Molecular dynamics simulation of Escherichia coli dihydrofolate reductase and its protein fragments: Relative stabilities in experiment and simulations

Abstract

We have carried out molecular dynamics simulations of the native dihydrofolate reductase from Escherichia coli and several of its folded protein fragments at standard temperature. The simulations have shown fragments 1–36, 37–88, and 89–159 to be unstable, with a C_αRMSD (C_α root mean squared deviation) >5 Å after 3.0 nsec of simulation. The unfolding of fragment 1–36 was immediate, whereas fragments 37–88 and 89–159 gradually unfolded because of the presence of the β-sheet core structure. In the absence of residues 1–36, the two distinct domains comprising fragment 39–159 associated with each other, resulting in a stable conformation. This conformation retained most of its native structural elements. We have further simulated fragments derived from computational protein cutting. These were also found to be unstable, with the exception of fragment 104–159. In the absence of α₄, the loose loop region of residues 120–127 exhibited a β-strand-like behavior, associating itself with the β-sheet core of the protein fragment. The current study suggests that the folding of dihydrofolate reductase involves cooperative folding of distinct domains which otherwise would have been unstable as independent folded units in solution. Finally, the critical role of residues 1–36 in allowing the two distinct domains of fragment 104–159 to fold into the final native conformation is discussed.

Proteins play an important biological role in all living organisms. Understanding protein folding is a key element in addressing a structure–function correlation in biological molecules. Being able to predict how a given protein sequence folds into a three-dimensional structure is expected to have a significant impact on protein structure prediction and protein design.

One of the most interesting observations in structural biology today is the rapid folding rate of a protein sequence into its native conformation. The vast number of potential conformations that need to be searched by any given protein sequence to find its native conformation has given rise to the so-called ``Levinthal paradox'' (Levinthal 1968). The paradox describes the protein as ``unfoldable'' within any reasonable experimental time frame. However, recent experimental (Onuchic et al. 1995), statistic mechanic (Shaknovich and Gutin 1989; Karplus and Shaknovich 1992), and lattice model (Dill et al. 1995) studies have clarified that such a problem is overcome by the fact that the conformational search is nonrandom and that protein folding is an energetically biased process that favors the structure with the lowest free energy of formation, that is, the native state.

Recent hierarchical folding models further state that the folding process initiates locally, and that the formation of the native local structures precedes the formation of tertiary interactions (Baldwin and Rose 1999a,b). A basic unit from which a fold is constructed, that is, a hydrophobic folding unit (HFU), may be viewed as an outcome of a combinatorial assembly of microdomains, foldons, or building block folding elements (Karplus and Weaver 1994; Panchenko et al. 1996, 1997; Tsai et al. 1999a, 2000). The HFUs in turn associate to create intramolecular domains, which subsequently assemble to build either an intramolecular multidomain protein fold or an intermolecular quaternary structure. The building block itself is defined as a highly populated, contiguous fragment in a given protein structure. It may be composed of a single secondary structure element or a contiguous fragment consisting of interacting structural elements, such as observed in supersecondary structures. On the other hand, an HFU has been defined as an independent, compact, thermodynamically stable folding unit with a buried hydrophobic core (Tsai et al. 1999a; Kumar et al. 2000). If we were to splice out the building block from the native protein structure, the most populated conformation of the resulting peptide in solution would very likely be similar to that of the conformation of the building block when it is embedded in the native protein. Such fragments should be relatively more stable than fragments generated at random. Finally, the population of these building block fragments should be greatly enhanced through their assembly into higher-order native protein structure.

Dihydrofolate reductase (DHFR) is a 159-amino-acid, monomeric enzyme that catalyzes the reduction of 7,8-dihydrofolate to 5,6,7,8-tetrahydrofolate using nicotinamide adenine dinucleotide phosphate (NADPH) as the reducing factor. DHFR has been the subject of numerous folding and unfolding studies (Touchette et al. 1986; Jennings et al. 1993; Frieden 1990; Kuwajima et al. 1991). The unfolding of DHFR by urea can be well described by a two-state model and has been postulated as having an either multiple or sequential pathways with kinetically observable folding intermediates, whose structures are still unknown. In addition, of the eight DHFR protein fragments previously studied by Gegg et al. (1997), only the fragment that consists of residues 37–159 is observed to be stable, with significant secondary and tertiary structure.

Visual inspection of the X-ray structure identifies three distinct building block elements, two of which make up the experimentally observed stable, though non-native, 37–159 fragment. The third element, the fragment consisting of residues 1–36, is located in the middle of the β-sheet core of the DHFR structure, mediating the interactions of the other two folding elements in this fragment. Such a folding element fragment may be crucial in facilitating correct association of the other elements into the final native conformation. If this building block fragment is missing, folding may be hindered, leading to misassociation of the other two, sequentially connected building block elements. Here we study the relative stabilities of the DHFR protein fragments, by carrying out molecular dynamics simulations on fragments generated by experiments, and via computations (Fig. 1 ▶). Because fragment 37–159 has been observed to be stable in non-native conformation, we simulate this fragment and compare its conformation with those of the individual building block fragments from which it is composed. We find that the observed stable conformation retains the native conformations of the two building blocks, however, they mis-associate, leading to the non-native contacts observed experimentally.

Fig. 1.

Structure of E. coli dihydrofolate reductase (DHFR) taken from the Protein Data Bank (7DFR) and its corresponding double mutant AS-7DFR, where Cys 85 and Cys 152 are replaced by Ala and Ser, respectively (in CPK rendering). The molecular dissection is based on the Gegg et al. (1997) study and on the Tsai et al. (2000) dissection algorithm (the cutting result can be viewed at our web site at http://protein3d.ncifcrf.gov/tsai/anatomy.html. Six of the seven folded protein fragments used in the study are shown in red, green, and yellow in the two structures. The last fragment, AS-7DFR:37–159, consists of both the yellow and green pieces in the AS-7DFR structure.

Results

Protein

The X-ray crystallographic structure of dihydrofolate reductase from E. coli (7DFR) was solved by Bystroff et al. (1990) in complex with folate and NADP⁺. The structure of this enzyme consists of four α-helices and an eight-stranded β-sheet that forms the core of the protein structure. The structure consists of an adenine binding domain (ABD) between residues 38–88. The notation of the secondary structure used in this study is based on the Protein Data Bank (PDB; Bernstein et al. 1977) assignment and is as follows: α₁: 24–35; α₂: 43–50; α₃: 77–86; α₄: 96–104; β₁: 73–75; β₂: 58–63; β₃: 39–43; β₄: 91–95; β₅: 1–8; β₆: 108–116; β₇: 150–159; β₈: 132–141.

For the experimental cleavage, we simulate the fragments obtained in the study by Gegg et al. (1997). For the computational cutting (Tsai et al. 2000), a list of the local minima found by cutting the protein into building blocks are given in Table 1. The table shows the scores of each of the building blocks as a function of compactness, hydrophobicity, and isolatedness. For a fragment to be also considered as a building block, the fragment must have the highest score compared with its cousin fragments (fragments with <7% deviation in size or in position in the protein sequence). All possible combinations of these building blocks, which can form the final native structure, are considered. The protein is cut into building blocks according to the combination involving building blocks with the highest average scores. This latter part of the procedure is applied recursively to each of the building blocks at each level of the cutting until no further cutting is possible. For DHFR, the algorithm has identified three levels of cutting (see Fig. 2 ▶). The first level constitutes the entire native DHFR, as the structure does not contain any extended loops or noncompact structure. The second level of cutting identified three building blocks consisting of residues 5–35, 35–103, and 104–159 with scores of −4.6, 4.02, and −1.16, respectively. Here building block 35–103 is an HFU, whereas fragments 5–35 and 104–159 are considered building blocks by our definition. The final level of cutting identified three additional building blocks making up fragment 35–103. These building blocks consist of residues 31–63, 59–84, and 85–103 with the scores of −1.13, 0.47, and −6.64, respectively. For the purpose of comparison with the stabilities of the experimentally cut fragments, we use the second level of dissection.

Table 1.

Local minima found by the protein dissection into building

#	Size	Compactness	Hydrophobicity	Isolatedness	Score	Residue range
1	159	1.604	0.79	0.00	4.09	1–159
2	69	1.466	0.74	0.12	4.02	35–103
3	73	1.507	0.74	0.10	3.88	31–103
4	60	1.456	0.72	0.14	3.35	35–94
5	64	1.497	0.72	0.12	3.29	31–94
6	49	1.462	0.70	0.15	2.85	37–85
7	128	1.576	0.77	0.09	2.85	1–128
8	55	1.495	0.70	0.15	2.41	31–85
9	86	1.637	0.71	0.16	0.58	18–103
10	102	1.660	0.72	0.16	0.48	2–103
11	26	1.501	0.63	0.19	0.47	59–84
12	90	1.654	0.71	0.16	0.35	14–103
13	130	1.805	0.74	0.10	0.05	30–159
14	77	1.628	0.69	0.18	0.04	18–94
15	28	1.607	0.63	0.20	−0.69	132–159
16	96	1.770	0.71	0.17	−0.81	31–126
17	68	1.625	0.66	0.21	−0.81	18–85
18	65	1.716	0.67	0.20	−0.90	95–159
19	32	1.618	0.62	0.19	−0.93	128–159
20	51	1.681	0.65	0.21	−1.10	109–159
21	33	1.492	0.63	0.30	−1.13	31–63
22	56	1.695	0.65	0.20	−1.16	104–159
23	46	1.646	0.64	0.23	−1.25	58–103
24	81	1.722	0.67	0.22	−2.13	5–85
25	83	1.828	0.67	0.20	−2.36	77–159
26	102	1.926	0.68	0.17	−2.81	58–159
27	107	1.946	0.68	0.18	−3.52	53–159
28	29	1.628	0.58	0.32	−3.63	75–103
29	46	1.602	0.60	0.33	−3.63	18–63
30	59	1.690	0.62	0.33	−4.17	5–63
31	75	1.916	0.64	0.25	−4.49	59–133
32	71	1.893	0.63	0.26	−4.58	58–128
33	31	1.648	0.56	0.33	−4.60	5–35
34	81	1.931	0.63	0.25	−4.99	53–133

The minima are determined by first evaluating the scores of all possible protein fragments using Equation 1. Fragments with the highest scores compared to their ``cousin'' fragments (fragments with less than 7% deviation in size or in position in the protein sequence) are classified as local minima on the score surface and are considered as stable building blocks.

Fig. 2.

Anatomy tree of the protein dissection into building block algorithm for dihydrofolate reductase (DHFR). The tree shows three levels of the protein cutting. Because the structure is relatively compact and stable, with no extended disordered regions, the first level consists of the entire fragment (residues 1–159). The second level of cutting divides the protein into three distinct building blocks, consisting of residues 5–35, 35–103, and 104–159. The final level of cutting shows that building block 35–103 is composed of three smaller overlapping building blocks, containing residues 31–63, 59–84, and 85–103. The cores evaluated by the scoring function are shown next to the fragment range.

Native DHFR

The C_αRMSD between the conformers generated in the simulations and the respective native conformations as a function of time are given in Figures 3 ▶ (a-c). Our control simulation of DHFR is shown in black in the figures. In this control simulation the C_αRMSD of the native DHFR increases rapidly in the first 100 psec to an average value of 2 Å, followed by a gradual rise of the C_αRMSD to about 3 Å in the next 400 psec. The C_αRMSD of the entire DHFR became nearly constant for the remaining 2.5 nsec at about 3.2 Å. The C_αRMSD in the current simulations is comparatively larger than that in other explicit solvent simulation of stable proteins (Caflisch and Karplus 1995; Li and Daggett 1996; J. Tsai et al. 1999; Wang et al. 1999). Nevertheless, the profile of the C_αRMSD as a function of time is typical, similar to profiles obtained for stable protein structures. Simulation of the staphylococcal protein A E-domain using the same simulation procedure for 3.0 nsec also yielded similar C_αRMSD values (Y. Sham, unpubl.) Recent simulation of DHFR using an implicit solvent model has also reported a similar C_αRMSD around 3.4 Å (Dams et al. 2000). The calculated C_αRMSD of the eight-stranded β-core of the DHFR was 2.3 Å, showing that the core of the β-structure is relatively stable during the course of the simulation. The X-ray structure of DHFR and the structure of DHFR at the end of the 3-nsec simulation are shown in Figure 4 ▶. In the absence of the substrates several disordered regions can be observed. These include the expanded loose coil region formed between residues 63–71 and the disordered α₁ and β₈.

Fig. 3.

C_αRMSD (C_α root mean squared deviation) of the protein fragments and of the native dihydrofolate reductase (DHFR) as a function of simulation time. Fragments 1–36, 89–159, and 37–88, generated based on Gegg et al. (1997) study, are shown in a; fragments 5–35, 35–103, and 104–159, based on Tsai et al. (2000) dissection algorithm are shown in b. Fragment 37–159 is shown in c. Each fragment is denoted by its residual range; native DHFR is denoted as DHFR in the figure. As can be seen, fragments 1–36 and 5–35 are very unstable and undergo immediate unfolding within <1 nsec of simulation time. Fragments 37–88, 89–159, and 35–103 are found to be unstable and undergo gradual unfolding. The C_αRMSD of fragment 104–159 (b) and 37–159 (c) converges to around 4 Å after 1 nsec of simulation, showing that both fragments attained an alternate stable conformation. Such conformation was found to consist of newly formed non-native contacts based on our contact definition (see Materials and Methods).

Fig. 4.

X-ray structure (a) and the structure of dihydrofolate reductase (DHFR) (b) at the end of 3.0-nsec simulation. In the absence of its substrates, certain relatively mobile regions can be observed including the loop region of residues 63–71, α₁, and β₈.

Fragments 1–36 and 5–35

Simulations of fragments 1–36 and 5–35 show that both structures are highly unstable. The computational cutting resulted in a shortened α₁ and β₅. Both protein fragments yield large C_αRMSD values with large C_αRMSD fluctuations over the course of the simulation. The simulation of these two fragments shows that both structures undergo rapid unfolding (see Fig. 5a,b ▶) The unfolding of fragment 1–36 begins with the random coiling of β₅, collapsing itself into the random coil region of residues 9–23. Once isolated, the α₁ region slowly unwinds. At the end of the 3-nsec simulation, a β hairpin-like structure is observed to form between residues 15–20, extended away from the partially unfolded α₁ (residues 25–31). The native turn formed by residues 9–12 is conserved whereas the native turn 16–19 is broken during the simulation. On the other hand, the unfolding of the shortened α₁ and β₅ of fragment 5–35 occur simultaneously. The unfolding of β₅ also collapsed into the random coil region of residues 9–23, whereas the α₁ undergoes only partial unfolding. The turn region of 9–12 in the simulation of both fragments is conserved. The final structure of fragment 5–35 is observed to be more compact than that of fragment 1–36, resulting in a significantly lower C_αRMSD of 4.5 Å (see Fig. 5a,b ▶).

Fig. 5.

Snapshots of the MD simulation for (a) fragments 1–36, 37–88, and 89–159 and (b) fragments 5–35, 35–103, and 104–159 at 0.5-nsec time intervals.

Evaluation of the C_αRMSD of the individual secondary structural components of both structures (Fig. 6a,b ▶) indicates that the sequence undergoes a significant secondary structural loss. This observed instability appears to be consistent with the overall make-up of the fragments, as both consist of >60% nonpolar residues and are found deeply buried within the hydrophobic core of the DHFR structure. Because of the cutting, >60% of the total exposed surface area is hydrophobic. In addition, two key regions in contact in the native structure interact: first, via the hydrogen bonding of β₅ with the backbone of β₄ and β₆ of the β-sheet core of DHFR; and second, the nonpolar sidechain of the random coil region (residues 9–24) interaction with the loose loop region of residues 110–130. Only two stabilizing contacts are observed between α₁ and β₅ involving the nonpolar sidechains of residues I5 to W30 and I5 to F31 in the two fragments. As such, it is understandable why fragments 1–36 and 5–35 are so unstable as independent fragments in solution.

Fig. 6.

C_αRMSDs (C_α root mean squared deviations) of the secondary structure elements for each of the fragments as a function of simulation time. The C_αRMSD of α₁, α₂, α₃, α₄, and the β-core structure of the fragments are shown in red, green, blue, magenta, and yellow, respectively. The C_αRMSD of the fragment as a whole is shown in black. Stable β-sheet and α-helices are observed with a C_αRMSD of <1 Å.

This is consistent with our scoring function, scoring fragment 5–35 at −4.60, the least stable of the three building blocks in our second level of cutting. The percentage native contact evaluated for fragments 1–36 and 5–35 are 37.1% and 54.5% respectively.

Fragments 37–88 and 35–103

Simulations of fragments 37–88 (the experimental cutting) and 35–103 (the computational cutting), both of which consist of the ABD located between residues 38–88, indicate that both are unstable protein fragments. The difference between the two cuttings translates to an extra turn formed by residues 88–91, β₄ (residues 91–95), and α₄ (residues 96–104) found in fragment 35–103.

Comparison of our cutting results between the second and third levels illustrates that fragment 37–88 lacks one of the three building blocks (85–103) found in our third level of protein cutting (Fig. 2 ▶). As such, it is expected that fragment 37–88 would be less compact than 35–103, and the stability of fragment 37–88 should be lower than that of fragment 35–103. Simulation of both fragments supports this finding, based on the percentage native contacts for each of the fragments at the end of the simulation (see Table 2). The unfolding of these two fragments is gradual, because of the presence of a β-sheet core. The calculated C_αRMSD is shown in green in a and b. For fragment 37–88, the C_αRMSD rises sharply in the first 250 psec to about 3 Å, followed by a gradual increase over the remaining course of the simulation. The final C_αRMSD's for fragments 37–86 and 35–103 are 5.7 and 5.2 Å, respectively. Comparison between the two simulations shows that all helices except α₂ undergo partial to full unfolding (Fig. 6c,d ▶). Examination of the β-sheet for fragments 37–88 and 35–103 illustrates that the unfolding of the β-sheet involves a slow twisting of the β-strands along the perpendicular axis of the β-sheet core (Fig. 5a,b ▶). Because both structures appear to be slow unfolders, the current simulation time does not allow a study of the complete unfolding of the fragments. However, it is clear from the C_αRMSD and the percentage native contacts that both of these fragments are unstable. The final percentage of native contacts in fragments 37–88 and 35–103 (see Table 2) are 38.0% and 59.0%, respectively, showing that fragment 35–103 is more stable than fragment 37–88.

Table 2.

Calculated percentage native contacts % NC

Fragment	simulation time (ns)	% NC(a)	% NC(b)	% NC(c)
1–36	2.5	31.6	37.1	41.0
37–88	3.0	31.6	38.0	38.0
89–159	3.0	40.4	59.0	61.3
5–35	2.5	44.4	54.5	57.8
35–103	3.0	50.1	59.0	60.9
104–159	3.0	56.8	68.9	66.0
37–159	3.0	56.4	66.5	73.4
1–159	3.0	52.9	66.9	70.8

The reference fragments are generated from the original X-ray structure (7DFR). All contacts between any two C_α-atoms that are within a specified cutoff distance of each other in the reference structure are considered native contacts. The percentage native contact % NC is expressed as the final number of native contacts remaining at the end of the simulation relative to the starting number of native contacts as a percentage. The current percentage native contacts are evaluated with a cutoff distance of (a) 6, (b) 7, and (c) 8 Å, respectively.

Fragments 89–159 and 104–159

Simulation of fragments 89–159 and 104–159 were also carried out. The unfolding of fragment 89–159 β-core region is also gradual. The structure of α₄ undergoes a partial structural change within the 500 psec of simulation leading to a stable conformation. Several structural changes are observed in the simulation of fragment 89–159. The C_αRMSD of both α₄ and the β-sheet core of the structure (consisting of β_4,6–8) undergo a sharp rise in the first 0.5 nsec, suggesting a partial or total unfolding of the secondary structure. Examination of the structure confirms that α₄ unfolded during the course of the simulation whereas the sharp rise of the C_αRMSD of the β-core structure is due largely to the disorder of β₄ and β₈ (Fig. 5a,b ▶). The interaction between β₆ and β₇ appears to remain intact within the 3 nsec of the simulation. Several structural changes were also observed in the simulation of fragment 104–159. In the absence of α₄ and β₄, the loose coil region consisting of residues 110–130 aligned itself with β₆ becoming part of the β-core structure of the protein fragment, whereas β₈ continued to exhibit high flexibility. The final percentage of native contacts of fragments 89–159 and 104–159 are 59% and 69% respectively. Hence, it appears that fragments generated by the computational cutting (Tsai et al. 2000) are generally more stable.

Fragment 37–159

Fragment 37–159 has an average C_αRMSD of 4 Å after 0.5 nsec of simulation. The percentage of native contacts at the end of the simulation is 66.5%. Examination of the final structure shows that the two distinct domains resulting from the protein cutting retained most of their secondary and tertiary structure characteristics. The cavity created by the removal of fragment 1–36 is replaced by the simple association of these two building blocks into a more compactly assembled structure (Fig. 7 ▶). Experimentally it was found that this fragment has a stable native fold with unique packing of its aromatic sidechains (Gegg et al. 1997). Although this structure is not solved experimentally in atomic detail, we assume that this fragment should contain substantial amount of native contacts as in the whole protein. In this sense our simulation results are consistent with the experimental spectroscopic observation. Only β₈ is observed to exhibit high flexibility. Superposition of the X-ray crystal fragments 35–103 and 104–159 over the final structure at 3.0 nsec yields C_αRMSD's of 2.08 Å and 3.30 Å, respectively, showing that the two distinct building blocks retained most of their native conformation and are indeed stable, as a result of their association. This is consistent with the building block folding model, which suggests that local building blocks are greatly stabilized by their binding.

Fig. 7.

Structure of the AS-DHFR:35–159 at the beginning and the end of the simulation. The secondary structure assignment is based on the Kabsch and Sander (1983) method. The structure shows a collapse of the native into a more compact fold, yet retaining most of its secondary structure [or its native contacts as observed by Gegg et al. (1997)]. The collapsed structure also shows a significant retention of the structures of the two distinct building blocks over the course of the simulation. The cavity created by the removal of fragment 1–35 has allowed the non-native association between the two building blocks.

Discussion

Loops and disordered regions

The observed disordered regions in the simulation can be correlated with experiment. Major structural movements have been observed previously in crystallographic studies of the binding of DHFR to its cofactor and substrate (Bystroff and Kraut 1991). These structural changes are associated with various mobile loops that include residues 9–24, 64–72, 117–131, and 142–149. Residues 9–24 are the most mobile and participate in the binding of the cofactor and substrates (Sawaya and Kraut 1997). Part of this loop, residues 15–20, commonly referred to as the M20 loop, is observed to acquire both open and closed conformations. The closure of this loop over the reactant in the active site is believed to shield the reactant from the solvent, resulting in a hydrophobic environment that facilitates hydride transfer in the reduction of the dihydrofolate (Bystroff and Kraut 1991). In our simulations, after the substrates are removed from the DHFR complex, such mobility is observed, with the M20 loop folding inward, into the active site (see Fig. 4 ▶). The disordered region of β₈ in the simulation can also be explained as a result of the mobile loop 142–149 (Ohmae et al. 1998).

Substitution of residues within the mobile loop was shown to have a large effect on the overall stability of DHFR (Ohmae et al. 1998). Movement of the loop region can greatly affect the orientation of the sequentially connected β-strands as observed in the disordered region of β₈. Further, the expansion of residues 64–76 is consistent with the high mobility of the 142–149 loop, as indicated by the increased temperature coefficient and the poorly defined electron density generally observed in the X-ray structure (Bystroff and Kraut 1991).

Relative stability of protein fragment: Experiment and simulation

This study applies molecular dynamics simulation to compare the relative stabilities of various protein fragments. The results of the simulations of fragments 1–36, 37–88, 89–159, and 37–159 are in most cases consistent with the experimental spectroscopic observations of these fragments (Gegg et al. 1997). Of the eight overlapping fragments studied by CD (four of which are simulated here) and fluorescence spectroscopy as a function of denaturation by urea, six fragments were found to be disordered. One of these six contains the ABD.

The fragment, which shows a significant extent of native secondary structural characteristics, is composed of residues 37–159. Simulation of this fragment revealed a stable conformation involving a non-native association of the two fragments containing residues 35–103 and 104–159. This is interesting, as it suggests that binding increases the stability and the population times of building blocks by their simple association with each other during the folding process. The computationally generated protein fragments are generally more stable than those generated by experimental cutting. As can be seen in Figure 8 ▶, a–c, more native contacts are lost in the simulations of the experimental cutting than in those of the computational cutting. Finally, fragments with a large β-sheet as their core are generally more stable.

Fig. 8.

Contact maps calculated for (a) the X-ray dihydrofolate reductase (DHFR) structure and the structures at the end of the simulation using (b) the three AS-DHFR fragments based on Gegg's cutting (Gegg et al. 1997), and (c) the three DHFR fragments based on the Tsai et al. (2000) cutting into building block algorithm. Each of the fragments is designated by the area enclosed by the rectangular box. The designation of the secondary structure is based on the X-ray PDB assignments. The location of each of the secondary structures within the protein sequence is shown along the axis next to the residual numbers, with the β-strands and α-helices denoted by rectangles and arrows, respectively. The contacts associated with each secondary structure are circled within each contact map to show the different extent of contact loss over the course of the simulation between the experimental (b) and computational (c) cutting as compared to the X-ray (a). For the purpose of comparison, the rectangular boxes used to show the Gegg et al. (1997) cutting are also placed over the X-ray DHFR. This is done to highlight the native contacts (contacts outside the box) that are present in the native protein, but are lost because of the cutting. As can be seen, significant number of native contacts are lost as a result of the cutting as well as over the course of the simulation for all the fragments. The exception is the C-terminal fragment, residues 104–159.

Fragment 104–159, which was shown to be thermodynamically unstable in the experiment by Gegg et al. (1997), was found to be the most stable building block with a significant amount of β-structure retained at the end of the simulation. This observation is related to the fact that our current simulation times for this slow unfolding fragment are relatively short compared with experiment. As such, fragments that are found to be unstable in our simulation are expected to be unstable in experiment although it is possible for fragments that appear to be stable in simulation to be either stable or unstable in experiment (discussed in Ma and Nussinov 1999). To establish the absolute stability of this fragment, further study such as thermal denaturation simulation is necessary. Interestingly, recent thermal denaturation simulations of the entire DHFR using an implicit solvent model (Lazaridis et al. 1997) support fragment 104–159 as being a slow unfolder. At transition temperature simulations, the region containing this fragment was observed to retain >60% of its native contacts, whereas the remaining protein undergoes total denaturation. At higher temperatures, this region was observed to undergo unfolding last (Y. Sham, unpubl.).

For the ABD there is a disagreement between the experimental stability and the computational cutting scores. According to the experimental results, the ABD is unstable. In the computational cutting (Tsai et al. 2000), the scoring function indicates that this domain is a stable unit. It is important to emphasize that the scoring function does not predict the absolute values of the stability. Only relative values are produced. This is largely because the function does not include electrostatic interactions. It assumes that the electrostatics have already been optimized. This omission might be particularly gross in cases where the building block binds a charged ligand, such as in the case of the ABD, which binds a nucleotide. In the 37–159 fragment, the C-terminal fragment compensates for the absence of the ligand, stabilizing the domain.

Building blocks and protein folding

The building block folding model describes the protein fold as consisting of a set of HFUs, each with a buried hydrophobic core and capable of an independent thermodynamically stable existence. These HFUs associate into domains, which in turn assemble to give rise to a multidomain protein fold or intermolecular multisubunit quaternary structure. An HFU is thought to be the outcome of a combinatorial assembly of a set of building blocks. A building block is defined as a highly populated fragment in a given protein structure with a continuous sequence. It may be composed of a single secondary structure or a combination of contiguous secondary structures. In contrast to the HFU, a building block may not have a stable defined conformation in solution by itself and may flip flop among several conformations with different population times. The building block conformation observed in the native state of the protein may (or may not) be the one with the highest population time in solution when it exists as a peptide fragment.

A building block is a contiguous sequence fragment, with a variable size. It is a highly populated, transient structural unit. The stability of a building block derives from its intrafragment interactions. A building block constitutes a local minimum among all potential fragments. The building block folding model postulates that protein folding is a hierarchical process and that the basic unit from which the fold is constructed is the outcome of a combinatorial assembly process of a set of building blocks. The thermodynamic stability of these building blocks can be low, but because of their binding to complementary building blocks, they can associate into higher-order, more stable structures. This enhances substantially the populations of each of these building blocks. As seen in the simulations of fragments 35–103, 104–159, and 35–159, protein fragments that are otherwise unstable independently in solution may become stable when complemented by other protein fragments.

Critical building blocks versus intramolecular chaperone

The building block protein model (Tsai et al. 1998; 1999b) has been introduced previously to describe protein folding. It has postulated that protein folding occurs as an assembly of local stable building units, which associate with one another to form the final native structure. Building blocks, which are in direct contact with several other building blocks, can be viewed as critical for the correct folding of the protein. Removal of such a building block may lead to misfolding, in which the remaining building blocks reassociate to form an alternate stable, though non-native conformation. Building blocks showing such a property are critical building blocks and may be viewed as exhibiting chaperone-like behavior (Ma et al. 2000).

All chaperones known to date can be classified as either intermolecular substrate chaperones or intramolecular proregion chaperones that catalyze the folding of a protein sequence into its correct native structure and then leave, either by dissociation or by proteolysis. In the present case our critical building block is an ``uncleaved intramolecular chaperone-like'' fragment that catalyzes the correct folding by binding to, stabilizing, and increasing the populations of native conformations of adjacent building block fragments. Unlike intramolecular chaperones whose function becomes inhibitory after the folding, necessitating their cleavage, intramolecular critical building-block chaperones are required to remain in the structure. In their absence, the other building blocks reassociate, collapsing upon each other. As seen in Figure 7 ▶ in the simulation of fragment 35–159, the assembly of the two building blocks (35–103 and 104–159) is non-native because of the absence of the amino-terminal, 1–35 critical building block.

Conclusions

This study applies molecular dynamics to compare the relative stabilities of various protein fragments. The simulations of fragments 1–36, 37–88, 89–159, and 37–159 are consistent with experimental spectroscopic measurements of the stability of these protein fragments. Protein fragments resulting from the computational cutting into building blocks algorithm are generally more stable than those of the experimental cutting. Fragments with a large extended β-sheet at their protein core are generally more stable. Fragment 37–159, consisting of the two (37–88, 89–159) distinct, sequentially adjacent, spatially separated (by residues 1–36) building blocks identified by our protein-cutting algorithm are found to be stable with a non-native association, consistent with the building block folding model.

This simulation at standard temperature only allows us to determine the relative stabilities of various protein fragments obtained from the different cutting procedures. For fragments that contain a large β-sheet core, only the early events of unfolding are observed. To fully understand the stability of individual protein fragments, it is necessary to carry out further simulation studies, such as thermal denaturation and mutational studies, to determine the specific forces that stabilize the protein. This, however, is beyond the scope of our current focus. Here we are interested in understanding the effect of the relative stability of various protein fragments on folding. According to the hierarchical protein folding concept (e.g., Karplus and Weaver 1994; Panchenko et al. 1996; 1997; Baldwin and Rose 1999a,b; Tsai et al. 1999a; 2000) folding initiates locally. Small folded domains are initially formed. These subsequently associate to form the final native structure. For such a model to be valid, the conformation of these ``foldons,'' ``microdomains,'' or ``building blocks'' should be thermodynamically the most stable, and hence the most highly populated. Alternatively, if their conformation in the native structure is not the most stable one, their stability, and hence population times, may be enhanced via their association. Here we show that such an approach is consistent with results obtained from simulations. The percentages of native contacts in protein fragments generated from the computational protein cutting are significantly higher than in fragments generated in previous experimental studies, which have less compact folds. In particular, however, it is important to note the overall remarkable agreement between the positions of the experimental and computational cuttings, indicating consistent folding pathway. This has also been observed between the experimental (Fontana et al. 1997; Polverino de Laureto et al. 1999) and the computational (Tsai et al. 2000) cutting in the case of the well studied α-lactalbumin.

In addition, it is interesting to see that fragments that are otherwise unstable can attain high populations by simple association with nearby building blocks. Consider a folding funnel based on the building block folding model. For folding to occur, there must be a sufficiently high population of individual building blocks. This is essential if the association of these building is to take place and to lead to the final native conformation. If the stability of any of the building blocks is low, it will affect its population time and be reflected in the folding kinetics of the protein. The association between the building blocks allows an equilibrium shift toward the formation of unstable building blocks and increases their population times in the protein-folding process. This is important as it gives us a way of folding proteins into more sophisticated structures by limiting the configurational search problem and overcoming the activation barrier of folding the unstable part of the protein. Folding is binding of conformationally fluctuating building blocks, via conformational selection.

Materials and methods

Protein cutting

Two molecular dissections were carried out. The first is based on an earlier experimental study carried out by Gegg et al. (1997), in which Cys residues 85 and 152 were replaced by alanine and serine, respectively. This double mutant, AS-DHFR, studied previously by Iwakura et al. (1995) has been shown to have a similar stability and function as the native DHFR. Using this structure, three fragments containing residues 1–36, 37–86, and 87–159 were generated (see Fig. 1 ▶).

The second dissection is based on the Tsai et al. (2000) computational protein cutting into building blocks algorithm. The cutting procedure is based on a previous scoring function that has been successfully applied to locate compact hydrophobic folding units (Tsai and Nussinov 1997). This scoring function is given as

1

where Z, H, and I are, respectively, the compactness, the hydrophobicity, and the degree of isolatedness of a candidate fragment. The corresponding arithmetic average, X_Avg, and standard deviation, X_Dev, are determined from a nonredundant data set of 930 representative single-chain proteins. The standard deviation and average with superscript 1 are calculated with respect to fragment size, whereas the values with superscript 2 are calculated as a function of the fraction of the fragment size to the whole proteins.

Z, the compactness of a protein, is evaluated as the solvent accessible surface area of a given structure, divided by its minimum possible surface area and is given by

2

where Vol is evaluated by the integration of all the solvent exposed accessible area, ASA_surf. I, the isolatedness of the protein, is the fraction of the change of nonpolar solvent accessible surface area to the total accessible surface area, when the fragment is exposed. It is given by

3

A value close to zero indicates the highest degree of isolatedness and a value close to unity indicates the lowest degree of isolatedness.

H, the hydrophobicity, is given as the fraction of the buried nonpolar area out of the total nonpolar area:

4

All possible protein fragments are generated from a given protein sequence and their corresponding scores are first evaluated using Equation 1. Candidate fragments with the highest score, as compared with their respective cousin fragments (fragments with <7% deviation in size or in position in the protein sequence are considered cousin fragments) are classified as local minima on the scoring surface and are considered as possible stable building blocks. Once all the building blocks are identified, all possible combinations of these building blocks in the protein are determined. The combination with the highest average score as compared with its two most stable building blocks is considered as the most likely pathway in the assembly process of these building blocks into the final native structure. The procedure is reapplied to each of the building blocks at each level of the protein cutting until no further cutting is possible. [For details of the protein cutting into building blocks algorithm, see Tsai et al. (2000) or visit our Web site at http://protein3d.ncifcrf.gov/tsai/anatomy.html.]

Applying this procedure to the native DHFR structure, the second level of dissection generates fragments 5–35, 35–103, and 104–159 (see Fig. 1 ▶). To understand the critical role of fragment 1–36, and the relative stability of the other building blocks in its absence, simulations of both 1–36, and 37–159 fragments are carried out. Finally as a control for the study, simulation of the entire native DHFR was also carried out.

Simulation procedure

The structure of DHFR from E. coli (7DFR) was taken from the protein data bank (Bernstein et al. 1977). Both crystallographic waters and substrates were deleted. InsightII's Biopolymer module was used to obtain all the missing sidechain coordinates of residues glu 17, arg 44, glu 48, arg 52, arg 98, lys 106, asp 116, glu 120, glu 129, and asp 131. The ionization state of the system is set at pH 7 and all the missing hydrogen coordinates are added accordingly.

The simulations were carried out using the DISCOVER program (MSI, Inc., San Diego, CA). Fragments AS-DHFR:1–36, 37–88, and 89–159 and DHFR:5–35, 35–103, and 104–159 were simulated in a 40 × 40 × 40 ų explicitly solvated periodic box whereas fragments AS-DHFR:37–159 and the native DHFR were simulated in a solvent sphere of 37 Å radius (our version of DISCOVER was unable to handle periodic boundary condition for the latter two systems). The simulations were carried out using the Class II Consistent Force Field (CFF91) (Maple et al. 1988) with a distance cutoff of 12 Å and a constant dielectric constant of 1. Each simulation was initialized with 500 steps steepest decent minimization followed by 10 psec of system equilibration. The average C_αRMSD at the end of the initialization was ∼1 Å. (Alternative initialization procedure, involving fixing the heavy atoms, followed by a stepwise release of atomic restraints also resulted in similar C_αRMSD values of 1 Å after 10 psec of initialization for both the protein fragments and the native structure.) A 2.5-nsec simulation was then carried out for each of the protein structures described above at 300 °K at 1-fsec time steps. If the C_αRMSD of the final structure was >4.0 Å, an additional 0.5-nsec simulation was carried out to further observe the stability of the protein fragment. Under such simulation conditions, if a protein fragment was unstable in the simulation, it should also be expected to be unstable in solution. However, if it was stable, it is possible that the structure will be either stable or unstable in solution (discussed in Ma et al. 2000). The coordinates were saved at 1-psec time intervals. The solvent coordinates in the simulation were discarded to save disk space. The total time required for the simulation of each of the protein fragments ranges from 1.5 to 2 wk using 8 R10K 250 MHz processors on the SGI Origin2000.

Analysis of trajectories

The structures of the fragments, derived from the X-ray structure of the native protein, were used as reference. The C_αRMSD of each simulation trajectory, recorded at 1-psec time interval, was evaluated after superimposing all of the C_α atoms with the reference. The secondary structure contents were evaluated with the Kabsch-Sander algorithm (Kabsch and Sander 1983) implemented in the Insight98 software package (Biosym Technologies, Inc., San Diego, CA). Any two nonsequential residues within a specified inter-C_α atomic distance were considered to be in contact. The percentage native contacts was evaluated by expressing the total number of contacts in a given structure over the total number of contacts in the native structure. The percentage native contact was used to determine the degree of conformational changes occurred during the simulation. The distance cutoff used allowed the identification of all secondary structural elements such as αs, βs and turns in the native structure. For unstable proteins, which undergo large conformational changes as well as partial to total unfolding of secondary structural motifs, a low value of percentage native contacts was expected that correlate directly to its protein instability. The native contact percentage was evaluated with an in-house program.