Functional conservation with mechanistic drift: AMP activation in the evolution of archaeal sugar kinases

Abstract

Although allosteric regulation has been pointed out as one of the cornerstones of biological function, it has been a scarcely studied phenomenon in Archaea carbohydrate metabolism. Given its central role in metabolism, we experimentally investigated how allosteric regulation and its underlying kinetic mechanism evolved along evolutionary pathways within the archaeal ADP-dependent kinase family. Using ancestral sequence reconstruction, we resurrected key ancestors of this family and show that AMP regulation is an ancestral feature retained exclusively in lineages encoding bifunctional ADP-dependent phosphofructokinase (PFK)/glucokinase (GK) enzymes, which are restricted to methanogenic organisms, whereas it is lost in lineage-specific PFK enzymes. Notably, although AMP-dependent allosteric regulation is conserved among bifunctional ADP-PFK/GK enzymes, the kinetic mechanisms underlying activation are not. Instead, we observed a diversity of activation mechanisms (increased affinity for substrates, enhanced catalytic efficiency, or a combination of both), distributed along a 2-billion-year evolutionary trajectory, and that persists across different temperatures studied, both in extant and ancestral enzymes. These results highlight that the structural scaffold of this protein family is evolutionarily robust, preserving function while allowing substantial diversification of the underlying activation mechanisms under sequence variation. Based on these findings, we propose the concept of mechanistic drift, in which evolutionary pressures primarily act on adaptive functional traits that confer an adaptive advantage, rather than on the specific molecular mechanisms by which they are achieved. This framework has broad implications for macromolecular evolution, illustrating how long-term functional conservation can coexist with extensive physicochemical mechanistic diversity.

Introduction

Allostery, the regulation of a protein's activity through the remote action of binding an effector molecule to a site distal to the active site, is a fundamental requirement for function in cell life. Its importance leads Monod to propose it as “the second secret of life” (Monod 1972), recognizing its relevance for understanding biological systems, disease mechanisms, and for establishing new paradigms for drug discovery. For allosteric regulation to occur, enzymes must evolve effector-binding sites distinct from the catalytic site. Binding the effector to the allosteric site enables efficient transmission of information across long distances within the protein, ultimately modulating activity at remote functional sites. The current view of allostery is the ensemble model, which proposes that proteins populate a distribution of conformational states defined by a free energy landscape (Astore et al. 2024; Millard et al. 2025). Within this framework, allosteric regulation is intrinsically embedded in protein dynamics and arises from redistributions of the conformational ensemble (Wrabl et al. 2011; Campitelli et al. 2020).

In the case of the highly regulated glycolytic pathway, it has been proposed that the evolutionary relationship between prokaryotic and eukaryotic phosphofructokinase (PFK) enzyme involved gene duplication, tandem fusion, and the divergence of redundant catalytic sites into new allosteric sites (Poorman et al. 1984). Recently, Fenton et al. (2025) reviewed whether allosteric mechanisms are conserved among homologs by comparing two extant pyruvate kinases with 66.5% sequence identity. The authors found a lack of conservation in structural features of the allosteric network and divergent thermodynamic coupling between the allosteric and active sites, suggesting that allosteric mechanisms may evolve independently of effector binding sites. Despite its metabolic importance, a systematic study of allosteric regulation and the conservation or divergence of its underlying mechanisms along the evolution of a natural lineage of enzymes has been scarcely tackled.

One approach to addressing this issue is the ancestral sequence reconstruction (ASR) methodology, first proposed by Pauling et al. (1963), which enables the laboratory reconstruction of inferred ancestral proteins, allowing for direct study of their evolutionary trajectories. For example, through this methodology, Hadzipasic et al. (2020), addressed the evolution of the allosteric regulation for a modern Ser-Thr protein kinase regulated by two distinct allosteric mechanisms: autophosphorylation and specific protein–protein interactions, concluding that autophosphorylation is the most ancient activation mechanism and, subsequently, regulation by protein-protein interaction gradually evolved.

Nonetheless, allosteric regulation has been scarcely studied in enzymes from the Archaea domain. Moreover, initially, it was claimed that enzyme regulation in Archaea occurs mainly at the transcriptional level (Bräsen et al. 2014). However, some examples of allosteric regulation in Archaea have been recently reported, such as activation by 3PG or AMP in the pyruvate kinases of Thermoproteales and Methanococcales, respectively (Johnsen et al. 2019). Another example is the activation of the bifunctional ADP-dependent PFK/glucokinase (GK) enzyme from the methanogenic organism Methanococcus maripaludis (MmPFK/GK) by AMP, as reported by us (Vallejos-Baccelliere et al. 2022). This enzyme belongs to the ADP-dependent sugar kinase family, whose members exhibit either specific PFK and GK, like the enzymes from Thermococcales organisms, or bifunctional enzymes performing both activities (GK/PFK) at the same active site, which are present in methanogenic organisms such as Methanococcales and Methanosarcinales. Methanogenic organisms and their metabolism have attracted significant interest due to their potential to capture and convert the primary source of global climate concerns, namely, CO₂ emissions, into a valuable fuel, methane. Although these organisms cannot grow in the presence of complex sugars, peptides, or compounds of three or more carbon atoms due to the lack of specific transporters (Hendrickson et al. 2004; Castro-Fernandez et al. 2017b), in a nutrient-rich medium, they exhibit gluconeogenic metabolism and synthesize glycogen (König et al. 1985; Yu et al. 1994). Under starvation conditions, when methanogenic precursors are depleted, glycogen is degraded, and glycolysis is activated for energy production and the synthesis of methanogenic precursors, with the concomitant inhibition of gluconeogenesis (Goyal et al. 2016; Gonzalez-Ordenes et al. 2024). In this metabolic switch, the activation of the bifunctional PFK/GK ADP-dependent enzyme by AMP may play a significant role.

In this work, we address the evolutionary history of the AMP allosteric activation of ADP-dependent kinases to assess, on the one hand, whether activation is a conserved trait related to bifunctionality in methanogenic enzymes and, on the other, whether AMP activation and its underlying kinetic mechanism are conserved along the evolutionary pathway of this enzyme family. Through ASR and comprehensive kinetic characterization of ancestral and extant enzymes, we show that AMP activation is an ancestral trait conserved throughout the evolutionary trajectory of bifunctional ADP-PFK/GK enzymes from methanogenic organisms. This trait is subsequently lost during enzyme specialization, leading to specific PFK or GK activity branches. Our findings reveal that while activation by AMP is a conserved trait across both ancestral and modern bifunctional enzymes, the kinetic mechanisms driving this activation differ significantly across all temperatures tested.

This observation leads us to propose the concept of “mechanistic drift.” This concept posits that distinct physicochemical mechanisms may emerge over time as selective pressure is applied to the trait that confers adaptive advantage to the organism, regardless of the underlying mechanisms.

Results

Allosteric activation by AMP is an ancestral trait that correlates with bifunctionality in ADP-dependent kinases from archaea

Recently, our group reported the AMP activation of the bifunctional ADP-dependent PFK/GK from M. maripaludis (Castro-Fernandez et al. 2014; Vallejos-Baccelliere et al. 2022). To determine whether this regulatory trait is present in other members of this family, we evaluate the effect of AMP on enzymes from different orders, including Thermococcales, Methanococcales, and Methanosarcinales, which represent different branches of the phylogeny of this protein family (Fig. 1). It is worth noting that enzymes in the last two orders are bifunctional, whereas in Thermococcales organisms, both activities (GK and PFK) are performed by distinct, specific enzymes encoded by separate genes. This has been attributed to possible horizontal gene transfer, which would explain the phylogeny's topology for this family of enzymes (Castro-Fernandez 2017a).

Figure 1.

AMP activation in extant and ancestral ADP-dependent kinases. a) Schematic illustration of the dual role of AMP, as activator and as inhibitor. b and c) AMP activation of the GK and PFK activities, respectively, of extant enzymes. d and e) AMP activation of the GK and PFK activities, respectively, of ancestral enzymes. All measurements were performed at sub-saturating concentrations of both substrates. f) Schematic phylogenetic relationships of bifunctional and specific enzymes from different orders, modified from Castro-Fernandez (2017a). Ancestral enzymes of interest are shown as colored circles. The check indicates AMP activation, and the cross-mark symbols indicate no activation. The statistical reliability of each node is indicated by the aLRT SH-like branch support parameter.

Initial velocity measurements were conducted at various AMP concentrations in specific and extant bifunctional enzymes. The assays were carried out at sub-saturating concentrations of both substrates to ensure that the activation effect could be detected. However, an inhibitory effect may occur at higher concentrations due to AMP acting as a reaction product, thereby decreasing reaction velocity.

The results indicate that specific enzymes from the order Thermococcales, such as GK from Thermococcus litoralis (TlGK) and PFK from Pyrococcus horikoshii (PhPFK), are not activated by AMP (see Fig. 1a and b, represented by the blue and red lines). Instead, only the inhibitory effect of the product is observed. On the other hand, the effect of AMP was assessed in one extant bifunctional enzyme from the order Methanococcales (Methanothermococcus thermolithotrophicus, MttPFK/GK) and one from the order Methanosarcinales (Methanosarcina burtonii, MbPFK/GK), both of which were activated by AMP. Interestingly, in the enzyme from the order Methanosarcinales (MbPFK/GK), only the GK activity is activated by AMP (Fig. 1b and c, purple and green lines), showing that, among extant enzymes, the bifunctional ones are activated by AMP, whereas this regulatory trait is absent in specific enzymes, either GK or PFK.

Since all these enzymes are homologous and share a common ancestor, this raises the question of whether AMP activation is an ancestral trait or an evolutionary novelty. To understand the evolutionary trajectory of AMP activation, we examine this trait in the reconstructed ancestors of this enzyme family (Castro-Fernandez 2017a). Specifically, we selected the ancestor of the bifunctional enzymes from Methanococcales (ancM), the ancestor of the specific PFKs from Thermococcales (ancT), their common ancestor (ancMT), the ancestor of the bifunctional PFK/GK enzymes from Methanosarcinales (ancMs), and the common ancestor of all three lineages (ancMMT) (Fig. 1f).

Interestingly, the AMP activation trait is already present in ancMMT, the oldest ancestor assessed, as well as in ancMs, ancMT, and ancM, all of which are ADP-PFK/GK bifunctional ancestors (Castro-Fernandez 2017a). In contrast, ancT, the ancestor of specific PFK, shows only marginal activation (Fig. 1d and e). The results show that AMP activation is an ancient feature of the ADP-dependent kinase family, correlated with bifunctionality throughout the evolutionary history of this protein family.

The AMP kinetic activation mechanism has not been conserved throughout evolution

According to the general modifier model for kinetic mechanisms (Botts and Morales 1953; Baici 2015), the modifier (activator or inhibitor) exerts its effect by modifying either K_M, k_cat, or both, which is reflected in different activation profiles (activity vs. effector concentration). If the activator exerts its effect mainly on substrate affinity, the effect will disappear or be minimized at saturating substrate concentration on the activation profile. Conversely, if the effect mainly enhances catalysis, or if the affinity for the substrate is unaffected, the activation will remain constant or even increase at saturating substrate concentrations.

For MmPFK/GK, we reported a kinetic mechanism of activation, primarily driven by an increase in sugar-binding affinity (Vallejos-Baccelliere et al. 2022). This means that when the sugar substrate is at saturating concentration, the activator effect of AMP tends to be minimized, and its inhibitor effect on the product reaction is maximized (Fig. 2, blue panel, dashed line). On the other hand, at a saturating concentration of MgADP, the inhibitory effect of AMP is minimized while its activator effect is maximized (Fig. 2, blue panel, red line), which occurs due to the competition of both nucleotides at the active site (Fig. 2, blue panel, red line). Testing activation at sub-saturating and saturating concentrations of both substrates suggests the kinetic activation mechanism involved, that is, whether it affects affinity, catalysis, or both.

Figure 2.

Evolutionary trajectory of AMP activation profiles in ADP-dependent sugar kinases. The AMP activation profiles for both GK and PFK activities of extant and ancestral enzymes are shown under three different substrate conditions: low sugar and low MgADP (open circle), high sugar and low MgADP (filled circle), and low sugar and high MgADP (red filled circle). A sketch of the activation profile previously published for MmPFK/GK is displayed in the top left corner (Vallejos-Baccelliere et al. 2022). Briefly, activation through increased substrate affinity is characterized by a profile in which AMP activation decreases under substrate-saturating conditions. Conversely, when AMP activation persists even at saturating substrate concentrations, it suggests a mechanism driven primarily by enhanced catalytic efficiency. All measurements were performed at 25 °C. Normalization was performed based on an extrapolation to the theoretical value at 0 mM AMP (see Kinetic Appendix).

To assess whether the kinetic activation mechanism has been conserved throughout the evolution of this protein family, AMP activation of extant and ancestral enzymes was measured under three substrate concentration conditions: low sugar and low MgADP, low sugar and high MgADP, and high sugar and low MgADP. “Low” refers to concentrations equal to or lower than the K_M determined for the enzyme in the absence of AMP, while “high” indicates saturating conditions. A list of the K_M values used is provided in Table S1.

Extant and ancestral enzymes were assessed, and it was surprising to find that most displayed activation profiles that differed from those described for MmPFK/GK (see Fig. 2, blue panel). In contemporary enzymes from the order Methanococcales, we assayed AMP activation in bifunctional enzymes from MttPFK/GK and Methanocaldococcus jannaschii (MjPFK/GK). The activation profile of MttPFK/GK indicates a mechanism mediated by sugar and nucleotide affinity. Consequently, activation of both GK and PFK activities is reduced under substrate-saturating conditions (see Fig. 2, MttPFK/GK dashed and red lines). In contrast, the GK reaction of MjPFK/GK shows similar activation profiles across all three conditions, reaching a peak around 0.5 mM of AMP and steadily decreasing at higher concentrations. Nonetheless, the PFK reaction is activated only at low substrate concentrations and is significantly inhibited at saturating concentrations of both substrates, exhibiting only the inhibitory product inhibition component.

Additional activation profiles were examined for extant bifunctional enzymes of the order Methanosarcinales; Methanococcoides burtonii (MbPFK/GK) and Methanosarcina mazei (MzPFK/GK). MbPFK/GK exhibited AMP-dependent activation exclusively for its GK activity, suggesting that the effect is primarily mediated through enhanced glucose and MgADP binding affinity. Notably, its PFK activity showed no activation by AMP at any substrate concentration. On the other hand, the MzPFK/GK activation profile suggested catalytically driven AMP activation of its GK activity, with activation remaining at saturating concentrations of both substrates. However, the PFK reaction showed no significant activation by AMP. Finally, we tested the extant specific PFK enzyme from P. horikoshii, which displayed no evidence of AMP activation under any substrate condition.

Some of these findings align with the previous report on the enzyme from M. maripaludis (MmPFK/GK). Both MttPFK/GK (which belongs to the same taxonomic order as M. maripaludis) and MbPFK/GK significantly decrease the activator effect of AMP when the sugar substrate concentration is saturating. However, when MgADP is the saturating substrate, activation decreases significantly (see Fig. 2, MttPFK/GK and MbPFK/GK red lines). This suggests an activator effect stemming from increased affinity for MgADP, a finding that differs from that observed with MmPFK/GK. Additional differences are observed among the remaining extant enzymes. MjPFK/GK displays GK activation under all conditions tested, including substrate saturation, consistent with an activation mechanism driven by enhanced catalysis. In contrast, its PFK reaction shows a divergent activation profile: no activation is detected at saturating concentrations of F6P and MgADP, indicating an affinity-mediated mechanism involving both substrates. Similarly, the GK reaction of MzPFK/GK exhibits an AMP-dependent activation profile consistent with enhanced catalysis, as activation persists even at saturating substrate concentrations. However, for the PFK reaction, and in agreement with its homolog MbPFK/GK, no significant activation is observed under any substrate condition tested.

To trace how these different activation profiles emerged during the evolutionary trajectory of this enzyme family, we analyzed the ancestral enzymes under the same three substrate concentration conditions. Beginning with the ancM ancestor, the activation profile of the GK shows a clear dependence on sugar affinity, with activation being minimized when glucose is in excess (see Fig. 2, ancM GK activity). In contrast, the PFK activation profile displays a striking difference: the activation mechanism appears to result from an increase in catalysis rather than enhanced affinity for F6P or MgADP, as activation is observed even under saturating concentrations of both substrates (see Fig. 2, ancM PFK activity).

Moving further back to the ancestor ancMT, the activation profiles for both GK and PFK activities display activation under saturation of both substrates, suggesting that AMP activation occurs predominantly through enhanced catalysis rather than increased substrate affinity (see Fig. 2, ancMT). Finally, at the most ancestral point examined, ancMMT, the activation profiles of the two activities diverge: the PFK activity suggests that AMP activation is driven by catalysis, whereas the GK activity indicates that activation primarily results from increased affinity for glucose and MgADP.

The activation profiles for two additional ancestral enzymes were obtained, ancestors ancMs and ancT. The activation profiles for ancMs suggest that GK activation is primarily driven by catalysis, whereas PFK activation occurs by an increased F6P and MgADP affinity (see Fig. 2, ancMs).

Finally, ancT, the ancestor of the specific PhPFK enzyme, is only marginally activated by AMP, reaching approximately 160% of the activity observed in the absence of AMP. Notably, it exhibits significant inhibition at high AMP concentrations when both substrates are at low concentrations, as well as at high F6P concentrations. Moreover, the activation is still maintained at saturating MgADP concentrations (see Fig. 2, ancT black and dashed lines), which suggests that the marginal activation is primarily due to an increase in F6P affinity.

Using ASR, it was possible to access the evolutionary trajectory of the AMP activation trait within this family of enzymes. The results show that AMP activation is an ancient feature of the ADP-dependent kinase family, correlated with bifunctionality throughout its evolutionary history. Overall, the activation profiles of ancestral enzymes differ markedly. Among them, ancMT is the only enzyme whose activation is suggested to occur exclusively through enhanced catalysis. In contrast, ancMMT, ancM, and ancMs each display distinct activation profiles for their two enzymatic activities, and these profiles differ from one another. Another advantage of employing ASR is illustrated by our findings on ancT, which exhibits slight activation, potentially a vestigial trait that has been lost during the evolutionary path of specific PFK enzymes. These findings indicate that activation mechanisms have diverged significantly along the evolutionary trajectory from ancestral to modern enzymes, as well as between the GK and PFK activities within the same enzyme.

Given that several of the enzymes analyzed are thermophilic, and that ASR frequently infers thermophilic ancestors, we evaluated the effect of temperature, as this factor could perturb the conformational landscape and thereby influence the mechanistic divergence observed (Katava et al. 2020).

We measured selected enzymes from Fig. 2 at two additional higher temperatures (37 °C and 45 °C) to assess whether mechanistic divergence is preserved across temperatures. All enzymes examined displayed AMP-dependent activation at the temperatures tested. At both 37 °C and 45 °C, the enzymes maintained their characteristic activation profiles, differing only in the magnitude of activation, in the apparent K_a for the activator, and the extent of AMP-mediated inhibition (Fig. S4).

For example, both extant enzymes, MmPFK/GK and MttPFK/GK, retain AMP-dependent activation of their GK activity through increased sugar affinity. However, MmPFK/GK shows a reduced magnitude of AMP activation, accompanied by a more pronounced inhibitory component, whereas in MttPFK/GK, AMP activation is stronger and AMP inhibition is attenuated in the GK reaction. In contrast, the activation profiles associated with PFK activity in both enzymes remain largely unchanged across the three substrate concentrations tested (Fig. S4).

MbPFK/GK, the extant enzyme from the Methanosarcinales branch, exhibits affinity-dependent activation for both substrates, with an overall increase in activation magnitude across all conditions tested. Notably, at 37 °C, a minor activation component in the PFK activity that was barely detectable at 25 °C becomes more pronounced, followed by the expected AMP inhibition observed at both temperatures (Fig. S4).

Regarding the ancestral enzymes, both ancMT and ancM preserve their activation profiles. ancMT is activated through enhanced catalysis in both the GK and PFK reactions, whereas ancM continues to display activity-specific activation mechanisms, characterized by increased glucose affinity in the GK reaction and enhanced catalysis in the PFK reaction. Overall, these results (Fig. S4) show that although some differences in the magnitudes of the activating effect and in the apparent K_a for the activator, as well as in product inhibition sensitivity are observed, the general trend, namely, the kinetic parameter affected and, consequently, the underlying kinetic mechanism, remains conserved.

Describing the evolutionary pathway of the AMP activation mechanism

Having established that divergence in the underlying activation mechanisms is a robust feature that is not affected by temperature, we next examined the evolution of AMP-dependent activation in this protein family through comprehensive kinetic characterization of both extant (MttPFK/GK) and ancestral enzymes (ancM and ancMT). Specifically, we measured initial reaction velocities across a range of substrate concentrations (MgADP and sugar substrates) and AMP concentrations at 25 °C.

Due to the complexity of these enzyme mechanisms, which include substrate inhibition and the dual role of AMP as both a product and an activator, we employ a phenomenological approach based on empirical equations, analogous to the general modifier model (Botts and Morales 1953; Baici 2015). This allowed us to evaluate how the kinetic parameters, V_max and K_M, for each substrate of both enzymatic activities depend on AMP concentration (see Kinetic Appendix).

Our phenomenological approach quantifies the magnitude of the activator on either enzyme-substrate affinity and the catalytic constant for both substrates as the ratio, $\alpha =K_{\mathrm{M}}^{\mathrm{\infty }}/K_{\mathrm{M}}^0$ for affinity, and $\beta =V_{max}^{\mathrm{\infty }}/V_{max}^0$ for catalysis. Here, $K_{\mathrm{M}}^0$ and $V_{max}^0$ correspond to the parameter values at 0 AMP concentration, and $K_{\mathrm{M}}^{\mathrm{\infty }}$ and $V_{max}^{\mathrm{\infty }}$ are the calculated values for the respective parameters extrapolated to infinite AMP concentration, considering only the activator effect. An α < 1 indicates an increase in substrate affinity, while a β > 1 signifies an enhancement in catalytic activity (Botts and Morales 1953; Baici 2015).

In the previously reported mechanism for MmPFK/GK (Vallejos-Baccelliere et al. 2022), the main effect of the activator was on the K_M values for the sugar substrate, which is reflected in α^glc and α^F6P of approximately 0.01 and 0.1, respectively (Fig. 3a). In contrast, the effect of AMP on the β^glc and β^F6P parameters is much less pronounced. A completely different picture emerges when examining MttPFK/GK, the other current enzyme studied. For the GK activity of MttPFK/GK, the glucose parameters (α^Glc and β^Glc) show a smaller magnitude than those of MmPFK/GK. However, the main activating effect is observed in nucleotide affinity: α^MgADP (0.001) is at least one order of magnitude lower than α^Glc (see Fig 3a and b for MttPFK/GK activity). In the case of PFK activity, the activating effect is apparent only in catalysis, β^F6P (3.66) and β^MgADP (5.36), with no impact on F6P or MgADP affinity (Fig. 3a and b  MttPFK/GK PFK activity). These results demonstrate that the AMP activation mechanism differs from that described for MmPFK/GK and, even more, differs between the two activities of the same enzyme.

Figure 3.

AMP activation mechanism in ADP-dependent kinases from the order Methanococcales. a) Fold change in V_max and K_M vs. AMP concentration for the substrates Glc (filled circle) and MgADP (open circle) of GK activity, and F6P (red filled circle) and MgADP (red open circle) of the PFK activity in extant (MttPFK/GK) and ancestral enzymes (ancM and ancMT). Lines through the data represent fits to kinetic models (see Kinetic Appendix). In cases where both activation and inhibition were observed, dashed lines represent the fit to a model that includes both effects, and dotted lines indicate the isolated activation component. b) Activation parameters α and β for the substrates of each activity obtained by the fitting of phenomenological equations (see Kinetic Appendix). The parameters were estimated by fitting the Michaelis–Menten or substrate inhibition equations to the data shown in Fig. S1. c) Reaction model at low and high AMP concentrations, shows the α and β parameters as the ratios between the saturated and zero AMP condition for K_M or V_max, respectivelly. All measurements were performed at sub-saturating concentrations of both substrates, and the previously published activation mechanism of the extant MmPFK/GK enzyme is incorporated for comparative analysis (Vallejos-Baccelliere et al. 2022).

An even more diverse mechanistic landscape emerged in the study of ancestral enzymes. In ancM, AMP increases glucose affinity (with an α^Glc of approximately 0.1) and has a significant impact on catalysis (_GKβ^MgADP = 13.45), while showing no effect on MgADP affinity (_GKα^MgADP = ∼1). However, in the context of PFK activity, AMP enhances the affinity for both substrates (α^F6P and α^MgADP < 1), with the effect on K_M^MgADP being predominant (Fig. 3a ancM PFK activity). Moreover, there is a substantial effect on catalysis, with β^F6P and _PFKβ^MgADP values of 10 and 100, respectively.

The activator effect of ancMT GK activity was found to be exclusively by an increase in catalysis with β^Glc and _GKβ^MgADP values close to 100. An increase in catalysis was also observed for the PFK activity, with β^F6P around 10 and _PFKβ^MgADP close to 100. Additionally, for PFK activity, there was also an increase in MgADP affinity, indicated by an _PFKα^MgADP value of about 0.01.

These results support the fact that activation mechanisms differ substantially throughout the evolutionary history of this enzyme family, as well as between the two activities within the same enzyme.

The impact of AMP activation on the kinetic parameters of the ADP-dependent PFK/GK enzymes analyzed is summarized in Fig. 4. Although the overall AMP activation mechanisms vary in a seemingly non-directional manner over evolutionary time (Fig. 2), the α and β parameters associated with different substrates exhibit a partial evolutionary trend (Fig. 4b).

Figure 4.

Evolutionary pathway of the kinetic AMP activation mechanism in ADP-dependent sugar kinases. a) Summary of the effect of AMP on K_M and V_max parameters for each substrate of GK and PFK activities. The substrates (glucose, F6P, and ADP) are represented by their molecular structures. Three AMP effects are illustrated: decrease in K_M (downward arrow), increase in V_max (upward arrow), and no effect (gray dash). The arrow size corresponds to the magnitude of the AMP effect on each parameter. b) α and β values for MgADP (open circle) and Glc (filled circle) of the GK activity and MgADP (red open circle) and F6P (red filled circle) of the PFK activity over divergence time (Gyr). The order of enzymes proceeds from ancMT to ancM (ancestral enzymes), followed by MttPFK/GK and MmPFK/GK (extant enzymes). All measurements were performed at 25 °C.

Analysis of the α parameter for the sugar substrate in the GK activity shows that this parameter decreases significantly over the divergence time (from ancMT to extant enzymes), suggesting that activation has been optimized to enhance glucose affinity (Fig. 4b, top left panel, gray filled circles). Interestingly, there is no discernible trend in the impact of AMP on MgADP affinity, as is only observed in the GK activity of extant enzymes and not in their ancestral counterparts (Fig. 4b, top left panel, black empty circles). In contrast, the α parameter for the PFK reaction demonstrates a clear trend toward a diminished effect on MgADP affinity over evolutionary time (Fig. 4b, top right panel, red empty circles).

Variation in both β parameters for GK activity reveals a decreasing trend with evolutionary divergence (Fig. 4b, bottom left). A similar pattern is observed for the β parameters associated with PFK activity, consistent with a progressive attenuation of AMP-mediated catalysis activation over evolutionary time (Fig. 4b, bottom right). Together, these results indicate that the overall activation mechanism within this enzyme family has undergone substantial evolutionary change. Importantly, however, the individual components of this mechanism are not entirely stochastic; analysis of the α and β parameters for both activities across divergence time reveals an underlying evolutionary pattern.

The great diversity of activation mechanisms observed in both extant and ancestral enzymes, together with differences between GK and PFK activities within the same enzyme across temperatures, is consistent with mechanistic drift over evolutionary time. Such drift may occur if organismal fitness is maintained by preserving the adaptive advantage conferred by the trait, irrespective of the specific molecular mechanism underlying it. In this scenario, if the functional outcome is conserved, the molecular mechanisms underlying it may vary across evolutionary trajectories.

Discussion

Allosteric regulation

Allosteric regulation is essential to numerous biological processes, ranging from synaptic transmission to enzyme modulation. Despite its central role in metabolic control—famously described by Monod as the “second secret of life”—this phenomenon has been largely overlooked in archaeal enzymes. Early studies proposed that carbohydrate metabolism in archaea is primarily regulated at the transcriptional level (Bräsen et al. 2014). However, growing evidence over the past few years has shown that allosteric regulation also plays a significant role in archaeal enzymatic function. For instance, in methanogenic archaea, AMP has been identified as an activator of several glycolytic enzymes, including GAPOR, PK, ADP-PFK, and ADP-GK (Park et al. 2007; Bräsen et al. 2014; Johnsen et al. 2019; Vallejos-Baccelliere et al. 2022; Gonzalez-Ordenes et al. 2024), and as an inhibitor of gluconeogenic enzymes such as FBPase from Methanosarcina acetivorans (Santiago-Martínez et al. 2016).

In the glycolytic pathway, PFK has long served as a paradigm of allosteric regulation, with both mammalian and prokaryotic enzymes exhibiting tight regulatory control (Atkinson and Walton 1965). The mammalian enzyme has activator sites for AMP or ADP and Fru-2,6-P₂ and inhibitor sites for ATP and citrate (Mor et al. 2011; Compton and Patrick 2025).In the case of pyruvate kinase, another highly regulated enzyme, it has been reported to exhibit evolutionarily divergent allosteric strategies. Structural comparison of extant PK from pathogenic protists like Trypanosoma cruzi, Trypanosoma brucei, and Leishmania mexicana with those from bacteria and mammals shows that, even when in all cases, the underlying principle is to maximize k_cat/S_0.5 by stabilizing the tetramer in an active R conformation, it was achieved by different strategies (Morgan et al. 2014). On the other hand, Raman et al. (2016), propose a model in which the origin of allostery lies in the capacity of proteins for adaptation to new functions (evolvability). By employing a PDZ family member, they found that conditional neutrality is generally allosteric, enabling a specific set of distantly positioned residues to reveal new structural and functional states at the ligand-binding site.

However, the evolution of the underlying mechanisms of allosteric regulation has been scarcely tackled. One of the few examples is the work of Kern’s group that, employing ASR to resurrect ancestors of two colocalizing proteins, Aurora A kinase and its allosteric activator TPX2, determined that autophosphorylation of the activation loop is the most ancient activation mechanism, and then binding to TPX2 evolved to increase fitness by colocalization (Hadzipasic et al. 2020). ASR reconstruction has also been used to identify amino acid residues responsible for the reversal of the allosteric effect in the Tryptophan synthase heterotetrameric complex. While the last bacterial common ancestor (LBC) LBCATrpA allosterically downregulates the activity of LBCA-TrpB, the modern TrpA from Neptuniibacter caesariensis (ncTrpA) allosterically enhances the activity of its partner subunit, ncTrpB. Through ASR, the authors identify key residues involved in the propagation of the allosteric signal within this multienzyme complex (Schupfner et al. 2020).

In the field of directed evolution, Leander et al. (2020), use the tetracycline repressor as a model to describe the mutational pathways that can lead from the loss of the allosteric effect to its recovery without disturbing the allosteric site and the binding of the allosteric effector. Using deep mutational scanning, they demonstrated a lack of conservation of residues crucial to the allosteric effect, indicating that multiple mutational pathways can restore allosteric function. A similar conclusion regarding the plasticity and convergence of mutation effects was reached by Buller et al. (2018), using tryptophan synthase as a model; they show that mutations that emulate the allosteric effect do so through changes in protein dynamics rather than structural features. Coquille et al. (2025), address the evolutionary pathway by which allosteric properties have been acquired. By introducing a few mutations associated with the emergence of allosteric LDHs into the non-allosteric MalDH from Methanopyrus kandleri, the enzymatic profile gradually shifted to resemble that of allosteric LDHs. This finding suggests that both homotropic and heterotropic interactions—distinct from those observed in modern FBP-activated LDHs—may have existed during the evolutionary transition from MalDH.

Our work expands the current understanding of the evolution and mechanisms of allosteric regulation. We support evidence that allostery is an ancient regulatory strategy already present in archaeal enzymes, and we further show that allosteric control of the glycolytic pathway is conserved across all three domains of life. This conservation underscores the evolutionary importance of regulating this central metabolic pathway, a conclusion reinforced by the presence of allosteric regulation in the deeply rooted PFK/GK ancestor reconstructed in this study.

By examining the evolution of the underlying physicochemical mechanisms of AMP activation, we show that this regulatory trait is associated with bifunctionality and is executed through divergent kinetic mechanisms. AMP activation was subsequently lost during the evolutionary transition from a bifunctional ancestor to a specialized monofunctional PFK enzyme. Interestingly, monofunctional specific enzymes are present in organisms such as Thermococcales, whose metabolism depends on carbohydrate-based nutrients (Bräsen et al. 2014), whereas bifunctional enzymes occur in methanogenic organisms that are unable to assimilate sugars, peptides, or compounds containing three or more carbons (Gonzalez-Ordenes et al. 2024). This distribution emphasizes the context-dependent relevance of allosteric regulation within metabolic pathways.

Divergent kinetic strategies for AMP activation

Screening of AMP activation in the ADP-dependent kinase family reveals that this trait is correlated with the presence of GK/PFK bifunctional enzymes in the organisms. In contrast, AMP does not activate enzymes from organisms in which these relevant glycolytic reactions are catalyzed by distinct, specific enzymes (GK and PFK). Bifunctional enzymes are present in methanogenic organisms that cannot grow on sugars but accumulate glycogen (König et al. 1985; Murray and Zinder 1985; Santiago-Martínez et al. 2016), raising questions about the role of AMP in the regulation of methanogenic metabolism. In this respect, it has been proposed that energy charge may signal the metabolic switch from gluconeogenesis and glycogen storage to glycolysis and methanogenesis (Gonzalez-Ordenes et al. 2024).

In this context, AMP-mediated activation of bifunctional ADP-dependent GK/PFK kinases may have played a crucial role in cellular energy acquisition by enhancing glycolytic flux following glycogen degradation. Here, we show that AMP activation in ADP-dependent sugar kinases is an ancestral trait, present even in the last common ancestor (ancMMT) of both bifunctional lineages and in the PFK specific-lineage. Nonetheless, this trait is lost along the evolutionary pathway leading to specific PFK enzymes, suggesting that this regulation is no longer necessary for enzymes belonging to organisms with carbohydrate metabolism as their primary energy source, highlighting the potential role of AMP activation in the metabolic switch in methanogenic organisms. Moreover, we obtained unexpected insights by exploring the underlying kinetic mechanism of AMP activation in extant and ancestral enzymes. A comprehensive examination of the activation mechanism reveals that the kinetic parameters, K_M and V_max exhibit random variation in relation to effector concentration. This variability is observed among both extant and ancestral enzymes, as well as within the activities (GK and PFK) of the same enzyme. However, a closer examination of the α and β parameters, which correspond to the activating effect of AMP on K_M and V_max for each substrate along the evolutionary trajectory of this enzyme family, reveals some trends. For example, the α parameter for the sugar substrate in the GK activity indicates an optimization of the AMP effect over glucose affinity. In contrast, the α parameter of the PFK reaction exhibits a clear trend toward a diminished effect on MgADP affinity over the divergence time. On the other hand, the variation of the β parameters for both substrates (sugar and MgADP) of the GK and PFK shows a loss of the activating effect of AMP on catalysis as these enzymes evolved.

From an evolutionary perspective, we acknowledge that, given the current data, potential biases introduced by ambiguous residues cannot be fully excluded. The original reconstruction of the ancestral sequences followed the methodology described by Hall (2006). Residues were classified as ambiguous when the ratio between the posterior probabilities of the most probable and second-most probable amino acids was lower than 1.5. No ambiguous sites were present within or near the active site (first and second shells), and, based on this ratio, the total reliable sites ranged from 92% to 96% in the ancestors.

We performed a reexamination of the ancestral sequences using the more strict “altALL” approach described by Eick et al. (2017), increasing the percentage of sites labeled as unreliable between 16% and 9%. These percentages fall within the uncertainty range examined (Eick et al. 2017) across different protein families, who found that all the functions examined are robust to stochastic uncertainty in the precise ancestral sequences, with traits remaining qualitatively unchanged even when very large numbers of alternate plausible amino acids are incorporated into the protein. In this context, we expect that the quantitative parameter of AMP activation can be affected by sequence variability, but that the functional qualitative trait, namely the kinetic mechanism of activation, remains robust.

Importantly, the mechanistic drift proposed here is also fully supported when analyses are restricted to extant enzymes; all five extant bifunctional PFK/GK enzymes studied exhibit distinct AMP activation profiles (see Fig. 2). Despite significant divergence across both extant and ancestral enzymes, specific properties remain conserved between ancestors and their descendants. For example, the glucose-affinity component observed in the GK activity of ancM persists in the GK reaction of MttPFK/GK. For its PFK reaction, MttPFK/GK displays catalysis-driven activation with respect to MgADP, a characteristic shared by both ancM and ancMT. Furthermore, the GK activation profile of MjPFK/GK indicates enhanced catalysis, a feature also observed with MgADP in ancM and with both substrates in ancMT. Likewise, within Methanosarcinales, both ancMs and MzPFK/GK exhibit catalytically driven activation in the GK reaction. Taken together, these observations reinforce the conclusion that the mechanistic drift underlying AMP activation is robust and does not depend on the specific sequences of the reconstructed ancestors.

Moreover, the prevailing framework for understanding allostery is the ensemble model, which posits that proteins populate a range of conformational states whose relative populations are determined by their free energy. Consequently, any energetic perturbation affecting a given conformation results in the redistribution of the entire ensemble (Gunasekaran et al. 2004). In this context, temperature has been identified as a key modulator of allosteric responses, enhancing or attenuating temperature-dependent allosteric crosstalk (Knight et al. 2023). Consistent with this view, Katava et al. (2020) showed that, in a thermophilic malate dehydrogenase, temperature can act as an external regulatory parameter, revealing an intrinsic, previously hidden allosteric potential. In our study, we showed that temperature can either enhance the activating effect of AMP (decreasing K_A) or strengthen its inhibitory component (decreasing K_i), consistent with temperature reshaping the conformational ensemble.

Nonetheless, it does not substantially influence the mechanistic drift underlying AMP-dependent allosteric regulation in the ADP-dependent sugar kinase family, underscoring the robustness of the observed mechanistic differences.

The mechanistic drift hypothesis

The recognition of distinct AMP activation mechanisms throughout the evolution of this enzyme family underscores the value of a vertical approach to studying the evolution of allostery. In an evolutionary context, a trait may be favored because it provides an adaptive advantage, or it may be preserved simply because its loss would be detrimental. In either case, what ultimately matters are the trait's impact on organismal fitness and its ability to be inherited, regardless of the specific underlying mechanisms that sustain it. As long as the trait is preserved, its underlying mechanism becomes “invisible” to natural selection and is susceptible to drift. In the case studied, selection is exerted on the organism's ability to regulate carbohydrate metabolism, enabling it to adapt to nutrient availability by switching between gluconeogenesis and glycolysis. In this context, activating ADP-PFK/GK enzymes by AMP would be crucial for meeting the organism's energy demands, independent of the mechanism that supports activation. An analogous case of a mechanism undergoing evolutionary drift has been described for the adaptation to thermal stability in bacterial ribonuclease H1 (Hart et al. 2014). In that study, the selected high-level trait—thermostability—was reflected in the optimization of melting temperature values. The authors demonstrated that this trait was achieved through distinct thermodynamic mechanisms, each shaped by functional constraints over evolutionary time. A comparable phenomenon, albeit at a different biological level, is developmental system drift in evolutionary genetics and developmental biology, in which the genetic underpinnings of homologous traits diverge despite the conservation of the resulting phenotype (McColgan and DiFrisco 2024). Collectively, these observations support the notion that mechanistic drift may represent a general evolutionary principle that operates across different molecular and organizational levels.

In this context, an important question arises: how can even minor variations in initial conditions lead to distinct evolutionary outcomes? Specifically, it raises the question of whether evolutionary outcomes are inherently stochastic or influenced by a protein's initial state, inherent constraints, and constraints imposed by natural selection (Buda et al. 2023).

The occurrence of a mechanistic drift would require at least three conditions to be fulfilled. First, intense selective pressure imposes a functional constraint on the protein; second, the protein must exhibit mutational robustness in terms of function and stability; and third, there must be plasticity at the level of the underlying mechanisms.

In the lineage studied here, allosteric activation of PFK and GK by AMP emerges as a key adaptive trait. Accordingly, this trait is conserved along the evolutionary trajectory of bifunctional enzymes, although it is implemented through distinct physicochemical mechanisms, revealing a high degree of regulatory mechanistic plasticity. The inferred mechanistic drift is robust, being supported not only by ancestral reconstructions but also by multiple extant enzymes from different orders, and even by the two catalytic activities within the same protein. Collectively, these results indicate that the structural scaffold of this protein family is evolutionarily robust, preserving function while allowing substantial diversification of the underlying activation mechanisms under sequence variation.

Directed evolution studies have demonstrated that strong selection for a trait under neutral drift can promote protein evolvability (Bloom and Arnold 2009; Romero and Arnold 2009); variations that preserve function may also lead to the emergence or optimization of non-deleterious promiscuous activities as a side effect. This relies on mutational robustness, which refers to a protein's increased tolerance to mutations, thereby preserving stability and expression. This mutational robustness enables the protein to explore various sequences without compromising its stability and function, provided that the threshold is not exceeded (Bloom et al. 2007; Tokuriki and Tawfik 2009). In this context, some changes could modify, at the structural or dynamic level, the underlying mechanism of the selected phenomenon.

Traits whose underlying mechanisms depend on global protein properties, such as allosteric transitions or overall stability, are expected to exhibit greater mechanistic plasticity while preserving higher-level functional outcomes, compared with traits governed primarily by localized features, such as active-site catalysis. In some cases, only a small number of amino acid substitutions may be sufficient to alter the underlying mechanism of a protein. In others, however, mechanistic changes may not be readily attributed to specific substitutions but instead arise from shifts in global protein properties, such as dynamics (Campitelli et al. 2025).

In this work, we explored the evolution of an allosteric mechanism within the natural lineage of an enzyme family using ancestral protein reconstruction. This vertical approach highlights the power of evolutionary inference and has led us to propose the concept of mechanistic drift, a concept we anticipate will extend to other systems, thereby enriching current frameworks for understanding the landscape of molecular evolution.

Materials and methods

Ancestral sequence reconstruction

The phylogeny scheme shown in Fig. 1f and all the ancestral sequences were originally published by our group in 2017 (Castro-Fernandez 2017a). In that article, a comprehensive phylogeny of ADP-dependent sugar kinases was constructed, and ASR was used to study the evolution of substrate specificity. Here, we summarize the methodology used to infer ancestral sequences in this study.

Protein sequences from ADP-dependent sugar kinases were obtained with PSI-BLAST on the non-redundant protein sequence database (nr), and accession codes are available in the 2017 JBC article (Table S5). Multiple sequence alignment was performed using Promals3D (Pei et al. 2008), applying 3D and secondary structure constraints.

The original tree was inferred from protein sequences using Bayesian inference with MrBayes version 3.1.2, using the CpRev+I+G model (Ronquist and Huelsenbeck 2003). For comparison, a maximum-likelihood phylogeny was inferred from the protein sequences using PhyML 3.0 with the same CpRev+I+G model (Castro-Fernandez 2017a). Additionally, protein sequences were back-translated into DNA using the RevTrans server, and a third phylogeny was generated by Bayesian inference using the GTR+I+G model, which was selected with jModelTest (Posada 2008).

All trees presented the same overall topology. Relevant nodes for ASR were strongly supported by posterior probabilities and aLRT SH-like branch support in the Bayesian inference and maximum likelihood phylogenies, respectively (Castro-Fernandez 2017a). Ancestral sequences were inferred using three different methods: (i) a hierarchical Bayesian approach implemented in MrBayes 3.1.2 using gene sequences, (ii) Bayesian inference in MrBayes 3.1.2 using protein sequences, and (iii) maximum likelihood (empirical Bayes) inference performed with protein sequences with PAML 4.4. The models and parameters used were the same as those applied for phylogenetic inference. The protein sequences for the ancestors inferred by the hierarchical Bayesian approach using gene sequences were experimentally characterized (Huelsenbeck and Bollback 2001; Castro-Fernandez 2017a).

Expression and purification of recombinant enzymes

All ancestral and extant protein gene sequences were codon-optimized for Escherichia coli expression and cloned into a pET-TEV vector (pET-28b modified), which includes a 6xHis tag at the N-terminus and antibiotic resistance.

BL21 E. coli cells were transformed with the vector of interest, and protein expression was induced at an OD⁶⁰⁰ of approximately 0.6 using 1.0 mM IPTG overnight at 30 °C. Cells were harvested by centrifugation (8,000 × g for 15 min at 4 °C), resuspended in binding buffer (50 mM Tris–HCl, pH 7.8, 500 mM NaCl, 20 mM imidazole, 5 mM MgCl₂, and 5 mM β-mercaptoethanol), and disrupted by sonication (12 pulses of 20 s at 40% amplitude with 60 s stops). After centrifugation (18,000 × g for 30 min at 4 °C), the supernatant was loaded onto a HisTrap column (Ni²⁺-Sepharose, 5 mL, GE Healthcare) pre-equilibrated with binding buffer. The proteins were eluted with a linear gradient of 20 to 500 mM imidazole using an ÄKTA system (GE Healthcare), and fractions with enzyme activity were pooled. Enzyme purity was analyzed by SDS-PAGE stained with Coomassie blue.

Reagent concentration titrations

Glucose concentration was determined by measuring the refractive index (Lide 1990) and enzymatic titration using ADP-GK from T. litoralis. Fructose-6-phosphate concentration was determined by enzymatic titration using ADP-PFK assay from PhPFK. ADP was quantified by enzymatic titration using ADP-GK from T. litoralis. The concentration of AMP was measured by absorbance at 259 nm, using a molar extinction coefficient of 15.4 mM⁻¹ cm⁻¹. Protein concentration was measured using the Bradford Bio-Rad protein assay with bovine serum albumin as the standard.

AMP is a common contaminant in ADP stocks; therefore, extra care was taken in preparing ADP to prevent hydrolysis. The ADP stock was dissolved in 50 mM Tris–HCl buffer at pH 9.0, immediately neutralized with NaOH after dissolution, and kept cold on ice. The final purity of ADP solutions and the proportion of AMP contamination were assessed by anion-exchange chromatography (Mono Q 5/10 column, Pharmacia, GE Healthcare) coupled to an HPLC system (Waters 1525). ADP samples were loaded and eluted using a linear gradient from 0 to 1 M NaCl, and peaks were detected by absorbance at 259 nm. The AMP content in the ADP solutions was determined by calculating the areas under each nucleotide peak (AMP, ADP, and ATP) and normalizing the AMP area to the total peak area.

Enzymatic assays

GK activity was measured spectrophotometrically in a continuous assay by following glucose-6-P oxidation coupled with NAD⁺ reduction using glucose-6-P dehydrogenase from Leuconostoc mesenteroides as an auxiliary enzyme. The assays were performed in 50 mM HEPES-NaOH (pH 7.8), 0.5 mM NAD⁺, and 1 mM free Mg²⁺ with different glucose, MgADP, and AMP concentrations. The initial velocity was measured by absorbance of NAD⁺ reduction to NADH at 340 nm.

PFK activity was measured spectrophotometrically in a continuous assay coupling the production of F1,6bP to NADH oxidation using α-glycerophosphate dehydrogenase, triosephosphate isomerase, and aldolase (all from rabbit muscle, Sigma-Aldrich). The assays were performed in 50 mM PIPES-NaOH pH 6.5, 0.2 mM NADH, and 1 mM free Mg²⁺ with different F6P, MgADP, and AMP concentrations. The initial velocity was measured by absorbance of NADH oxidation to NAD⁺ at 340 nm.

Measurements at 25 °C were performed either on a temperature-controlled UV/Visible 96-well microplate reader spectrophotometer (Sinergy 2, BioTek, Winooski, VT, USA) or a photodiode array spectrophotometer (Hewlett Packard/Agilent 8453, Santa Clara, CA, USA) connected to a thermoregulated bath. Experiments were performed at 37 °C and 45 °C using either a Jasco V-730 double-beam spectrophotometer (JASCO Corporation, Tokyo, Japan) equipped with a PAC-743 water-cooled Peltier automatic cell changer, or a photodiode array spectrophotometer (Agilent 8453, Santa Clara, CA, USA).

All enzymatic assays were performed at a constant free Mg²⁺ concentration of 1 mM, calculated using a dissociation constant (K_d) of 676 µM, as described by Merino et al. (2012).

Kinetic data analysis

The Michaelis–Menten equation or a substrate inhibition model was fitted to each substrate saturation curve (at various fixed concentrations of AMP and co-substrate) using nonlinear regression. The kinetic parameters V_max and K_M were obtained for each substrate at each AMP concentration. Phenomenological equations were used to analyze these data and to dissect the activator and inhibitor components of AMP. Additionally, a global fit analysis of initial velocity data as a function of one substrate and AMP, at a fixed co-substrate concentration, was performed using the same phenomenological equations (see Kinetic Appendix). Experimental data were normalized to account for the amount of contaminant AMP present in the ADP solution.

Author contributions

S.M.H., G.V.-B., D.M., L.H-C., V.C.-F., and V.G. designed the research and experiments; S.M.H., G.V.-B. L.H-C., and D.M., performed experiments such as purification of proteins and kinetics assay and performed data analysis; G.V.-B. developed and applied the kinetic models; S.M.H., G.V.-B., D.M., and V.G. wrote the original manuscript draft; V.G. and V.C.-F. critically reviewed the draft and made valuable intellectual contributions. S.M.H. and V.G. Reviewed and edited the final manuscript; V.G. led and supervised the study and provided the means and resources to perform this research.

Supplementary material

Supplementary material is available at Molecular Biology and Evolution online.

Funding

This work was funded by grant Fondecyt 1231263 to V.G. from the Agencia Nacional de Investigación y Desarrollo ANID, and ANID Fellowship for PhD complementary funds 21220807 (S.M.H).

Data availability

Kinetic models and the underlying equations are available in the article and in its online supplementary material. The data underlying this article will be shared on reasonable request to the corresponding author.