Guangyu Wang
Network Basis for the Heat-Adapted Structural Thermostability of Bacterial Class II Fructose Bisphosphate Aldolase
The sufficient structural thermostability of a biological macromolecule is an overriding need for green nanoreactors and nanofactories to secure high activity. However, little is still known about what specific structural motif is responsible for it. Here, graph theory was employed to examine if the temperature-dependent noncovalent interactions and metal bridges, as identified in the structures of Escherichia coli class II fructose 1,6-bisphosphate aldolase, could shape a systematic fluidic grid-like mesh network with topological grids to regulate the structural thermostability of the wild-type construct and its evolved variants in each generation upon decyclization. The results indicated that the biggest grids may govern the temperature thresholds for their tertiary structural perturbations but without affecting the catalytic activities. Moreover, lower grid-based systematic thermal instability may facilitate structural thermostability, but a highly independent thermostable grid may still be required to serve as a critical anchor to secure the stereospecific thermoactivity. Its end melting temperature thresholds, together with the start ones of the biggest grids in the evolved variants, may confer high temperature sensitivity against thermal inactivation. Collectively, this computational study may have widespread significance in advancing our complete understanding and biotechnology of the thermoadaptive mechanism of the structural thermostability of a biological macromolecule.
Network Basis for the Heat-Adapted Structural Thermostability of Bacterial Class II Fructose Bisphosphate Aldolase

The sufficient structural thermostability of a biological macromolecule is an overriding need for green nanoreactors and nanofactories to secure high activity. However, little is still known about what specific structural motif is responsible for it. Here, graph theory was employed to examine if the temperature-dependent noncovalent interactions and metal bridges, as identified in the structures of Escherichia coli class II fructose 1,6-bisphosphate aldolase, could shape a systematic fluidic grid-like mesh network with topological grids to regulate the structural thermostability of the wild-type construct and its evolved variants in each generation upon decyclization. The results indicated that the biggest grids may govern the temperature thresholds for their tertiary structural perturbations but without affecting the catalytic activities. Moreover, lower grid-based systematic thermal instability may facilitate structural thermostability, but a highly independent thermostable grid may still be required to serve as a critical anchor to secure the stereospecific thermoactivity. Its end melting temperature thresholds, together with the start ones of the biggest grids in the evolved variants, may confer high temperature sensitivity against thermal inactivation. Collectively, this computational study may have widespread significance in advancing our complete understanding and biotechnology of the thermoadaptive mechanism of the structural thermostability of a biological macromolecule.

The activity of a biological macromolecule is based on its structural thermostability, which is generally controlled by a melting temperature threshold (Tm) at which the secondary structure starts unfolding. Nonetheless, the point mutation-based evolution can weaken the tertiary structural thermostability, causing thermal inactivation of the relevant activity. A well-known example is the deletion of F508 in the cystic fibrosis transmembrane conductance regulator (CFTR), which results in the most popular cystic fibrosis. On the other hand, the evolution by family DNA shuffling and random mutagenesis also allows the suppressor point mutation to enhance the structural thermostability in favor of the higher activity at elevated temperatures. A good example is Escherichia coli (E. coli) or Edwardsiella ictaluri (E. ictaluri) class II fructose 1,6-bisphosphate (FBP) aldolase, which employs a bimetallic-binding site to catalyze the reversible aldol condensation of dihydroxyacetone phosphate (DHAP) and glyceraldehyde-3-phosphate (G3P) to make FBP along the glycolytic pathway. Although both parental wild-type (WT) metal-dependent enzymes were rapidly inactivated at temperatures above 48 °C and had no stereospecific activity at 55 °C, variants from four generations between two shuffled bacterial enzymes can increase the systematic thermostability so that both the start and end temperature thresholds for the enzyme activity are raised by about 10 °C, but the catalytic function is not influenced at room temperature. Despite the available high-resolution crystal structures of this ligand-free E. coli class II FBP aldolase, the structural factors or motifs for the heat-adapted thermostability are still missing until a DNA hairpin thermal biosensor was reported in 2013. It employs the different loop sizes or H-bonds in the stem to tune the initial structural melting temperature (Tm) as a critical functional threshold (Tth) and thereafter to monitor a change in the environmental temperature with high sensitivity. Generally, the smaller hairpin size and the more H-bonds in the stem facilitate a higher Tm and Tth. Since both a single DNA hairpin and a grid in a grid-like noncovalent interaction mesh network in the enzyme share a common topological circle in general terms and the dissociation of this network grid by heat is analogous to DNA hairpin melting, it is exciting to hypothesize that WT class II E. coli FBP aldolase and its evolved variants exploit a fluidic system of temperature-dependent grid-like noncovalently interacting mesh networks with topological grids to keep the three-dimensional (3D) structures of this bacterial enzyme for the different thermoadaptive structural stabilities. In this in silico study, graph theory was used to examine the hypothesis by carefully decoding each grid in the respective grid-like noncovalently interacting mesh networks as identified in the crystal structures of WT class II E. coli FBP aldolase at 293 K. Two equations based on the findings of the DNA hairpin thermal detector were also developed to assess the melting temperature threshold (Tm) of the biggest grid and grid-based systematic thermal instability (Ti) so that the structural factors or motifs for the heat-adapted structural thermostability against thermal inactivation could be revealed and discussed. The melting temperature threshold of the DNA hairpin thermosensor above 34 °C can be raised by 20 °C with the H-bonded G–C base pairs doubled or the loop length diminished from 20 to 10 As. Thereby, a grid size (S) and grid size-governed equivalent H-bonds in the network grid may be important for the melting temperature threshold. In this in silico study, after the grid size was defined and calculated by graph theory as the minimal number of the total side chains of residues in the protein that did not engage in any noncovalent interactions and metal bridges in a grid, the biggest grid along the single polypeptide chain could then be screened and identified. For the biggest grid to carry out the single-rate-limiting-step melting reaction like DNA hairpins in favor of a change in the tertiary structures in the bacterial enzyme and its variants, the calculated melting temperature threshold (Tm) of the biggest grid should be comparable to the experimental threshold (Tth). On the other hand, in light of smaller loops or more H-bonds in the stem favoring the higher thermostability of a DNA hairpin, the systematic grid-like noncovalent interaction mesh network along the single polypeptide chain can reorganize along with the melting of the biggest grid. Accordingly, after the systemic thermal instability (Ti) was also defined and calculated as a ratio of the total grid sizes to the total noncovalent interactions and metal bridges along the same single polypeptide chain, this new parameter could render an important energetic reference for the heat-adapted structural thermostability. Following those two newly defined parameters, the traditional temperature coefficient or sensitivity (Q10, the ratio of the activities of an enzyme for 10 °C intervals) of the thermostability-dependent thermal inactivation was also analyzed and discussed. Taken as a whole, it was amazing to find that the systematic thermal instability of this bacterial enzyme was significantly decreased by the one-by-one suppressor mutation during several generations, along with the increased start and end melting temperature thresholds, which were matched theoretically and experimentally very well with high sensitivity. Of special note, an independent, stable, and thermoadaptive anchor grid is very important to secure a dynamic active site of proteins including enzymes. Therefore, this novel grid thermodynamic model may be useful to predict the melting temperature thresholds precisely for the thermoadaptive structural thermostability of a biological macromolecule once the accurate 3D structure is determined. The precise and successful prediction may, in turn, stimulate broad scientific and commercial applications.

In this computational study, the X-ray crystallographic structures of the class II E. coli fructose 1,6-bisphosphate aldolase dimer at 293 K in the presence of (NH4)2SO4 (PDB ID, 1DOS, model resolution = 1.6 Å) were analyzed with graph theory to uncover the roles of the biggest grids with minimal sizes and strengths in regulating the melting temperature threshold (Tm) parameters for their heat-adapted thermostability.

In order to secure results to be reproduced with high sensitivity, the same standard definition as described previously, together with structure visualization software, UCSF Chimera, was exploited to identify stereo- or regioselective interdomain diagonal and intradomain lateral noncovalent interactions in WT class II E. coli FBP aldolase at 293 K and to examine their potential roles in shaping topological grids with minimal sizes to govern the Tm for the changes in the tertiary structures of the WT enzyme and the evolved variants in each generation and related Ti values. Those noncovalent interactions included salt bridges, cation/CH/lone pair/π–π interactions, and H-bonds along the single polypeptide chain from D15 to F349.

Once noncovalent interactions were scanned along the single polypeptide chain from D15 to F349, a grid was then defined by graph theory as the smallest topological circle with a minimal size to stabilize a noncovalent interaction in it. The whole grids with minimal sizes were geometrically mapped for class II E. coli FBP aldolase at 293 K. A black line represented the initial amino acid sequence from D15 to F349. Each vertex (v) represented a single amino acid side chain involving a noncovalent interaction or a metal bridge along the single polypeptide chain and was marked with an arrow in different colors. Each edge represented a noncovalent interaction or a metal bridge between two vertices in a biochemical network and was marked in the same color for the same kind of interaction, otherwise in a different one. A topological grid was shaped between two vertices, i and j (vi and vj), if and only if there was a path from vi to vj and a return path from vj to vi. The grid size (S) was then defined as the minimal number of the total side chains of residues that did not engage in any noncovalent interaction or metal bridge in a grid. For a given grid-like biochemical reaction mesh network, the grid size between vi and vj was the total shortest return path distance from vertex j to i as the direct shortest path distance from vertex i to j was zero once there was a noncovalent interaction or a metal bridge between them. Here, the Floyd–Warshall algorithm was exploited to calculate the shortest return path between the two vertices i and j (vi and vj). For example, in the biochemical reaction network of Figure 1A, a direct path length from N62 and Q79 is zero because of an H-bond between them. However, another shortest return path existed from Q79 to N62 in this grid. Since the sum of residues, 63GGASFIAGKGVKSDVP78 (Figure 3), which did not involve any noncovalent interaction in the grid, was 16, the grid size was 16. Once each noncovalent interaction, together with metal bridges, was tracked by a controlled grid size and the uncommon sizes were marked in black, a grid with an x-residue size in monomer A or B was denoted as Gridx-A or Gridx-B, respectively. If the same size was involved in several grids, n was also, in turn, inserted as Gridx-n-A or Gridx-n-B. Taken together, the total noncovalent interactions and metal bridges and the total grid sizes along the single polypeptide chain were shown in black and blue circles beside the mesh network map for the calculation of the systematic thermal instability.

When a noncovalent interaction in the grid is broken at a temperature, that temperature is defined as a melting threshold (Tth). If both a DNA hairpin and the biggest grid melt in a similar manner and the melting is rate-limiting for the thermal inactivation, the Tth for the changes in the thermostability of proteins was calculated from the Tm of the biggest grid along the single polypeptide chain using the following equation, as described previouslywhere n is the total number of the H-bonds equivalent to noncovalent interactions in the biggest grid and Smax is the size of the biggest grid. In either state, the grid-based systemic thermal instability (Ti) along the single polypeptide chain was defined using the following equation, as described previouslywhere S is the total grid sizes along the single polypeptide chain of one subunit in a functional state and N is the total noncovalent interactions and metal bridges along the same single polypeptide chain of one subunit in the same functional state. The temperature coefficient (Q10) of the thermal inactivation of this bacterial enzyme was calculated using the following equation:where X1 and X2 are the relative activities obtained at temperatures T1 and T2 (measured in Kelvin), respectively.

Monomers A and B from the same primary sequence in the ligand-free WT class II E. coli FBP aldolase dimer are paired as twins. The dimeric interface had the H99-L84′, W293-Y328′, W296-W333′, and Y303-Y303′ swapping π-interactions. In each subunit, H110, E174, H226, and H264 formed common Zn2+ bridges, leading to the smallest grid with a zero-residue size. Similarly, H107, D109, E172, K284, and N286 are connected together via K+ to generate another smallest common grid with a zero-residue size. In addition, the following noncovalent interactions were shared by both monomers along the single polypeptide chain from D15 to F349 (Figure 1). First, three salt bridges were found between several charged pairs. They included K51-E346, D290-R344, and D329-R331 (Figure 1). Second, fifteen π-interactions were present between aromatic residues and nearby residues. For example, π-interacting pairs had P32-F349-V52, T39-H92, L46-Y100, F130-I167, Y204-E208, Y206-S210/H252, F222-F263, R242-Y280, H256-N257, L259-F261, Y302-N306, Y309-Y327, and K325-Y328 (Figure 1). Third, nineteen H-bonds were observed between a variety of hydrophilic residues. The H-bonding pairs included D15-R215, D16-K19, Q18-T170, K25-N260, N35-D288, E47-R335, Q59-K284, N62-Q79, H107-S140, T108-H141, D120-Y160, D124/E127-R163, D203-T207/K251, E208-K211, R242-D243, T270-E273, and N316-N324 (Figure 1). On the other hand, there were some different noncovalent interactions between amino acid side chains in the two subunits. For example, the Y247-K251 and Q313-Y328 H-bonds were present in monomer A but absent in monomer B. In contrast, a D288-Q292 H-bond in monomer B was not shown in monomer A (Figure 1). These differences brought about different total noncovalent interactions together with metal bridges and total grid sizes as 48 and 123 for monomer A and 47 and 128 for monomer B, respectively. Thus, the systematic thermal instability (Ti) values were 2.56 and 2.72 for monomers A and B of the WT construct, respectively (Tables 1 and 2). In addition, despite those differences, the grid size ranges were the same from 0 to 16 in monomers A and B (Figure 1).

In the first generation, the K211A mutation was found along with the deletion of A82 in the evolved variant 1-37D6 of class II E. coli FBP aldolase (Table 1).Figure 1 shows that the deletion of A82 did not affect any noncovalent interaction (Figure 1). However, the K211A mutation disrupted two grids. In monomer A, one was Grid2 with a 2-residue size via the shortest path from K211 to E208; the other was Grid12 with a 12-residue size via the shortest path from D15 to Q18, T170, E172, K284, Y280, R242, D243, Y247, K251, D203, Y204, E208, K211, and R215 and back to D15 (Figure 2). In monomer B, the broken Y247-K251 H-bond increased the grid size from 12 to 16 (Figure 2). When these grids were broken, the biggest Grid16-1A in monomer A and Grid16-2B in monomer B were still maintained (Figure 1). Both grids had a 16-residue size via the shortest path from N62 to Q79 and back to N62 (Figure 3). Therefore, the calculated start Tm values were 42 °C when two equivalent H-bonds sealed Grid16-1A and Grid16-2B (Figure 3 and Tables 1 and 2). This value was not affected by the K211A mutation, so the whole start melting temperature thresholds should be 42 °C (Tables 1 and 2). In consonance with this prediction, the measured start Tth value for thermal inactivation is about 43.0 °C (Tables 1 and 2). Of special note, the K211A mutation reduced the total noncovalent interactions and metal bridges to 46 and 45 and the total grid sizes to 109 and 110 residues for monomers A and B, respectively. Hence, the systematic thermal instability (Ti) values decreased to 2.37 and 2.44 for monomers A and B, respectively (Tables 1 and 2).

Following the K211A mutation, the Q79L mutation was observed in the evolved variant 1-44F2. Such a mutation disconnected the N62-Q79 H-bond and related Grid16-1A in monomer A and Grid16-2B in monomer B (Figure 3). In this case, both the biggest grids had a common 13-residue size via the shortest path from T39 to L46, Y100, and H92 and back to T39 (Figure 1). When the L46-Y100 and H92-T39 π-interactions sealed the common grid, the calculated start Tm was 48 °C (Tables 1 and 2). Thus, it was reasonable that the evolved variant 1-44F2 had a measured Tth 47.9 °C to start thermal inactivation (Tables 1 and 2). Once the N62-Q79 H-bond was disrupted, the total grid sizes and the total noncovalent interactions and metal bridges were further diminished to 93 and 45 for monomers A and 94 and 44 for monomer B, respectively (Figure 1 and Tables 1 and 2). In this regard, the systematic thermal instability (Ti) values were further lowered to 2.07 for monomer A and 2.14 for monomer B, respectively (Tables 1 and 2).

Based on the K211A and Q79L mutations in the first generation, V45 was further mutated to alanine in the evolved variant 2-15B2 during the second generation. When this mutation disrupted the L46-Y100 and H92-T39 π-interactions in Grid13-1A and Grid13-1B (Figure 4), the first biggest Grid13-2A in monomer A and Grid13-2B in monomer B had 2.5 equivalent H-bonds to produce a start Tm value as 53 °C (Figure 5 and Tables 1 and 2). Meanwhile, the second biggest Grid11-A in monomer A and Grid10-B in monomer B with 2.0 equivalent H-bonds had start Tm values of 52 and 54 °C, respectively (Figure 5 and Tables 1 and 2). Hence, in direct line with these predicted values, the measured start Tth value was 52.8 °C (Tables 1 and 2). On the other hand, along with the broken L46-Y100 and H92-T39 π-interactions in Grid13-1A and Grid13-1B, the total grid sizes and the total noncovalent interactions and metal bridges were further decreased to 80 and 43 for monomer A and 81 and 42 for monomer B, respectively (Figure 1 and Tables 1 and 2). Thus, the systematic thermal instability (Ti) values further declined to 1.86 for monomer A and 1.93 for monomer B (Tables 1 and 2).

Grid13-2A in monomer A and Grid13-2B had a common 13-residue size via the shortest path from E47 to K51, E346, and R335 and back to E47. Meanwhile, Grid11-A in monomer A had an 11-residue size via the shortest path from K51 to Q59, K284, N286, D290, R344, and E346 and back to K51; Grid10-B in monomer B had a 10-residue size via the similar shortest path from K51 to E346 but with a D288-Q292 H-bond to shorten the return path to 10 (Figure 5). Because these grids involved K347, the key mutation K347R in the evolved variants 3-4C10, 4-4C10, and 4-43D6 during the third and fourth generations may interact with nearby E346 and thus disrupt both strong E47-R335 and Q59-K284 H-bonds in these grids. In this case, Grid9-1A in monomer A and Grid9-1B in monomer B became sensitive to elevated temperature (Figure 6). As both had a 9-residue size via the shortest path from K25 to Q18, T170, E172, D109, H110, H264, F261, L259, and N260 and back to K25 to control two H-bonds between Q18 and T170 and between K25 and N260, the calculated start Tm was about 56 °C, which was close to the measured start Tth values 54.9 °C for thermal inactivation in the variant 4-4C10 and 56.8 °C in the variants 3-4C10 and 4-43D6 (Figure 6 and Tables 1 and 2). Following the broken E47-R335 H-bonds in Grid13-3A and Grid13-2B and the disrupted Q59-K284 H-bonds in Grid11-A and Grid10-B, the total grid sizes and the total noncovalent interactions and metal bridges were further decreased to 56 and 41 for monomer A and 58 and 40 for monomer B, respectively. Thereby, the systematic thermal instability (Ti) values were inherently weakened to 1.37 and 1.45 for monomers A and B, respectively (Tables 1 and 2).

Once the Q18-T170 and K25-N260 H-bonds in Grid9-1A and Grid9-1B were broken above the predicted 56 °C, Grid9-2A and Grid9-2B were, in turn, sensitive to higher temperatures. They also exhibited a 9-residue size via the shortest path from D15 to Q18, T170, E172, D109, H110, H264, F263, F222, and R215 and back to D15 to control the Q18-T170 and D15-R215 H-bonds (Figure 6). However, D15 also formed an additional salt bridge with R215. Therefore, once the total 3.0 equivalent H-bonds sealed the grids, a common calculated Tm was about 66 °C, which was near the experimental end threshold of 66.9 °C for thermal inactivation in both variants 4-4C10 and 4-43D6 (Figure 6 and Tables 1 and 3). Thus, Grid9-2A and Grid9-2B may serve as basic anchors to secure the catalytic activity of the enzyme by stabilizing the metal-dependent enzyme structure. Once this anchor is dissociated, the systematic thermal instability (Ti), even if may be still low, would not make sense for the heat-adapted structural thermostability against thermal inactivation.

Heat- or cold-adapted structural thermostability of a biological macromolecule is very important not only for life to keep functionally active over a wide range of environmental temperatures in each organism but also for durable industrial biocatalysts and multitasking synthetic chemistry. However, not all of the macromolecules including proteins have had their tertiary structures captured at more than one temperature, and hence it is still a challenge to predict the effect of temperature on their conformations without any priori information except for the high-resolution 3D structure. Recently, a graph theory-based grid thermodynamic model has been successfully employed to predict the melting temperature thresholds for the changes in the specific tertiary and secondary structures and in the specific functional activity of class I aldolase B. In this case study, graph theory was further used as a structure-based ab initio approach independently to investigate what structural factors control the heat-adapted structural thermostability of two model glycolytic enzymes, E coli and E. ictaluri class II FBP aldolases, and the evolved variants in each generation against thermal inactivation. The results demonstrated that the melting temperature threshold of the biggest grid in the grid-like noncovalently interacting mesh network along the single polypeptide chain may determine a start threshold for a change in the structural thermostability, while the melting temperature threshold of the basic anchor grid in the same network system may control the end threshold for the thermostability during thermal inactivation. Although the systematic thermal instability (Ti) declined with the increased start and end melting temperature thresholds, the combined thresholds with a small interval in each generation still maintained a high-temperature sensitivity (Q10) for the thermal inactivation. For WT E coli and E. ictaluri class II FBP aldolases, the biggest Grid16-1B and Grid16-2B in monomer B had a common calculated start Tm as 42 °C (Figures 1–3 and Tables 1 and 2), which was consistent with the measured start Tth 43 °C for those two WT constructs (Tables 1 and 2). When the R242-Y280 π-interaction in Grid16-1B and N62-Q79 H-bonds in Grid16-2B and Grid16-1A were broken above 42 °C, the basic anchor Grid9-2A in monomer A and Grid9-2B in monomer B may have 2.0 equivalent H-bonds to seal both grids so that they would have a common calculated 56 °C as an end Tm. This value was in agreement with the measured end Tth 55.0 °C (Figure 6 and Tables 1–3). For the evolved variant 1-37D6 in the first generation, the biggest Grid16-1A in monomer A and Grid16-2B in monomer B had the predicted start Tm 42 °C (Figure 3 and Tables 1 and 2), which was similar to the experimental start Tth 43 °C (Tables 1 and 2). When N62-Q79 H-bonds were disrupted above 43 °C, the basic anchor Grid9-2A and Grid9-2B may still have 2.0 equivalent H-bonds for a predicted 56 °C as an end Tm, which was also near the measured end Tth 57.9 °C (Figure 6 and Tables 1–3). For the evolved variant 1-44F2 in the first generation, the calculated start Tm of both Grid13-1A and Grid13-1B was 48 °C (Figure 4 and Tables 1 and 2), which was near the measured start Tth 47.9 °C (Tables 1 and 2). With the L46-Y100 and H92-T39 π-interactions in Grid13-1A and Grid13-1B disconnected, the basic anchor Grid9-2A and Grid9-2B may still allow at least 2 equivalent H-bonds to have a predicted end Tm 56 °C, which was similar to the measured Tth 58.8 °C (Figure 6 and Tables 1–3). For the evolved variant 2-15B2 in the second generation, the biggest Grid11-A and Grid13-2A in monomer A generated a calculated start Tm range from 52 to 53 °C (Figure 5 and Tables 1 and 2). On the other hand, the biggest Grid10-B and Grid13-2B in monomer B created a calculated start Tm range from 53 to 54 °C (Figure 5 and Tables 1 and 2). Therefore, the average start Tm was about 53 °C (Figure 5 and Tables 1 and 2), which was also in accordance with the measured Tth 52.8 °C (Tables 1 and 2). Upon the disruption of the E47-R335 H-bonds in Grid13-2A and Grid13-2B and the Q59-K284 H-bonds in Grid11-A and Grid10-B above 53 °C, the number of the equivalent H-bonds in the basic anchors Grid9-2A and Grid9-2B may also increase to 2.5 so that the calculated end Tm was about 61 °C (Tables 1–3), which approximated the measured end Tth 61.9 °C (Figure 6 and Tables 1–3). For other evolved variants 3-4C10, 4-4C10, and 4-43D6 during the third and fourth generations, the calculated start common Tm of Grid9-1A and Grid9-1B was about 56 °C, which was similar to the measured start Tth from 54.9 to 56.8 °C. When the K25-N260 H-bond was disconnected, the remaining Grid9-2A and Grid9-2B may still have at least 2.5 equivalent H-bonds so that the calculated end Tm was about 61 °C, which was comparable to the end Tth 63 °C for the variant 3-4C10 (Figure 6 and Tables 1–3). However, for 4-4C10 and 4-43D6, the equivalent H-bonds in Grid9-2A and Grid9-2B may be increased up to 3 so that the calculated end Tth would be about 66 °C, which was in line with the measured end Tth 66.9 °C (Figure 6 and Tables 1–3). Because rotamer simulations between Q16 and T170 and between D15 and R215 demonstrated that the maximal equivalent H-bonds were 3.5, the maximal end Tth limit may be 71 °C (Figure 6). When K71 was reinstated in the presence of the K211V mutation in variant 4-4C10, the biggest Grid13-1A and Grid13-1B with a 13-residue size via the shortest path from T39 to L46, Y100, and H92 and back to T39 may allow a lower calculated start Tm 48 °C (Figure 4 and Tables 1 and 2), which was near the calculated start Tm of 48 °C in the evolved variant 1-44F2 (Tables 1 and 2). Therefore, that may be why the measured T1/2 for thermal inactivation was back to 51.4 °C. It is interesting that the systematic thermal instability (Ti) of the bacterial metalloenzyme decreased from 2.56 to 1.37 in monomer A and from 2.72 to 1.45 in monomer B during four generations (Tables 1 and 2). This decreasing trend was consistent with the increases in the calculated start Tm values from 42 to 56 °C and the measured start Tth values from 43 to 56.8 °C (Tables 1 and 2), and the calculated end Tm values from 56 to 66 °C and the measured end Tth values from 55.0 to 66.9 °C (Tables 1–3). Further studies are necessary to define the temperature range of the rational and precise design along with the prediction of thermoadaptive enzyme activity on the grounds of graph theory and the grid thermodynamic model. The enzymes include but are not limited to other class II fructose 1,6-bisphosphate aldolases. Finally, the thermal inactivation curves of purified WT E. coli and E. ictaluri class II FBP aldolases and most of the evolved variants exhibited a high-temperature sensitivity (Q10) for thermal inactivation in a range from −47.0 to −92.1. Such a high Q10 may be achieved by the small intervals between start and end melting temperature thresholds (Tables 1–3). For example, when the relative activity of WT class II E. coli FBP aldolase declined from 0.9 to 0.1, the corresponding temperature increased by 5 °C. Therefore, Q10 was −81. Of special note, when the H-bonds Grid9-1A and Grid9-1B and Grid9-2A and Grid9-2B were broken from K25-N260 to shared Q18-T170 and then to D15-R215, for the most stable variant 4-43D6, Q10 was about −88.6. Therefore, an independent and stable basic anchor is the overriding need to secure a dynamic active site in proteins including enzymes against thermal inactivation. Generally speaking, molecular dynamics simulations can link the global thermal movements from the corresponding starting structure at room temperature to catalysis and the unfolding region so as to illuminate the thermoadaptive mechanisms of enzymes. However, in this special computational study, two groups of strong metal bridges coupled the stable basic anchor Grid9-2A or Grid9-2B with the prior biggest grids from Grid16-1A and Grid16-2B to Grid11-A and Grid10-B together to secure the long-term local structural stability against thermal inactivation (Figures 1–6). Therefore, those biggest grids could function as a series of heat fuses to be melted one by one independently upon elevated temperatures but without a global conformational change to affect the catalytic activity of the enzyme. Therefore, the thermodynamic molecular simulations may be unnecessary.

This computational study has mechanistically related the crystallographic static conformation to the biochemical findings on detailed atomic scales, conferring a creative and insightful bioinformatics solution. With regard to the start and end melting temperature thresholds of the bacterial class II FBP aldolases and the evolved variants during generations, the successful theoretical and experimental comparisons demonstrated that once the systematic fluidic grid-like mesh network of noncovalent interactions and metal bridges are available, graph theory can be used to establish a powerful grid thermodynamic model for the rational and precise prediction and design of durable thermoadaptive structural stability of proteins including enzymes, thereby meeting the increasing needs for promising robust biocatalytic applications and stereo-, regio-, or enantioselective synthetic chemistry in biotechnology, food, and pharmaceutical industries.