Prediction of Reduction Potential Changes in Rubredoxin: A Molecular Mechanics Approach

Abstract

Predicting the effects of mutation on the reduction potential of proteins is crucial in understanding how reduction potentials are modulated by the protein environment. Previously, we proposed that an alanine vs. a valine at residue 44 leads to a 50-mV difference in reduction potential found in homologous rubredoxins because of a shift in the polar backbone relative to the iron site due to the different side-chain sizes. Here, the aim is to determine the effects of mutations to glycine, isoleucine, and leucine at residue 44 on the structure and reduction potential of rubredoxin, and if the effects are proportional to side-chain size. Crystal structure analysis, molecular mechanics simulations, and experimental reduction potentials of wild-type and mutant Clostridium pasteurianum rubredoxin, along with sequence analysis of homologous rubredoxins, indicate that the backbone position relative to the redox site as well as solvent penetration near the redox site are both structural determinants of the reduction potential, although not proportionally to side-chain size. Thus, protein interactions are too complex to be predicted by simple relationships, indicating the utility of molecular mechanics methods in understanding them.

INTRODUCTION

Electron transfer proteins function as electron carriers in both primary and secondary cellular processes. The driving force of the electron transfer is determined by the reduction potentials of the different proteins involved in the reaction. Interestingly, reduction potentials of homologous proteins with the same prosthetic group can vary by hundreds of millivolts even though the redox sites themselves are highly similar (Moura et al., 1979; Lovenberg and Sobel, 1965; Meyer et al., 1983), suggesting that the protein environment is partly responsible for determining its reduction potential. Thus, determining the effects of the protein environment on the reduction potential is important in understanding the function of electron transfer proteins.

The ability to predict the effects of sequence on the reduction potential of a protein is crucial in understanding how the protein environment influences the reduction potential. However, the results of many site-specific mutational studies have run contrary to simple physicochemical arguments (Gleason, 1992; Shen et al., 1994; Zeng et al., 1996), because mutations can cause a multitude of changes at a molecular level. Here, a sequence determinant of a reduction potential is a residue whose identity can cause a change in reduction potential and a structural determinant is the underlying physical basis for the change in reduction potential. Our combination of electrostatic calculations of crystal structures and sequence analysis (Ichiye, 2001) is a bioinformatic-type approach to predict differences in potentials as small as 50 mV. We find that structural determinants are not always straightforward to deduce from the physicochemical properties of the amino acids found at a sequence determinant.

Our early studies of rubredoxin, a small iron-sulfur protein (Fig. 1), predicted that a change from alanine to valine at residue 44 would lower its reduction potential by 50 mV and vice versa based on comparisons of homologous rubredoxins with different reduction potentials (Swartz et al., 1996). This is counterintuitive, inasmuch as a small nonpolar residue mutated to another small nonpolar residue would generally be considered a silent mutation for an electrostatic property such as the reduction potential. However, our electrostatic calculations of crystal structures of four homologous rubredoxins indicated that the difference is due at least partly to a small 0.4 Å shift in the backbone due to the larger side chain of valine relative to alanine, which changes the electrostatic potential at the redox site. In addition, sequence analysis and reduction potential measurements of nine homologous wild-type (WT) rubredoxins indicated that the rubredoxins may be separated into a low potential class with a valine 44 and a 50-mV higher potential class with an alanine 44. Also, chimeras composed of Clostridium pasteurianum (Cp) and Pyrococcus furiosus (Pf) rubredoxins, which are from each of the two reduction potential classes, follow the same trend (Eidsness et al., 1997). Recently, the reduction potential shift has been confirmed by site-directed mutagenesis (reduction potentials of Val44Ala vs. WT Cp are 31 vs. −55 ± 5 mV vs. standard hydrogen electrode (SHE), respectively, and WT vs. Ala44Val Pf are 31 vs. −58 ± 5 mV vs. SHE, respectively) and the backbone shift has been confirmed in crystal structures (Fe···44N distances of Val44Ala vs. WT Cp are 4.90 ± 0.15 vs. 5.24 Å, respectively) (Eidsness et al., 1999). Of course, these studies indicate only that residue 44 is a sequence determinant of the reduction potential and that the backbone shift is a structural determinant for this change. Specifically, solvent accessibility has not been ruled out as an additional structural determinant.

FIGURE 1.

A ribbon diagram of Cp (1IRO) rubredoxin crystal structure is shown with β-strands in blue and backbone in gray. The iron (red) and the sulfurs (yellow) of the redox site and the side chains of residue 8 (green), 41 (purple), and 44 (blue) are also shown in a ball-and-stick model. This figure was generated using MOLSCRIPT (Kraulis, 1991) and RASTER3D (Merritt and Murphy, 1994).

The effects of valine vs. alanine at residue 44 on the reduction potential tempts the prediction of a general size relationship between the amino acid at residue 44 and the reduction potential for rubredoxin: the larger the side chain of residue 44, the bigger the shift in the backbone away from the redox site and the lower the reduction potential. However, recent studies of Cp rubredoxin in which the WT Val44 was mutated to other nonpolar amino acids indicate that this relationship is too simplistic. In one study, the reduction potentials of Val44Gly, Val44Ala, and WT (in order of increasing side-chain size) were 26, 31, and −55 ± 5 mV vs. SHE, respectively (Eidsness et al., 1997; Smith, private correspondence), while in a second study, the reduction potentials of Val44Gly, Val44Ala, WT, Val44Ile, and Val44Leu were 0, −24, −77, −53, and −87 ± 4 mV vs. SHE, respectively (Xiao et al., 2000). The 22-mV difference in the WT values may be the result of slight differences in pH, buffer, and electrode promoter or modifier; however, the relative shifts in the reduction potential observed for the mutants by one group should be comparable. The mutants do not really follow the relationship since there is little or no decrease between Val44Gly and Val44Ala, an increase rather than a decrease between WT and Val44Ile, and only a slight decrease between WT and Val44Leu.

The work presented here uses crystal structure analysis, energy minimization, molecular dynamics simulation, and sequence analysis to study shifts in the reduction potential caused by nonpolar mutations at residue 44 of Cp rubredoxin. The effects of glycine, alanine, isoleucine, and leucine mutations at residue 44, which is valine in WT, are studied. Specifically, the aims are to examine if the side-chain size relation with the reduction potential observed for valine vs. alanine holds for other nonpolar amino acids and to elucidate the structural determinants if it does not hold. Energy minimization and molecular dynamics simulations are used to predict mutant structures, whereas crystal structures of several of these mutants are used to test and refine these predictions. Electrostatic potential and other calculations of both crystal and simulated mutant structures are used to study the structural determinants. Sequence analysis is used to check for consistency with other homologous rubredoxins.

METHODS

Crystal structures

The crystal structures of oxidized wild-type (WT) Cp rubredoxin at 5RXN, 1.2 Å resolution (Watenpaugh et al., 1980) and 1IRO, 1.1 Å (Dauter et al., 1996); Val44Ala Cp rubredoxin at 1C09, 1.6 Å (Eidsness et al., 1999); Pf rubredoxin at 1BRF, 0.95 Å (Bau et al., 1998); Desulfovibrio gigas rubredoxin at 1RDG, 1.4 Å (Frey, 1993); and Desulfovibrio vulgaris rubredoxin at 1RB9, 0.92 Å (Dauter et al., unpublished results), along with crystal waters, were obtained from the Brookhaven Protein Databank. The root mean-square deviation (RMSD) between 1IRO and 5RXN is 0.16 Å. The crystal structure of Cp Val44Gly along with crystal waters was also used (Min et al., unpublished results). The hydrogen positions were built for all polar hydrogens using the HBUILD facility of CHARMM 25 (Brooks et al., 1983). If more than one structure exists due to multiple proteins in the asymmetric unit or two alternate conformations, the average and standard deviation are reported for calculated properties. The naming convention for C_γ1 and C_γ2 of valine is inconsistent with that for isoleucine, so here the C_γ1 and C_γ2 of valine will be referred to as C_γ2′ and C_γ1′, respectively, and χ₁′ is defined by N-C_α-C_β-C_γ1′.

Energy minimizations and molecular dynamics simulations

The energy minimizations and molecular dynamics simulations were performed with the molecular mechanics and dynamics program CHARMM 25 (Brooks et al., 1983). Energy minimizations used the steepest descent method so that only very gentle perturbations are made, because exhaustive minimization with robust methods can lead to structures that are highly perturbed from crystal structures (Shenoy and Ichiye, 1993). Molecular dynamics simulations used the Verlet algorithm with a time step of 0.001 ps in the microcanonical ensemble at a temperature of ∼300 K. For all calculations, truncated rectangular-octahedral periodic boundary conditions were used. The potential energy function used the parameters of CHARMM 19 (Brooks et al., 1983) plus additional parameters for the ions and the iron-sulfur site (Yelle et al., 1995), in which nonpolar hydrogens were treated by the extended atom method. All bonds containing hydrogens were constrained to their equilibrium bond lengths using the SHAKE algorithm (Rychaert et al., 1977). Long-range forces were switched smoothly to zero using an atom-based force-switch method (Steinbach and Brooks, 1994) between 10 Å and 14 Å. The nonbonded and image atom lists were updated heuristically using a cutoff distance of 15 Å.

The initial system of WT oxidized rubredoxin, which was the same for the energy minimizations and molecular dynamics simulations, was generated as follows. First, the crystal structure of Cp and crystal waters (5RXN) was minimized for 50 steps. Next, more solvent was added by placing the protein into a pre-equilibrated 54 × 51 × 47 Å truncated rectangular-octahedral box of 2192 TIP3P (Jorgensen et al., 1983) water molecules, and then deleting any water within 2.5 Å of any protein or crystal water atom. This system was then relaxed slightly with 2 ps of dynamics while assigning velocities every 0.2 ps in which only the water was allowed to move while the protein was fixed. Following this, counterions were added by replacing a water molecule with an ion near each charged group in the protein to make the system net neutral (a sodium ion for each negatively charged side chain and the C-terminus, and the oxidized redox site and a chloride ion for each positively charged side chain and the N-terminus). Finally, the solvent environment was equilibrated by 10 ps of dynamics while scaling velocities, if outside a temperature window of ±5 K every 0.2 ps, followed by 60 ps without perturbation in which the water and counterions were allowed to move while the protein was fixed. The system consists of 501 protein atoms, 1835 water molecules, 15 sodium ions, and five chlorine ions.

The initial systems for the mutant oxidized rubredoxins, which were also the same for the energy minimizations and molecular dynamics simulations, were generated as follows. First, structures for the mutations to glycine, alanine, isoleucine, and leucine at residue 44 in Cp rubredoxin were generated using the molecular graphics program QUANTA98 (MSI, 1986-193). The coordinates from the initial WT system were used for all equivalent atoms and then three dihedral conformations were generated for atoms beyond C_β of residue 44. Thus, there are nine structures each for Val44Ile and Val44Leu and one structure for Val44Gly and Val44Ala. In addition, structures for the two other dihedral conformations of the WT valine were generated. If the mutation had a larger side chain, 50 steps of energy minimization were performed on all residues with any atoms within a 10 Å sphere centered on the C_α of residue 44 while constraining all other residues and solvent molecules to their initial WT position.

Energy minimizations (EM) were carried out starting from the initial WT and mutant systems of rubredoxin, solvent, and counterions. In these calculations only, the nonbonded neighbor list was updated every 10 steps. The system was minimized for at least 5000 steps or until the total energy of the system no longer fell below the lowest energy point for 100 steps. When more than one initial conformation was used, the energies of the final conformations were evaluated via E_p, the total potential energy of all atoms of the protein excluding the water and counterions using the same conditions as in the energy minimization and molecular dynamics. Even though solvent can play a role in stabilizing conformations, the solvent energy was excluded because it is subject to large fluctuations and the energy of the EM configuration is not necessarily representative of the average energy.

Molecular dynamics (MD) simulations were carried out starting from the initial WT and mutant systems of rubredoxin, solvent, and counterions. In addition, MD simulations for the Val44Gly and Val44Ala were carried out starting from the EM structures (reported here) because the other simulations had indications of instability. The systems were equilibrated by scaling the velocities if outside a temperature window of ±5 K every 0.2 ps until 10 ps after the last scale for a total of 15–25 ps, followed by 160 ps unperturbed. After equilibration, each system was propagated for 0.5 ns with analysis utilizing coordinates at 0.01-ps intervals. The MD quantities were the average over the entire simulation, with the standard deviations calculated from the average values of the quantity for successive 50-ps intervals of the simulation (i.e., 10 intervals).

Electrostatic calculations

The contributions of protein residues to the electrostatic potential at the redox site were calculated for the crystal, EM, and MD structures. The electrostatic potential may be related to the reduction potential as follows (Ichiye, 2001). The free energy change upon reduction, ΔG, is related to the reduction potential, E°, by

(1)

where ℐ is Faraday's constant, n is the number of electrons transferred, E is energy, PV is pressure and volume, T is absolute temperature, and S is entropy. Based on previous work (Swartz et al., 1996; Beck et al., 2001),

(2)

where and φ_i refer to the reduction potential and the electrostatic potential at the redox site, respectively, of protein i in the oxidized state. Although the protein will relax upon reduction, the degree of relaxation for a set of nonpolar residues will be small in magnitude and similar to each other. Thus, the contribution of relaxation to a difference in reduction potential will be small (Beck et al., 2001).

Because the change in charge upon reduction is delocalized over several atoms, a delocalized φ can be defined as

(3)

(4)

where φ(k) is the electrostatic potential of residue k, Δq_i is the change in charge of atom i upon reduction, q_j is the charge of atom j, and r_ij is the distance from atom i to atom j. The summation over i is over all atoms of the redox site (i.e., those atoms that change charge upon reduction: the iron and the C_β and S_γ of the four cysteinyl ligands), the summation over j is over all atoms of a given residue, and the summation over k is over all residues of the protein. The partial charges are the same as for the energy minimization and molecular dynamics simulations.

Solvent accessibility

The solvent accessibility of the redox site was calculated as the solvent contact surface area (SCSA) of the nine atoms of the redox site (Fe plus C_β and S_γ of residues 6, 9, 39, and 42). In practice, the only atoms of the redox site with nonzero values of SCSA are the C_β of residue 9 and residue 42, which are the cysteinyl ligands of the iron site. The Lee and Richard's algorithm was used with a probe radius of 1.6 Å (Lee and Richards, 1971).

Sequence alignment

Sequences of 40 known and probable rubredoxin sequences were found and aligned using the online version of BLAST (Schaffer et al., 2000) and the SwissProt database. The sequence of Cp rubredoxin was used as the search criteria, which resulted in 48 hits, 44 of which were rubredoxin sequences whereas the other four were flavorubredoxins. Of these, 40 were chosen because they had BLAST scores >37 and Expect-values (E) of <0.01.

RESULTS

Crystal, EM, and MD structures of wild-type and mutant Cp rubredoxins are analyzed to determine the effects of point mutations on the protein structure and electrostatic potential of the redox site. No global changes to the structure due to the molecular mechanics were indicated by the RMSD of all backbone atoms. The EM relative to crystal structures for WT (5RXN), Val44Ala, and Val44Gly have small backbone RMSDs of 0.25, 0.47, and 0.45 Å, respectively. Also, the WT MD relative to the WT (5RXN) crystal structure has a small backbone RMSD of 1.89 Å and an all-atom RMSD of 2.15 Å, which is typical for such simulations (McCammon and Harvey, 1987). The global changes upon mutation were also small. For the crystal structures, the backbone RMSD of the Val44Ala and Val44Gly relative to WT (1IRO) were 0.42 ± 0.04 Å and 0.47 ± 0.04 Å, respectively. For the EM and MD structures, the backbone RMSD of the mutant relative to WT were ∼0.1 and 1.0 Å, respectively.

The local changes near residue 44 are discussed individually below. Local structural changes are monitored by the torsion angles of residue 44 (ϕ₄₄ and ψ₄₄) and by the distance between the redox site iron and the residue 44 backbone nitrogen (r_Fe···44N). Since residue 44 is only one residue away from the fourth cysteinyl ligand (residue 42) of the redox site, which does not change its structure upon mutation of residue 44, the backbone distance r_Fe···44N and torsion angle ϕ₄₄ are simple indicators of the distance and orientation, respectively, of the peptide dipoles of residues 43 and 44 with respect to the redox site. The solvent accessibility of the redox site is monitored by the solvent contact surface area (SCSA) of the redox site for the static structures and by the average number of waters (N_w) in the MD simulations that are 3.8 Å from S_γ9 or S_γ42. Possible effects on the reduction potential are monitored by the change in electrostatic potential at the redox site due to residues 43 and 44 relative to WT (Δφ_43,44, where φ_43,44 = φ (43) + φ (44)), since previous work indicates the change is mainly in these two residues (Swartz et al., 1996). The major dipolar contributions to Δφ_43,44 come from the NH of residue 44 and the CO of residue 43 while the smaller contributions of the NH of residue 43 and the CO of residue 44 tend to cancel each other in the given backbone conformation. Thus, Δφ_43,44 is determined mainly by the peptide dipole between residues 43 and 44, hence giving rise to the correlation with Δr_Fe···44N and ϕ₄₄. Finally, sequence effects are monitored by the sequence analysis of 40 homologous rubredoxins.

Wild-type

Crystal structures

The WT crystal structure (Fig. 1) has several features that are important in the analysis of the mutants. First, Leu41 has two conformations (Dauter et al., 1996): an open conformation (occupancy 0.76), which exposes the redox site with a SCSA of 12 Ų, and a closed conformation (occupancy 0.24), which covers it with a SCSA of 8 Ų (Fig. 2). The water gates Leu41 and Val8 (Yelle et al., 1995; Swartz et al., 1996; Min et al., 2001) cover S_γ9 and S_γ42, respectively. Second, Val44 has χ₁′ = 71°, where the C_γ1′ points into the protein whereas the C_γ2′ points into solution (Fig. 3). Finally, the two C_γ of Val44 and Val8 interlock, which hinders the backbone from moving closer to the redox site (Fig. 3).

FIGURE 2.

A licorice model of the side chain of leucine 41 in both the open (purple) and closed conformation (translucent purple) reported in the crystal structure; the iron (red) and the sulfurs (yellow) of the redox site and the backbone of the protein (gray) are also shown. This figure was generated using MOLSCRIPT (Kraulis, 1991) and RASTER3D (Merritt and Murphy, 1994).

FIGURE 3.

A licorice model of the side-chain interaction of residue 44 and residue 8 for the WT (gray), Val44Ala (purple), and Val44Gly (magenta) and the iron (red) and the sulfurs (yellow) of the redox site in the crystal structures with the polar hydrogen atoms built in, and the van der Waals surfaces of WT represented with transparent spheres. The orientation of the peptide dipole of the WT protein is indicated by the red (−) to blue (+) arrow. This figure was generated using MOLSCRIPT (Kraulis, 1991) and RASTER3D (Merritt and Murphy, 1994).

Energy minimizations

Since minimizations were used to predict mutant structures, the WT protein was minimized from three different initial conformations of Val44 (χ₁′ = 71°, 180°, and −60°) with the Leu41 in the open conformation, which resulted in three unique final conformations of Val44 (χ₁′ = 68°, −147°, and −56°) compared to the WT crystal structure (χ₁′ = 71°). After minimization, the WT conformation has the lowest potential energy of the protein E_p (Table 1). For the WT EM structure, the local region shows little change due to minimization since the backbone torsions (Table 2), r_Fe···44N (Table 3), and solvent accessibility (Table 4) remain very close to the crystal structure values.

TABLE 1.

Side-chain torsions of χ₁ and χ₂

Protein	χ1	χ2	Ep	rFe···44N
Val44	67.5	NA	−1838.05	5.24
Val44	−146.5	NA	−1837.58	5.16
Val44	−56	NA	−1836.22	5.38
Val44Ile	−49	−53.5	−1836.77	5.42
Val44Ile	−57	−179	−1834.07	5.41
Val44Ile	−98	62.5	−1835.46	5.29
Val44Ile	−105	−65	−1836.00	5.06
Val44Ile	−149	161	−1835.27	5.24
Val44Ile	−144	74	−1838.46	5.07
Val44Ile	91	−55	−1830.67	5.71
Val44Ile	65	174	−1832.31	5.50
Val44Ile	55	74	−1835.87	5.37
Val44Leu	−89	−72	−1838.54	5.06
Val44Leu	−51	−161	−1834.86	5.39
Val44Leu	−81	69	−1837.39	5.30
Val44Leu	167	−82	−1830.69	5.46
Val44Leu	−105	155	−1834.03	5.26
Val44Leu	−174	65	−1832.13	5.36
Val44Leu	44	−83	−1829.09	5.80
Val44Leu	152.5	144	−1828.96	5.54
Val44Leu	48.5	66	−1830.89	5.66

Shown in degrees (χ₁ using C_γ2 instead of C_γ1 to correspond to the C_γ1 of Ile), energy of the protein E_p in kcal/mol, and the iron-to-nitrogen distance of residue 44 r_Fe···44N in Å for EM structures of different mutants. In order, the starting conformations were χ₁ = 60, 180, −60° and χ₂ = 60, 180, −60°, incrementing over the latter first when applicable.

TABLE 2.

Backbone torsion angles of residue 44

	ϕ44			ψ44
Mutant	x-tal	EM	MD	x-tal	EM	MD
Val44Gly	−71	−66	−136 ± 30	146	144	162 ± 11
Val44Ala	–66	–68	–88 ± 16	141	149	153 ± 3
Val44 (WT)	−82	−75	−90 ± 3	160	162	164 ± 2
Val44Ile	NA	−75	−104 ± 8	NA	158	161 ± 3
Val44Leu	NA	−73	−86 ± 2	NA	153	160 ± 1

Shown in degrees for crystal (x-tal; see Methods for references) and energy-minimized (EM) structures and molecular dynamics (MD) dynamical average for C. pasteurianum rubredoxin.

TABLE 3.

Iron-to-nitrogen distance of residue 44 r_Fe···44N

	rFe···44N
Mutant	x-tal	EM	MD
Val44Gly	4.85 ± 0.14	4.85	5.35 ± 0.25
Val44Ala	4.89 ± 0.02	4.92	5.01 ± 0.11
Val44 (WT)	5.24 ± 0.00	5.24	5.30 ± 0.05
Val44Ile	5.25 ± 0.10	5.07	5.27 ± 0.04
Val44Leu	NA	5.06	5.23 ± 0.06

Shown in Å for crystal (x-tal; see Methods for references) and energy-minimized (EM) structures and molecular dynamics (MD) dynamical average of C. pasteurianum rubredoxin.

TABLE 4.

Solvent contact surface area (SCSA) of the redox site

	SCSA (Å2)		Nw
Mutant	x-tal	EM	MD
Val44Gly	11.2 ± 0.8	10.9	0.91
Val44Ala	10.9 ± 0.5	11.1	0.60
Val44 (WT)	12 (8.3)	11.1	0.34
Val44Ile	NA	11.9	0.35
Val44Leu	NA	10.1	0.23

Shown for crystal (x-tal; see Methods for references) and energy-minimized (EM) structures and molecular dynamics (MD) dynamical average number of waters (N_w, i.e., the average number of waters that are 3.8 Å from S_γ9 and S_γ42) near redox site of C. pasteurianum rubredoxin. For WT, value for leucine 41 in open (closed) conformation.

Molecular dynamics

Most of the local features of the MD structure are fairly close to the crystal and EM structures. The side chain maintains a conformation (χ₁′ = 62 ± 1°) close to the WT crystal structure (χ₁′ = 71°). Also, the backbone torsions (Table 2) and the r_Fe···44N (Table 3) are very close to the WT crystal values. The simulation also shows a small degree of water penetration (Table 4) mainly near S_γ42.

Sequence analysis

The Val44 in Cp is fairly typical of the rubredoxins since the sequence analysis of 40 rubredoxins has 16 with a Val44 (Table 6). Of these, all but four have amino acids with branched C_β at residue 8, so that the interlocking of Val44 and residue 8 is likely to be common to these rubredoxins. Of the exceptions, the Pseudomonas oleovorans 2 sequence is from a protein with two rubredoxin-like domains, one with a Val44 (Po2a) and the other with an Ala44 (Po2b). On the other hand, there is considerable variability at residue 41, indicating that the interactions controlled by Leu41 may not depend on the amino-acid type.

TABLE 6.

Sequence alignment of 40 known and probable rubredoxin sequences found using BLAST and the SwissProt database

		1	10	20	30	40	50
Rd	#aa	↓	↓	↓	↓	↓	↓
Ach	72	…AVLECKICWHRYDPAVGDEVWQILAGTPFAALPAHWRCPQCDGDREQFMVVDD
Av	72	…AVLECKICWQRYDPAEGDPVWQIPPGTPFAALPAHWRCPRCDGDREQFMVVDG
Mj1	80	…RKYKCKVCGWVYDPLKGDPSQNIPPKTPFEELPDTWICPVCRGKVGKESFEPLD…
Reu	78	…ARLECKICWWEYDPEVGDPVWQIAPGTSFSALPAHWRCPNCDGEAEQFMVLGPQA
Ava	111	…DRFECRSCGYVYEPEKGDSKHDIAPETPFAELPINWRCPVCTAKKAAFSNIGPA…
Bj	69	…TRLECGICWTVYDPADGDDVAQIAPGTPFAALPEEWHCPNCDAPKSKFMAIES
Ct2	52	MEQWKCNICGYIYNPETGDPEGDIPAGTSFESLPDSWMCPVCGAGKEEFTKI
Dg	52	MDIYVCTVCGYEYDPAKGDPDSGIKPGTKFEDLPDDWACPVCGASKDAFEKQ
DvH	52	MKKYVCTVCGYEYDPAEGDPDNGVKPGTSFDDLPADWVCPVCGAPKSEFEAA
DvM	52	MKKYVCTVCGYEYDPAEGDPDNGVKPGTAFEDVPADWVCPICGAPKSEFEPA
Me	52	MDKYECSICGYIYDEAEGD-DGNVAAGTKFADLPADWVCPTCGADKDAFVKMD
Mts1	63	…KRYKCRVCGYIYDPEKGEPRTDTPPGTPFEDLPETWRCPSCGAKKKMFKPLD
Ns	111	…DRFECRSCGYVYEPEKGDNKHDIAPETPFAELPINWRCPVCTAKKAAFTNIGPA…
Pab	53	MAKWRCKICGYIYDEDEGDPDNGISPGTKFEDLPDDWVCPLCGAPKSEFERIE
Pas	53	MQKFECTLCGYIYDPALVGPDTPDQDGA-FEDVSENWVCPLCGAGKEDFEVYED
Pf	53	AKWVCKICGYIYDEDAGDPDNGISPGTKFEELPDDWVCPICGAPKSEFEKLED
Po2b	173	…LKWICITCGHIYDEALGDEAEGFTPGTRFEDIPDDWCCPDCGATKEDYVLYEEK
Rc	278	…AIMECKICWTPYDPASGDEFRQVLPGTPFTALPEDWHCPNCDAPKAQFIVQSDP…
Re4	60	…KLYQCAQCGFEYDEAVGWPEDGIEPGTRWDDIPEDWSCPDCGAAKSDFFMVEVERR
Rl	70	…DRMECGICWHVYDPAEGDPVWQIPPGTPFSNLTEDWRCPNCDALQSKFMRLGDGR
Ss	115	…PNHECRACGYVYIPSQGDQKTSVSPGTPFEALPLNWKCPVCGAPRNYFISTGET…
Aca	54	MKKYQCIVCGWIYDEAEGWPQDGIAPGTKWEDIPDDWTCPDCGVSKVDFEMIEV
Bm	53	MQKYVCDICGYVYDPAVGDPDNGVAPGTAFADLPEDWVCPECGVSKDEFSPEA
Cl	53	MQKYVCSVCGYVYDPADGEPDDPIDPGTGFEDLPEDWVCPVCGVDKDLFEPES
Ca	54	MKKYVCVVCGYIYDPAEGDPDNGVNPGTSFEDIPDDWVCPLCGVGKDQFEPSEE
Cp	54	MKKYTCTVCGYIYNPEDGDPDNGVNPGTDFKDIPDDWVCPLCGVGKDQFEEVEE
Cpe2	53	MKKFICDVCGYIYDPAVGDPDNGVEPGTEFKDIPDDWVCPLCGVDKSQFSETEE
Cs	53	MTKYVCTVCGYVYDPEVGDPDNNINPGTSFQDIPEDWVCPLCGVGKDQFEEEA
Ct3	53	MQKWVCVPCGYEYDPADGDPENGIEPGTAFEDLPEDWVCPVCGVDKSFFEPVS
Dd	45	MQKYVCNVCGYEYDPAEHD-------NVPFDQLPDDWCCPVCGVSKDQF
Hm	52	MKKYGCLVCGYVYDPAKGDPDHGIAPGTAFEDLPADWVCPLCGVSKDEFEPL
Mts2	177	MKICRICGYQI------------PEGEFNLLEDGWVCPRCGVGKEELQDSAEP…
Po1	132	MSRYQCPDCQYIYDENKGEPHEGFHPNTSWNDIPKDWACPDCAVRDKVDFIFLAD…
Po2a	173	MASYKCPDCNYVYDESAGNVHEGFSPGTPWHLIPEDWCCPDCAVRDKLDFMLIESG…
Re3	61	MSSYRCPVCEYVYDESKGAPREGFPAGTPWDAVPDDWCCPDCGVREKLDFEPMPATA…
Tp	52	MGTYMCDLCGWGYNPEVGDADGGIPAGTAFENLPDHWECPLCGVDKTSFVKV
Tt	52	MEKWQCTVCGYIYDPEVGDPTQNIPPGTKFEDLPDDWVCPDCGVGKDQFEKI
Mj2	55	…ARYQC-MCGWVYDEDKGEPSQNIPPGTKFEDLPDTFRCPQCGLGKNAFRKID
Cpe1	53	MEKFVCDVCGYIYDPVVGDPDNGVAPGTKFKDIPDTWVCPLCKLDKTHFSKVE
Ct1	69	…ASWMCAECGYIYDPAEGNLETNIRPGMPFDKLPDDWSCPVCNHPKNQFTKFISQL

Azotobacter chroococcum strain mcd 1 (Ach), Azotobacter vinelandii (Av), Methanococcus jannaschii 1 (Mj1), Ralstonia eutropha (Reu), Anabaena variabilis (Ava), Bradyrhizobium japonicum (Bj), Chlorobium tepidum 2 (Ct2), Desulfovibrio gigas (Dg), Desulfovibrio vulgaris strain Hildenborough (DvH), Desulfovibrio vulgaris strain Miyazaki (DvM), Megasphaera elsdenii (Me), Methanothermobacter thermautotrophicus (Mts1), Nostoc sp. PCC 7120 (Ns), Pyrococcus abyssi (Pab), Peptoniphilus asaccharolyticus (Pas), Pyrococcus furiosus (Pf), Pseudomonas oleovorans 2 subunit b (Po2b), Rhodobacter capsulatus (Rc), Rhodococcus erythropolis 4 (Re4), Rhizobium leguminosarum (Rl), Synechocystis sp. PCC 6803 (Ss), Acinetobacter calcoaceticus (Aca), Butyribacterium methylotrophicum (Bm), Chlorobium limicola (Cl), Clostriduim acetobutylicum (Ca), Clostridium pasteurianum (Cp), Clostridium perfringens 2 (Cpe2), Clostridium sticklandii (Cs), Chlorobium tepidum 3 (Ct3), Desulfovibrio desulfuricans (Dd), Heliobacillus mobilis (Hm), Methanothermobacter thermautotrophicus (Mts2), Pseudomonas oleovorans 1 (Po1), Pseudomonas oleovorans 2 subunit a (Po2a), Rhodococcus erythropolis 3 (Re3), Ralstonia eutropha (Reu), Treponema pallidum (Tp), Thermoanaerobacterium thermosaccharolyticum (Tt), Methanococcus jannaschii 2 (Mj2), Clostridium perfringens 1 (Cpe1), Chlorobium tepidum 1 (Ct1).

Mutations to smaller side chains

Crystal structures

The Val44Ala and Val44Gly crystal structures have small but significant changes relative to the WT near residue 44. The backbone torsion angles change by Δϕ₄₄ ≈ +15° and Δψ₄₄ ≈ −15° relative to WT (Table 2). Also, the backbone in Val44Ala and Val44Gly shifts closer to the redox site relative to WT (Fig. 3) so that Δr_Fe···44N ≈ −0.4 Å (Table 3). The values ϕ₄₄ = −66°, ψ₄₄ = 141°, and r_Fe···44N = 4.89 ± 0.01 Å for Val44Ala are also consistent with the average values ϕ₄₄ = −65 ± 3°, ψ₄₄ = 149 ± 6°, and r_Fe···44N = 4.87 ± 0.06 Å, respectively, for the three homologous rubredoxin crystal structures with alanine at residue 44 (see Methods). Val44Ala lacks the two C_γ of the WT valine so that the C_β touches the two C_γ of Val8, which allows the Val44Ala backbone to move closer to the redox site than the WT (Fig. 3). However, although Val44Gly lacks both the two C_γ and the C_β of the WT valine, the Val44Gly backbone does not move any closer to the redox site than the Val44Ala, apparently because of the backbone connectivity. The Val44Ala and Val44Gly crystal structures have only the open conformation for Leu41 and both have slightly smaller SCSA of the redox site than the WT crystal structure with the open conformation for Leu41 (Table 4). The Δφ_43,44 ≈ 30 mV for Val44Ala and Val44Gly is smaller than the experimental ΔE° ≈ 50–85 mV (Table 5). However, it is consistent with the average value for valine vs. alanine of 60 ± 8 mV calculated here from the homologous rubredoxin crystal structures and the original value of ∼40 mV, which used a slightly different definition of Δφ_43,44 and older crystal structures (Swartz et al., 1996).

TABLE 5.

Reduction potential vs. SHE

	ΔE°			Δφ43,44
Mutant	A	B	x-tal	EM	MD
Val44Gly	81	77	28	32	−160 ± 75
Val44Ala	86	53	32	25	1 ± 65
Val44 (WT)	0	0	0	0	0 ± 22
Val44Ile	NA	24	NA	42	−3 ± 16
Val44Leu	NA	−10	NA	8	−9 ± 3

Shown relative to WT ΔE° in mV (values in A are with respect to E° = −55 mV, see Eidsness et al. (1999) and Smith (private correspondence); and values in B are with respect to E° = −77 mV, see Xiao et al. (2000) and electrostatic potential at the redox site due to residues 43 and 44 relative to WT Δφ_43,44 in mV (x-tal are with respect to φ_43,44 = 210 mV; EM are with respect to φ_43,44 = 232 mV; and MD are with respect to φ_43,44 = 240 mV) for crystal (x-tal; see Methods for references) and energy-minimized (EM) structures and for the molecular dynamics (MD) dynamical average of C. pasteurianum rubredoxin.

Energy minimizations

The changes in the backbone torsions (Table 2), r_Fe···44N (Table 3), and the redox site SCSA (Table 4) for the Val44Ala and Val44Gly relative to WT EM were similar to the crystal structure results. Remarkably, the Δφ_43,44 of the Val44Ala and Val44Gly EM structures are within <10 mV (≈0.2 kcal/mol/e) of the Δφ_43,44 calculated from the crystal structures (Table 5).

Molecular dynamics

The Val44Gly and Val44Ala simulations exhibited two different backbone conformations: one with ϕ₄₄ ≈ −75°, which resembles the crystal and EM structures, and the other with ϕ₄₄ ≈ −160°, which has the loop opening outward (Fig. 4). This was reflected in the root-mean-square fluctuations of the backbone angles of residue 44 (〈Δϕ₄₄²〉^1/2 = 45°, 〈Δψ₄₄²〉^1/2 = 23° and 〈Δϕ₄₄²〉^1/2 = 27°, 〈Δψ₄₄²〉^1/2 = 12°, respectively), which were much higher than WT (〈Δϕ₄₄²〉^1/2 = 18°, 〈Δψ₄₄²〉^1/2 = 11°). In the ϕ₄₄ ≈ −75° conformation, the NH dipole points toward the redox site as in the crystal structures of WT and mutants, whereas in the ϕ₄₄ ≈ −160° conformation, the NH dipole tilts away from the redox site by ∼40° and hydrogen-bonds to the carbonyl group of residue 42. In addition, in Val44Gly, ψ₄₄ tends to a larger value when ϕ₄₄ ≈ −160°. There are ∼6 transitions during the Val44Gly simulation and ∼3 transitions during the Val44Ala, where a transition is defined as when the new conformation lasts for longer than ∼20 ps. Using a fit to two Gaussian distributions, the relative population of the ϕ₄₄ ≈ −75° conformation was 40% for Val44Gly and 85% for Val44Ala.

FIGURE 4.

A licorice model depicting the backbone conformations for the WT crystal structure (gray) and two snapshots from the MD simulation of the Val44Gly mutant in the φ ≈ −75° conformation (magenta) and the φ ≈ −160° conformation (pink); the iron (red) and the sulfurs (yellow) of the redox site are also shown. The change in the peptide dipole orientation between the two conformations is shown with a double-headed arrow pointing toward the respective H₄₄. This figure was generated using MOLSCRIPT (Kraulis, 1991) and RASTER3D (Merritt and Murphy, 1994).

The increased backbone flexibility of Val44Ala and Val44Gly relative to WT may be partly due to the small side chains of alanine and glycine being unable to interlock with Val8, unlike the two C_γ of the WT valine. Thus, the ϕ₄₄ ≈ −75° conformation of Val44Ala may be stabilized more than for Val44Gly by the contact of the Val44Ala C_β with Val8. In addition, the even larger backbone flexibility of Val44Gly relative to WT may be due to the two glycines that flank residue 44 in Cp rubredoxin resulting in three consecutive glycines. Interestingly, a 0.5-ns MD simulation under the same conditions of WT Pf rubredoxin (Gly43-Ala44-Pro45) has backbone torsions (ϕ₄₄ = −77 ± 3° and ψ₄₄ = 138 ± 1°) with smaller fluctuations (〈Δϕ₄₄²〉^1/2 = 17° and 〈Δψ₄₄²〉^1/2 = 9°) than for Val44Ala (Gly43-Ala44-Gly45). The relative population of the ϕ₄₄ ≈ −75° conformation was 95% and r_Fe···44N = 4.90 ± 0.06 Å.

Overall, the Val44Ala results for the backbone torsions (Table 2), r_Fe···44N (Table 3), and Δφ_43,44 (Table 5) are fairly consistent with the crystal and EM structures of Val44Ala, whereas the Val44Gly results are not, due to the large population of the ϕ₄₄ ≈ −160° conformation. The Val44Ala and Val44Gly MD simulations show an increased amount of water penetration near the site of mutation relative to WT (Table 4) near S_γ42. In both simulations, the ϕ₄₄ ≈ −160° conformation occurs when a water molecule comes close to S_γ42 whereas the ϕ₄₄ ≈ −75° conformation has water penetration similar to WT. Interestingly, the WT Pf and the Val44Ala Cp rubredoxin simulations both have a high degree of water penetration (0.80 and. 0.60, respectively) so that the ϕ₄₄ ≈ −160° conformation is not necessary for water penetration but perhaps is a consequence of it. A single water molecule near S_γ42 is estimated to contribute roughly 50 mV to the electrostatic potential at the redox site; however, the contribution to the reduction potential will be proportionate to the population of water and will presumably be reduced due to the entropic contribution, since the solvation free energy of a linearly responding solvent is half of the solvation energy (Hyun and Ichiye, 1998).

Sequence analysis

The sequence analysis of 40 rubredoxins has 17 sequences with Ala44 and four sequences with Gly44, indicating that both can be accommodated at residue 44 (Table 6). However, although Cp has the sequence Gly43-Val44-Gly45, Gly45 are rare whereas Gly43 are common. Moreover, of rubredoxins with Ala44, >40% have a Pro45, which might restrict the backbone, and only one has Gly43-Ala44-Gly45, indicating it may be disfavored. Furthermore, none of the four sequences with Gly44 has Gly43-Gly44-Gly45. In addition, of the 21 with either an Ala44 or Gly44, all but five have amino acids with branched C_β at residue 8, even though neither the alanine nor the glycine would be able to interlock with residue 8. As in the sequences with Val44, there is considerable variability at residue 41, indicating that the interactions controlled by Leu41 may not depend on the amino-acid type.

Mutations to larger side chains

Crystal structures

No crystal structures of Val44Ile or Val44Leu were available to us for analysis, although features of a Val44Ile have been described (Xiao et al., 2000).

Energy minimization

The minimizations of Val44Ile and Val44Leu had nine initial conformations each (χ₁ = 60° and χ₂ = 60°, 180°, −60°; χ₁ = 180° and χ₂ = 60°, 180°, −60°; χ₁ = −60°; and χ₂ = 60°, 180°, −60°), which each resulted in a unique final conformation. The χ₁ = −144°, χ₂ = 74°conformation of Val44Ile has the lowest E_p by 1.7 kcal/mol. The EM structure appears visually similar to the Val44Ile crystal structure, except that the backbone of residue 44 is closer by ∼0.2 Å to the iron site (Xiao et al., 2000) (Table 3). The χ₁ = −89° and χ₂ = −72° conformation of Val44Leu has the lowest E_p by 1 kcal/mol. However, other conformations for both Val44Ile and Val44Leu were close in energy to those with the lowest E_p and could become energetically favored by fluctuations. Apparently, the protein is able to relax enough to accommodate many different conformations of these side chains.

Comparing the Val44Ile and Val44Leu lowest E_p EM structures (henceforth referred to as the EM structures) with the WT EM structure, the backbone torsion angles show little change (Table 2), whereas the backbones are shifted closer to the iron site Δr_Fe···44N ≈ −0.2 Å (Table 3), even though isoleucine and leucine are larger than valine. Unlike WT, the two C_γ1 of Val44Ile are in the wrong orientation to interlock with Val8. Since the Val44Ile C_γ2 and C_γ1 point in the direction of the WT C_γ1′ and H_β, respectively, the backbone can move closer to the redox site (Fig. 5). In addition, the Val44Leu side chain does not interlock with the two C_γ of Val8 since the single C_γ points into solution in the direction of the WT C_γ2′, so the backbone can also move closer to the redox site (Fig. 5). The SCSA of the redox site for the mutant EM structures was similar to the WT EM structure (Table 4). The Δφ_43,44 of the Val44Ile and Val44Leu EM structures are within ∼20 mV (≈0.4 kcal/mol/e) of the experimental ΔE° (Table 5). The Δφ_43,44 of the Val44Ile EM structure is somewhat larger than might be expected from Δr_Fe···44N since the backbone has moved such that the CO of residue 44 now makes a large positive contribution. Although other side-chain conformations give rise to very different backbone shifts, the Boltzmann weighted averages (using E_p) over all conformations of Val44Ile are r_Fe···44N = 5.09 ± 0.02 Å and Δφ_43,44 = 36 ± 5 mV, respectively; of Val44Leu are r_Fe···44N = 5.09 ± 0.01 Å and Δφ_43,44 = 5 ± 2 mV, respectively; and of Val44 are r_Fe···44N = 5.22 ± 0.04 Å and Δφ_43,44 = 0 ± 7 mV, respectively (where Δφ_43,44 is relative to 232 mV, the value for the WT conformation).

FIGURE 5.

A licorice model depicting the side-chain interaction of residue 44 and residue 8 for the WT (gray), Val44Ile (blue), Val44Leu (green), and the iron (red) and the sulfurs (yellow) of the redox site in the EM structures with the van der Waals surfaces of WT represented with transparent spheres. The orientation of the peptide dipole of the WT protein is indicated by the red (−) to blue (+) arrow. This figure was generated using MOLSCRIPT (Kraulis, 1991) and RASTER3D (Merritt and Murphy, 1994).

Molecular dynamics

Three simulations for Val44Ile and five for Val44Leu were performed, which indicated that transitions between side-chain conformations are quite easy. For Val44Ile, the initial configuration χ₁ = 180°, χ₂ = 60°, which had the lowest E_p of the EM structures, has average torsions χ₁ = 136 ± 84°, χ₂ = 124 ± 37° because it reorients about halfway through the simulation from χ₁ = −150°, χ₂ = 60° to χ₁ = 60°, and χ₂ = 180° so that the Val44Ile C_γ are in similar positions to the Val44 C_γ in WT (Figs. 3 and 5). Moreover, the initial configuration χ₁ = 180°, χ₂ = 180° rotates during equilibration so that the average torsions are χ₁ = −147 ± 9°, χ₂ = 82 ± 10°, with two transitions back to χ₂ = 180°. Finally, the initial configuration χ₁ = 60°, χ₂ = 60° has average torsions χ₁ = 54 ± 4°, χ₂ = 130 ± 31°, with twelve major transitions from χ₂ = 60° to χ₂ = 180°. For Val44Leu, the initial configuration χ₁ = −60°, χ₂ = −60°, which had the lowest E_p, and the initial configuration χ₁ = −60°, χ₂ = 180° have average χ₁ = −82 ± 10°, χ₂ = −63 ± 1° and χ₁ = −68 ± 2°, χ₂ = 162 ± 11°, respectively, and show no transitions. On the other hand, the initial configuration χ₁ = −60°, χ₂ = 60° with average χ₁ = −73 ± 7°, χ₂ = −126 ± 68° rotates to χ₂ = −60° during the equilibration and then rotates again to χ₂ ≈ 170° halfway through the simulation. Also, the initial configurations χ₁ = 180°, χ₂ = −60° and χ₁ = 60°, χ₂ = −60° have average torsions χ₁ = −120 ± 41°, χ₂ = −106 ± 49° and χ₁ = −166 ± 2°, χ₂ = 80 ± 22°, respectively, showing transitions.

The MD simulations with structures closest to the lowest E_p structures for EM will henceforth be referred to as the MD structures. The MD structures had average side-chain conformations of χ₁ = −147 ± 9°, χ₂ = 82 ± 10° for Val44Ile, and χ₁ = −82 ± 10°, χ₂ = −63 ± 1° for Val44Leu. Root-mean-square fluctuations of the backbone angles of residue 44 for Val44Ile and Val44Leu (〈Δϕ₄₄²〉^1/2 = 26°, 〈Δψ₄₄²〉^1/2 = 10° and 〈Δϕ₄₄²〉^1/2 = 13°, 〈Δψ₄₄²〉^1/2 = 11°, respectively) were similar to those for WT (〈Δϕ₄₄²〉^1/2 = 18°, 〈Δψ₄₄²〉^1/2 = 11°). The backbone torsions are similar to WT and to the EM results (Table 2), although the MD results have larger values of ϕ₄₄. Both mutants show only a small inward shift of the backbone relative to WT (Table 3) and essentially no change in the amount of water penetration and Δφ_43,44 relative to WT (Tables 4 and 5).

Sequence analysis

The sequence analysis of 40 rubredoxins has only two sequences with Leu44 and none with Ile44, which indicates that both may be unfavored (Table 6). Of these two, the sequence from Methanococcus jannaschii has a methionine instead of a valine at residue 8 and an unusual deletion at residue 7 between the two cysteine ligands at residues 6 and 9.

DISCUSSION

The computational methods used here provided complementary information for understanding the modulation of reduction potentials in the rubredoxins. Although longer MD simulations could be performed to obtain better statistics, inaccuracies of the potential energy functions, complexities of the real protein environments, and the very small energies involved (ΔE° ≈ 50 mV ≈ 1 kcal/mol/e) imply that the combination of EM, MD, and sequence analysis with experimental mutational studies is a better strategy.

The EM calculations are useful for predicting reasonable structures for calculating electrostatic potentials. The EM structures here compare well with existing experimental data and the differences in the electrostatic potential at the redox site of residues 43 and 44 relative to WT (Δφ_43,44) calculated from the EM structures are remarkably consistent with the changes in the experimental reduction potential relative to WT (ΔE°) (Table 5). Many energetically close side-chain conformations may indicate that more than one conformation is present in solution and that different conformation(s) may be stable in another rubredoxin.

On the other hand, the MD simulations are useful for exploring dynamical behavior such as conformational changes. When such conformational changes are present such as in the V44G and V44A mutants, the MD simulations may not be as useful in predicting the actual changes to the electrostatics of the redox site upon mutation since the transition frequencies may be sensitive to details such as the potential energy function and treatment of the environment. Overall, the electrostatic potential is very sensitive to fluctuations and so the electrostatic potentials of individual low energy conformations from the EM minimizations are more useful. However, the simulations are useful in identifying multiple conformations that may exist in the real proteins so that alternative or secondary mutations can be proposed. The MD simulations are also useful in identifying differences in water penetration since the SCSA of the redox site for the crystal and EM structures does not seem to correlate with the water penetration observed in the simulation. Since the SCSA of the redox site for even the average MD structures (Val44Gly 8.3 Ų, Val44Ala 14.0 Ų, WT 11.0 Ų, Val44Ile 11.6 Ų, and Val44Leu 9.9 Ų) are only somewhat correlated with N_w in the MD simulations (Table 4) whereas the torsions, r_Fe···44N, and Δφ_43,44 of the average MD structure are close to the averages of these quantities over the simulation (within 2°, 0.02 Å, and 30 mV, respectively), the water penetration is not reflected well by the SCSA.

Finally, the greatest utility of the sequence analysis is in indicating mutations that are likely to be successful. An amino acid that occurs frequently in a sequence determinant is likely to be robust in terms of its structure and effects. Also, neighboring residues that are frequently paired with an amino-acid type at a sequence determinant may be necessary for the success of that mutation. The sequence analyses here are consistent with the observations from the molecular mechanics calculations.

Two major questions for the rubredoxins are whether the size and reduction potential relationship observed for valine vs. alanine at residue 44 in rubredoxin holds for other nonpolar residues and what are the underlying structural determinants of the observed reduction potential shifts. Experimental measurements of the reduction potential of WT and mutant Cp rubredoxins indicate that increasing the side-chain size of residue 44 correlates only somewhat with a decrease in reduction potential, which is explained by the work here.

For the mutations to smaller nonpolar residues, experimental measurements show an increase in reduction potential with respect to WT, in agreement with the extrapolation. The analysis of both the crystal and EM structures of Val44Ala and Val44Gly shows that the backbone shifts toward the redox site, giving rise to an increase in the electrostatic potential. However, there is a small or no increase in reduction potential between Val44Ala to Val44Gly than between WT and Val44Ala. The analysis of both the crystal and EM structures indicates that the backbone in Val44Gly cannot move any closer to the redox site than the backbone in Val44Ala. In addition, the increased backbone flexibility in the Val44Ala and Val44Gly MD simulations indicates that the crystal and EM structures may not give the full picture for the protein in solution. Evidence of this flexibility has now been seen in crystal structures of WT, Val44Ala, and Val44Gly, where the standard deviations between the three molecules in the asymmetric unit are largest for Val44Gly. This implies that the discrepancies in the experimental E° of Val44Gly, Val44Ala, and even WT (Table 5) might be due to differing stabilization of the two conformations by differences in the environmental conditions. More importantly, the greater number of waters near the redox site in Val44Ala and Val44Gly may contribute to the large shift in potential between these mutants and WT. Finally, the relative lack of glycines at residues 44 and 45 in the rubredoxin sequences may be due to an evolutionary selection against backbone flexibility near residue 44.

For the mutations to larger nonpolar residues than WT, experimental measurements show relatively small changes in reduction potential with respect to WT, contrary to the extrapolation. The reduction potential of Val44Ile increases compared to WT while extrapolation would predict it to decrease. Since Val8 is in van der Waals contact with Val44 in the WT crystal structure and Val8 is not in contact with Ile44 in the Val44Ile crystal structure, water might enter through the separation and thus increase the potential (Xiao et al., 2000). However, no evidence for greater water penetration relative to WT is seen in the MD simulations. Instead, the Val44Ile EM structure indicates that the separation closes up so that the backbone moves closer to the redox site even though the isoleucine side chain is bigger than the WT valine side chain, leading to the increased potential. In the other case, the reduction potential of Val44Leu is similar to WT while extrapolation would predict it to decrease. The Val44Leu EM structure also indicates that the leucine side chain adopts a conformation that allows the backbone to move closer to the redox site leading to the increased potential. In addition, the multiple side-chain conformations of Val44Ile and Val44Leu, which are relatively close in energy for the EM structures and are accessible via transitions in the MD, indicate that the reduction potential changes may differ for different homologous rubredoxins or even under different environmental conditions since the different conformations have different backbone shifts. Finally, the lack of isoleucines and leucines at residue 44 in the rubredoxin sequences may be due to an evolutionary selection against side chains with multiple conformations.

CONCLUSIONS

Sequence determinants of reduction potentials can be understood by a combination of energetic analysis, sequence analysis, and molecular mechanics, even though no technique by itself is predictive. First, sequence determinants are identified using energetic and sequence analyses of homologous proteins. Trends in the electrostatics of experimental structures and in the sequences are found that correlate with changes in the reduction potential. Previously, alanine vs. valine at residue 44 of rubredoxin was identified by this method as the sequence determinant and the side-chain size causing a backbone shift as the underlying structural determinant for a 50-mV change in reduction potential (Swartz et al., 1996). However, prediction of new sequence determinants by extrapolations based on physicochemical properties of the side chains is unreliable even in the simple case of extrapolating the side-chain size vs. reduction potential trend in the rubredoxins. Second, the feasibility of mutations based on these sequence determinants is examined using molecular mechanics calculations and sequence analyses. EM calculations are useful in identifying changes in the protein structure due to the mutation. On the other hand, MD simulations appear most useful in detecting conformational variability and solvent penetration. In addition, sequence analyses are useful in identifying mutations that may not be successful because they rarely appear in the sequences.

Overall, the combined analysis indicates that differences in the backbone position and the water penetration rather than the side-chain size are two structural determinants of the differences in reduction potentials of the Cp mutants, although other factors such as differences in the electrostatic potential beyond residues 43 and 44, differences in structural relaxation, and differences in entropic factors are not excluded. Thus, in Val44Ala and Val44Gly, larger backbone shifts and greater water penetration than WT lead to reduction potential increases whereas in Val44Ile and Val44Leu, small shifts and similar water penetration as WT lead to small changes in reduction potential, regardless of the side-chain size. Since WT Pf and Val44Ala Cp rubredoxins show similar water penetration in simulations and experimental reduction potentials, experimental studies of Val44Ala-Gly45Pro and Val44Gly-Gly45Pro Cp mutants would show if the reduction potential shift is affected by the backbone flexibility.

Finally, two important findings about mutations to shift reduction potentials in other rubredoxins based on the combined analyses are as follows. First, mutations of residue 44 to alanine, and especially glycine, may require a secondary mutation when residue 45 is a glycine, to reduce backbone flexibility. Second, mutations of residue 44 to isoleucine or leucine may cause inconsistent changes in reduction potential in different rubredoxins because the exact sequence may lead to different environments for residue 44 that stabilize different side-chain conformations. Overall, computational methods can be useful in designing mutations for altering properties of proteins because of the complexity of protein structure and function.