advantage would be considerably more probable, as addition of those residues would lead to monotonically increasing catalysis (i.e., be continually uphill on a fitness landscape and thus selected for after each addition). We first consider a simplified model with a single pathway of five successive steps that each lead to increased fitness, each with a one in twenty probability representing a single advantageous residue of the twenty possible residues (Figure 10A, top path, black numbers). The probability of achieving the final state for a multi-step process can be considered in terms of a mean waiting time, akin to a reaction's half-time or the inverse of its rate constant (scaled by ln 2). In this case, with five successive irreversible steps each with probability 1/20, the ‘rate constant’ is 1/100 and the mean wait time is 69 (in arbitrary units; Appendix 3). (Calculating probabilistic waiting times using a hidden Markov Model, such as is often used for probability calculations, gives the same relative values as the kinetic mean times [Appendix 3].) This kinetic mean wait time is about three orders of magnitude lower than that for the fully cooperative process, which is obtained by computing the mean waiting time: 4.7 × 10⁵ (=6.8 × 10⁵ × ln 2; Appendix 3). Thus, if it were functionally equally probable to obtain an active site with these different underlying energetic properties (i.e., fully cooperative vs stepwise; Figure 10A), evolution would favor the non-cooperative solution by greater than 1000-fold. In other words, for every enzyme that evolved five residues with full functional dependence on one another, there would be more than 1000 with active sites containing residues whose stepwise addition each provided a selective advantage.

As we observed functional units exhibiting a range of energetic behaviors within the AP active site, we asked the question: where does the energetic behavior of AP place it along this wide range of evolutionary probabilities? There are 120 possible pathways from AP minimal to WT AP (Figure 10B). To assess the range of possible mean waiting times, we consider two limiting cases (Figure 10A, top pathway): i. The case in which there is a single pathway of the 120 that is favorable; this is the simplified model presented above and gives a mean wait time of 69. ii. The case in which all 120 potential pathways are favorable—that is, proceed with a selective advantage at each step; in this case the mean waiting time is 32, even shorter than for case (i) because there are more ways to traverse the landscape from AP minimal to WT AP.

Because we have rate constants for each AP species (Table 1; Figure 2), we can determine which pathways would confer a selective advantage. Using an arbitrary minimal cutoff of >threefold increase in k_cat/K_M, 34 of the 120 pathways confer a fitness advantage; with a cut-off of a fivefold increase in k_cat/K_M, 28 of these pathways remain. Thus, although the AP active site residues studied herein have varied energetic behaviors, in many cases addition of a WT residue leads to a significant rate increase, providing multiple favorable evolutionary routes. While not all 120 pathways are favorable for AP, many are, and the mean waiting time will thus be within the range of 32–69, >1000-fold shorter than the expected waiting time to evolve a fully cooperative network.

Although a fully cooperative network would probably not have been anticipated, we were unaware of how strong the evolutionary pressure would be for stepwise increases in fitness. Similar conclusions have been drawn for the evolution of unlinked loci where largely additive rather than fully cooperative or synergistic effects have been observed (Arnegard et al., 2014). It will be fascinating to explore more broadly the interplay of functional effects and evolutionary probabilities and how this interplay has biased the complement of extant enzymes. Such underlying probabilistic preferences presumably also impact biological solutions at higher levels of function such as gene regulation and neuronal function (McLean et al., 2011).

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Author details

1. Fanny Sunden

   Department of Biochemistry, Beckman Center, Stanford University, Stanford, United States

   Contribution

   FS, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   For correspondence

   fsunden@stanford.edu

   Competing interests

   The authors declare that no competing interests exist.

2. Ariana Peck

   Department of Biochemistry, Beckman Center, Stanford University, Stanford, United States

   Contribution

   AP, Conception and design, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

3. Julia Salzman

   Department of Biochemistry, Beckman Center, Stanford University, Stanford, United States

   Contribution

   JS, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

4. Susanne Ressl

   Molecular and Cellular Biochemistry Department, Indiana University Bloomington, Bloomington, United States

   Contribution

   SR, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

5. Daniel Herschlag

   Department of Biochemistry, Beckman Center, Stanford University, Stanford, United States

   Contribution

   DH, Conception and design, Analysis and interpretation of data, Drafting or revising the article

   For correspondence

   herschla@stanford.edu

   Competing interests

   The authors declare that no competing interests exist.

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