Long-range protein–water dynamics in hyperactive insect antifreeze proteins
Konrad Meistera, Simon Ebbinghausa, Yao Xub, John G. Dumanc, Arthur DeVriesd, Martin Gruebelee, David M. Leitnerb, and Martina Havenitha,1
aLehrstuhl für Physikalische Chemie II, Ruhr Universität, 44801 Bochum, Germany; bDepartment of Chemistry, University of Nevada, Reno, NV 89557; cDepartment of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556; dDepartment of Animal Biology, University of Illinois at Urbana–Champaign, Urbana, IL 61801; and eDepartments of Chemistry and Physics, and Center of Biophysics and Computational Biology, University of Illinois at Urbana–Champaign, Urbana, IL 61801
Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved November 27, 2012 (received for review August 29, 2012)
Antifreeze proteins (AFPs) are specificproteinsthatareabletolower accepted molecular mechanism can explain hysteresis at fairly the freezing point of aqueous solutions relative to the melting point. high protein concentrations, but a completely local mechanism Hyperactive AFPs, identified in insects, have an especially high ability cannot fully explain how some AFPs prevent freezing at very to depress the freezing point by far exceeding the abilities of other low concentrations, when water is present in great excess. AFPs. In previous studies, we postulated that the activity of AFPs can Therefore, the role of water molecules in the hydration shell be attributed to two distinct molecular mechanisms: (i) short-range of the AFP protein has become the focus of attention (12–15). direct interaction of the protein surface with the growing ice face Evolution has produced two structurally different solutions to and (ii) long-range interaction by protein-induced water dynamics the antifreeze problem, the AFPs and AFGPs, which have similar extending up to 20 Å from the protein surface. In the present paper, terahertz excess and antifreeze activity on a mass-scaled basis. The we combine terahertz spectroscopy and molecular simulations to latter display many saccharide OH groups in a disordered manner prove that long-range protein–water interactions make essential con- (16), whereas AFP type-1 (wfAFP-1) displays a few threonine OH tributions to the high antifreeze activity of insect AFPs from the groups projecting from one side of a relatively rigid helix. beetle Dendroides canadensis. We also support our hypothesis by In our previous study on AFGP, we proposed a distinct mech- studying the effect of the addition of the osmolyte sodium citrate. anism for their antifreeze activity: using terahertz absorption CHEMISTRY spectroscopy to probe the hydration dynamics around proteins, hydration dynamics | THz spetroscopy and thus the change in the collective water network motions, we found a considerable long-range influence on the hydration dy- namics for antifreeze-active intrinsically disordered AFGP. The ntifreezeproteins(AFPs)and antifreeze glycoproteins presence of an extended dynamic hydration shell, which is asso- (AFGPs) are classes of proteins that suppress ice growth in A ciated with a retardation in the H-bond network dynamics, was organisms and thereby enable their survival in subfreezing hab- itats (1). Despite their similar function, many distinct structures proposed to be mandatory for its antifreeze activity (long-range fi fi hypothesis) (16). Studies of the short rigid α-helix wfAFP-1 have been identi ed so far. AFPs have been identi ed in several fl organisms, including polar fish (2), insects (3), bacteria (4), and revealed that inactive AFP mutants lacked a long-range in uence plants (5). Their common characteristic is the depression of the on the H-bond dynamics (17), but the long-range effect did not freezing temperatures of ice growth of a solution without de- predict the strength of the activity. Instead, we concluded that the occurrence of antifreeze activity requires short-range OH group pressing the melting point equilibrium of protein solutions. This wf nonequilibrium phenomenon leads to a difference between the binding by AFP-1, which needs to be assisted by changes in the freezing and melting temperature, which is referred to as thermal long-range hydration dynamics (17). hysteresis (TH). TH is used as a characteristic measure for an- This conclusion is in accordance with the proposal of Sharp (9), tifreeze activity of an AFP (6). AFGPs and AFPs, as extracted who states that the recognition event of AFP is more subtle, in- from the blood of polar fish, usually exhibit up to 2° of TH activity volving more than one kind of interaction. Only then would it be fi and are termed moderately active AFPs, whereas insect AFPs can possible to combine the required high af nity (i.e., by bond using exhibit over 5° of TH and therefore, are referred to as hyperactive the OH groups in AFP) with a high selectivity, which could be AFPs. The work by Raymond and DeVries (7, 8) proposed a achieved by a significant change of the hydration dynamics around mechanism in which freezing point depression is achieved by an the ice-binding site. Retardation of the H-bond dynamics at the adsorption-inhibition mechanism, in which the proteins recognize OH binding sites could reduce the entropic cost for binding of ice and bind “quasiirreversibly” to an ice surface, thereby preventing crystals and thus, could also further assist a local mechanism. growth of ice crystals. The adsorption of the protein is thought to Together with other adaptations, such as gut voiding and prevent macroscopic ice growth in the hysteresis gap, but micro- osmolyte production, hyperactive insect AFPs allow insects to scopic growth occurs at the interface in the form of highly curved survive even at temperatures as low as 243 K (−30 °C) (1). Their fronts between adsorbed antifreeze molecules. This effect will increased hysteresis activity at a comparable binding affinity to cause a decrease of the local freezing temperature because of ice (18) must be attributed to a special enhancement effect. The the Kelvin effect, while leaving the melting temperature relatively need for a new molecular mechanism that acts at low protein unaffected (7). As recently pointed out in the work by Sharp (9), concentration is supported by the recent finding of a moderately antifreeze activity involves one of the most difficult recognition active plant AFP that binds to both basal and primary-prism planes problems in biology, the distinction between water as liquid and of ice, normally a hallmark for hyperactive insect AFPs (19). ice. The initially proposed mechanism builds on a local mech- anism. In particular, threonine (Thr) residues were proposed to play a decisive role: their hydroxyl groups were thought to be Author contributions: M.G., D.M.L., and M.H. designed research; K.M., S.E., Y.X., J.G.D., and responsible for the high affinity required for binding of the AFP A.D. performed research; J.G.D. contributed new reagents/analytic tools; K.M., S.E., Y.X., to the ice crystals. Mutations in which Thr was replaced by Ala A.D., M.G., D.M.L., and M.H. analyzed data; and K.M., Y.X., A.D., M.G., D.M.L., and M.H. were ambiguous in the conclusions that could be drawn: in some wrote the paper. cases, the mutation Thr→Ala was found to decrease TH activity The authors declare no conflict of interest. (for AFP I) (10), whereas for AFP III, the opposite mutation, This article is a PNAS Direct Submission. Ala→Thr, was found to decrease activity (11). This generally 1To whom correspondence should be addressed. E-mail: [email protected].
www.pnas.org/cgi/doi/10.1073/pnas.1214911110 PNAS Early Edition | 1of6 Downloaded by guest on September 23, 2021 decreasing the temperature from 293 to 278 K, we find a shift of cmax from ca.12toca. 5 mg/mL. This shift indicates an increase in the size of the dynamic hydration shell for lower temperatures from ca. 20 to 27 Å (i.e., from seven to nine hydration layers). A similar behavior has been previously reported for AFGP (16). Previous CD and IR spectroscopic studies revealed that changes intemperatureofDAFP-1solutionhaveanegligibleeffecton secondary structure. Only a slight increase in the structural order and rigidity of the β-helix was found on lowering the temperature (29). Similar results were found for TmAFP and cfAFP using NMR techniques (30). Here, conserved side chains, like the thre- onine residues of the ice-binding plane, also revealed an increased rigidity when lowering the temperature (31).
Simulation. To provide a more complete molecular-level picture, we have further explored the underlying molecular and hydrogen bond dynamics by accompanying molecular dynamics (MD) simulations. In Fig. 3, we compare the calculated power spectra (i.e., the predicted vibrational density of states) for water mole- cules in the hydration layer around the protein DAFP-1 and bulk water at 250 and 300 K. We observe clear differences in the Fig. 1. Model of DAFP-1 tertiary structure from D. canadensis. DAFP-1 consists β fl spectral density. At both temperatures, we predict an increase in of seven repeats, forming a -helical right-handed helix that forms a at, the density of states for water in the hydration layer compared threonine-rich ice-binding site. Positions of threonine residues are shown with bulk water in the frequency range from 2.5 to 3 THz and in red. Labels indicate positions of mutation sites. above, consistent with our experimental results. The difference between the hydration water and the bulk water spectrum is more In this study, we have focused on the investigation of a hyper- noticeable when the temperature is lowered, which is also in good active AFP from the fire-colored beetle Dendroides canadensis agreement with our experimental results. Note that 250 and 300 K (DAFP-1) as shown in Fig. 1. Hyperactive insect AFPs, such as were chosen to examine temperature-dependent effects on the DAFP-1 or TmAFP from the mealworm Tenebrior molitor,are vibrational density of states at two different temperatures. These temperatures allowed us to compare the temperature trend of right-handed β-helical proteins with nearly identical 12- or 13-aa long-range solvation effects with the experimental temperature repeats (20, 21). By a combination of terahertz spectroscopy and trend. We make no attempt to simulate freezing of water, which molecular dynamic simulations, we can show that long-range fi – is very dif cult to achieve in simulations (32). Moreover, there protein water interactions play an important role in explaining would be no direct comparison with experimental data. the hyperactive antifreeze activity of insect AFPs. To evaluate the influence of the different surfaces of the protein Given that all AFPs, including the hyperactive insect antifreeze, fi fi on the hydration dynamics, site-speci c hydrogen bond correlation arebelievedtobindtoice,we,thus,con rmed our previous functions were calculated. Earlier studies of hydrogen bond life- prediction that a long-range dynamic hydration shell plays an times between water molecules and the protein HP-36 have important role in insect AFPs, enhancing their activity at very revealed a significantly heterogeneous distribution of hydrogen low concentrations. The importance of solvent dynamics for bond lifetimes, exhibited around different helices of the protein biological function has been pointed out before in the work by (33, 34). Experimental proof for this fact has been provided Frauenfelder et al. (22), which proposed that conformational motions of folded proteins are slaved to the solvent. However, numerous studies have pointed out the impact of the protein on the hydration water (23–25). AFPs show an increased activity on the addition of osmolytes (26,27).Themolecularmechanismforthisincreaseisstilla matter of discussion. We, therefore, investigated the effect of adding sodium citrate, which increases the TH from 1.2° (no citrate) to 6.8° (0.5 M citrate) at the same DAFP concentration (28). Using terahertz absorption spectroscopy, we found a cor- responding increase in the range of retarded hydration shell, further supporting the importance of a long-range mechanism that alters solvation water dynamics quite far from the surface of the hyperactive AFP. Results Experimental. All measurements were carried out above the freezing point at 293 and 278 K. This temperature range prevented the problem that condensation at the cell or small ice crystal formation might lead to systematic experimental errors. However, the long- range effect on the water dynamics is observed to become more prominent when the temperature is lowered from 293 to 278 K, and a similar trend is seen in the simulation. It, thus, seems that long- range activity is optimized at lower temperatures; however, it is Fig. 2. Concentration-dependent terahertz absorption of DAFP-1 (relative already present at temperatures close to the freezing point. Δα to pure water and integrated between 2.4 and 2.7 THz). Measurements were Fig. 2 shows the difference, , in terahertz absorbance carried out at 293.15 K (20 °C) ± 0.5 K (black data points) and 278.15 K of DAFP-1 dissolved in water. For the hyperactive insect AFP (5 °C) ± 0.5 K (blue data points). DAFP-1 shows a concentration-dependent −1 DAFP-1, we observe a terahertz excess of 15 cm , which is the excess of terahertz absorbance that shifts to lower protein concentration at largest Δα-value observed for AFPs investigated thus far. When the lower temperature (blue vs. black dashed vertical lines).
2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1214911110 Meister et al. Downloaded by guest on September 23, 2021 We propose that the pronounced long-range retardation of H-bond dynamics as found experimentally and in the simulation is responsible for the high hysteresis activity of insect AFPs. The simulation also supports the proposed mechanism involving an entropic favorable docking near the binding plane.
Citrate Buffer. It is well-known that the antifreeze activity can be enhanced significantly by the addition of sodium citrate, leading to a sixfold increased TH activity for DAFP (28). Terahertz ab- sorption measurements in Fig. 5 show that, on addition of 0.5 M sodium citrate, cmax is decreased from ∼12 to ∼4mg/mL,which corresponds to an increase in the size of the dynamic hydration shell to 27 Å. The addition of citrate is, thus, found to increase the distance over which the protein can affect hydrogen-bonding dy- namics and simultaneously increase TH. Accompanying MD simulations predict increased hydrogen bond lifetimes in the presence of sodium citrate, especially around the ice-binding face. As is shown in Fig. 3, the calculated power spectra show an enhancement of the terahertz excess when sodium citrate is present, particularly at lower temperature. The presence of so- dium citrate influences the hydrogen bond lifetimes and increases the time for hydrogen bond rearrangement on both the binding and nonbinding planes, which is displayed in Fig. 4. Nevertheless, hydrogen bond lifetimes on the binding plane remain significantly larger than on the nonbonding plane. CHEMISTRY
Fig. 3. Computed power spectra So for water molecules at 300 (Upper) and 250 K (Lower). Solid black curve, hydration water in pure aqueous solution; solid green curve, hydration water in citrate solution; dotted black curve, bulk water.
before by quasielastic neutron scattering, which showed a hetero- geneous dynamic signature for amphiphilic peptides (35). For proteins, the work by Zhang et al. (36) was able to map the heterogeneous distribution of the coupled solvation–protein fluc- tuations at tryptophan probes using coherent femtosecond laser preparation. Fig. 4 shows a remarkable difference between the water dy- namics in the vicinity of the binding and the nonbinding planes of DAFP-1. Both hydrogen bond correlation functions, C(t), are nonexponential, with C(t) decaying over longer times for water molecules near the binding plane than water molecules near the nonbinding plane: C(t) reaches a value of 0.2 for hydrogen bonds between water and the atoms of the ice-binding plane at 72 ps compared with 45 ps for bonds between water and the atoms of the nonbinding plane. These values can be compared with the value of 23 ps for hydrogen bonds formed between water molecules in the bulk. The hydrogen bond lifetimes between water molecules and the protein are heterogeneously distributed over the surface of the protein, with the longest lifetimes on average found on the ice- binding plane. In general, we find a clear trend of retardation of Fig. 4. Hydrogen bond lifetime correlation functions C(t). C(t) for water the hydrogen bond dynamics, with a gradient to the binding plane. molecules around the binding (solid black) and nonbinding plane (solid gray) of DAFP-1 at 300 K. (Upper) C(t) is also plotted for hydrogen bonds between The hydrogen bond lifetime is greater by about a factor of three water molecules at the binding plane (green) and nonbinding plane (blue) compared with bulk water. Interestingly, this heterogeneity is of the WT in sodium citrate solution. (Lower) C(t) is also plotted for the mutant correlated with antifreeze activity, which is further supported discussed in the text in both the binding (black dot dashed line) and nonbinding by the mutation studies discussed below. planes (gray dot dashed line).
Meister et al. PNAS Early Edition | 3of6 Downloaded by guest on September 23, 2021 distribution of the hydration dynamics) (38). Site-specific muta- tion has a clear nonlocal effect on the entire ice-binding plane. Based on these results, we conclude that, for the case of the insect protein, the long-range influence of the hydrogen bond dynamics facilitates the suppression of freezing. Discussion Our experimental and computational results provide evidence that changes in the fast dynamics at the water–protein interface area play an important role in the molecular mechanism of antifreeze hyperactivity of DAFP-1. Here, evolution has realized a concept in which a local binding site providing fixed OH groups for binding with high affinity is most efficiently supported by a long-range effect on the retardation in the H-bond dynamics. Insect AFPs, such as DAFP-1, have a well-defined surface including ice-binding and nonbinding sites. The threonine-rich ice-binding site consists of regularly spaced hydroxyl groups, which can form strong bonds to water. Therefore, one might expect that antifreeze activity is dominated by short-range H bonds at the binding site. Instead, we found, experimentally and theoretically, evidence for an addi- Fig. 5. Concentration-dependent terahertz absorbance of DAFP-1. The tional long-range influence on the hydration dynamics. MD sim- black data points are in water, and the green data points are in 0.5 M ulations indicate that the retardation is most pronounced in the
Na3Citrate. The corresponding buffer absorbance was subtracted to yield vicinity of the ice-binding site. Δα = α − α α Protein+buffer Buffer at each protein concentration. was integrated Therefore, we propose a long-range retardation of the H-bond from 2.4 to 2.7 THz. dynamics with a gradient to the ice-binding site. A similar gradient in the H-bond dynamics was found for enzymes near the catalytic site (39). Finally, we investigated the effect of adding sodium citrate on MD simulations indicate a retardation of H-bond dynamics at other AFPs. Fig. 6 shows the results of TH and terahertz meas- the ice-binding face on addition of sodium citrate, which goes along urements for AFGP and wfAFP-1. Both proteins show an increased with an enhancement of the DAFP-1 antifreeze activity. Based on antifreeze activity on addition of sodium citrate. In addition, we find the experimentally determined change in the terahertz absorption, — forAFGPashiftofcmax the concentration at which the terahertz we estimate an increase in the size of the dynamic hydration shell excess reaches its maximum—to lower protein concentration. This from ca. 20 to 27 Å. Citrate is known to interact with DAFP-1 shift indicates an increase in the size of the dynamic hydration shell, through the guanidinium group of arginine residues (21). How- which is in good agreement with the initial hypothesis that the ever, these interactions are known to exist along with hydrophobic antifreeze activity of AFGP is mainly accomplished by a change in interactions and/or hydrogen bonds with other amino acids. The the hydration dynamics (long-range effect). simple ion pairs between guanidinium cations and citrate anions For AFP-1, we postulated another mechanism, in which the are not very stable in aqueous solution, and water molecules will strength of the antifreeze activity depends mainly on the exact compete for the formation of ion pairs by solvating individual ions. positioning of the OH groups (17). In agreement with this previous Although for DAFP-1 and AFGP, we find a significant increase fi statement, we nd experimentally that the size of the dynamic in the size of the dynamic hydration shell on addition of sodium hydration shell remains constant on addition of sodium citrate, citrate, no significant change in the size of the dynamic hydration whereas the TH is increased in contrast to AFGP and DAFP-1. shell is found for AFP type 1. For all three AFPs, the addition Hence, a consistent picture emerges where short- and long-range of sodium citrate results in an increase of TH by factors of six mechanisms make different contributions to the overall antifreeze (DAFP-1), three (AFP-1), and two (AFGP). mechanism, depending on the class of AFP that we studied. For wfAFP-1, we propose that the specific binding of OH groups plays the decisive role. Thus, the strength of the antifreeze activity fl Mutation Studies. To gain more insight into the in uence of for AFP-1 will depend on the rigidity of the helix or proper DAFP-1 on hydrogen bond lifetimes in the dynamic hydration positioning of the threonine. For AFGP, which is intrinsically fi shell, we address speci cally the question of how the hydration less ordered, the long-range effects are more important. The dynamics are affected by mutations in the vicinity of the threo- most efficient antifreeze effect for hyperactive AFP relies on the nine-rich ice-binding plane vs. the nonbinding sites. As described optimization of both effects (short range as well as long range). Materials and Methods in , threonine 26, 39, 41, and 63 were mutated In summary, we have now investigated the three major classes to tyrosine, a mutation (called 4TXY) that has been shown ex- of AFPs: AFGP, wfAFP-1, and the insect DAFP-1. Based on the perimentally to result in 90% loss of TmAFP activity (37). The results of experimental and simulation studies, we have postulated simulated hydrogen bond correlation function, plotted in Fig. 4, two distinct mechanisms for antifreeze activity that can assist or reveals that the water around the ice-binding plane of mutant enhance antifreeze activity. Nature is probably more inventive 4TXY is much more mobile than in the WT, and the hydrogen than initially thought and makes use of short- and long-range bond dynamics over the binding and nonbinding plans are quite water perturbation to varying degrees in different classes of AFPs. similar to each other, in contrast to the WT. Mutation of the four threonine residues to tyrosine, thus, seems to have a nonlocal, Materials and Methods collective effect on water dynamics in addition to any direct Materials. DAFP-1, the predominant hemolymph AFP of the beetle D. canadensis effect on ice binding that may occur. We note that we found a fi Choristoneura (including a his-tag), was expressed and puri ed as previously described (27). similar trend for another AFP from spruce budworm Antifreeze glycoproteins were purified from the Antarctic nototheniid toothfish fumiferana , which also contains a threonine-rich ice-binding plane. Dissostichus mawsoni. AFP type I (HPLC6 from winter flounder Pleuronectes In that case, four point mutations, which are found experimentally americanus) was synthesized by GenScript. Trisodium citrate (trisodium salt) to dramatically lower antifreeze activity, lead to a similar trend was purchased from Sigma Aldrich. Aqueous solutions were prepared using inthehydrogenbonddynamicsasweobservehereforDAFP-1 Baker HPLC analyzed water. (i.e., the hydrogen bond dynamics around all planes are similar for the mutants, whereas they are significantly slower around the ice- Terahertz Measurements. Terahertz absorption spectroscopy measurements binding plane for the WT, thereby giving rise to a heterogeneous were carried out using our p-Germanium difference laser spectrometer.
4of6 | www.pnas.org/cgi/doi/10.1073/pnas.1214911110 Meister et al. Downloaded by guest on September 23, 2021 CHEMISTRY
Fig. 6. Concentration-dependent terahertz absorbance (Upper) and freezing point hysteresis (Lower) of AFP-1 (Left) and AFGP (Right). The black data points
are in water, and the green data points are in 0.5 M Na3Citrate. The corresponding buffer absorbance was subtracted to yield Δα = αProtein+buffer − αBuffer at each protein concentration. α was integrated from 2.4 to 2.7 THz.
Terahertz absorption spectroscopy was used as a sensitive tool to characterize decreases again at a characteristic protein concentration cmax (44). In our pre- the fast collective water network motions in the dynamic hydration shell of vious study, we could explain this general phenomenon by a shift in the vi- proteins (40, 41). brational density of states of the hydration water in the vicinity of the protein We recorded the change of the integrated absorption coefficient of the compared with bulk water (dynamic hydration shell). The increase in the ab- sample in the spectral range from 2.1 to 2.8 THz. The experiments were sorption coefficient could be related to a retardation of the H-bond dynamics carried out using our terahertz difference spectrometer with a double-beam by the protein compared with bulk water (45). Based on cmax, the size of the configuration with sample and reference cell to directly measure the change dynamic hydration shell can be estimated. of the intermolecular water network vibrations induced by the AFP sample (16). We analyze the transmitted terahertz radiation through the AFP sam- Thermal Hysteresis Measurements. TH was determined using a Clifton nanoliter ple solution in one channel of the setup while simultaneously measuring the osmometer as described previously (17). Resulting data were fitted to the
buffer solution as a reference under identical conditions (temperature and Langmuir equation (ΔT/ΔTmax) = (c/c1/2)/[(c/c1/2) + 1], where c1/2 corresponds humidity). The humidity was controlled to be <3%, and the temperature was to the AFP concentration at half-maximum. fixed at 293 ± 0.05 K. In general, the transmitted intensity I(n) and hence, the absorption of a sample can be described by Beer’slaw: Molecular Dynamic Simulations. The starting structure of DAFP-1 was created from a homology model of a T. molitor AFP, TmAFP (Protein Data Bank ð Þ¼ ð−αð Þ Þþ ; I n I0 exp n d c ID code 1EZG), by using the 3D-JIGSAW online structure prediction tool. Constraints were applied to all bonds to hydrogen with the SHAKE algo- with I0, α(n), d, and C corresponding to the intensity of the laser source, the absorption coefficient of the sample, the layer thickness of the sample, and rithm. Periodic boundary conditions were used. All MD simulations were the detector offset, respectively. We have recorded the changes in the ter- performed in the canonical (NPT) ensemble with the GROMACS software ahertz absorption of the solvated DAFP-1, AFGP, and AFP-1 in dependence of package (46). the protein concentration and the temperature. Furthermore, we have in- To investigate the specific role of chemical composition of the site on vestigated the effect of adding 0.5 M sodium citrate. Assuming a two- the water dynamics and hydrogen bond lifetimes, four threonine residues component model with protein and bulk water, an increase in protein (Thr26, -39, -41, and -63) on the binding plane were mutated to tyrosines concentration is expected to result in a decreasing absorption coefficient, using Swiss PDB Viewer (47). These mutations have been reported previously called terahertz defect (42, 43). However, at low protein concentrations, we to significantly reduce the antifreeze activity of the protein (37, 48). observe for solvated proteins an initial increase in the absorption co- Both the WT and mutated structure were first minimized for 5,000 steps efficient, the so-called terahertz excess, before the terahertz coefficients with the steepest descent algorithm using the AMBER03 force field (49) after
Meister et al. PNAS Early Edition | 5of6 Downloaded by guest on September 23, 2021 its solvation in a 60-Å cubic water box of TIP5P water model. To prepare Power spectra were obtained by Fourier transform of CV(t). The power 0.5 M sodium citrate solution of DAFP-1, 65 citrate anions and 195 sodium spectra correspond to the vibrational density of the water. The vibrational ions were added into the water box as cosolvents, with additional sodium density of protein molecules has been discussed in detail elsewhere (50). ions added to neutralize the system. Then, the systems, each of which con- Hydrogen bond time correlation functions, CHB(t), were computed for tained ∼6,700 water molecules, were equilibrated for 400 ps. For the first bonds between water molecules and the protein at 300 K. CHB(t)isdefined 100 ps, the positions of the proteins were restrained, and in the latter 300 ps, as the probability that, if a hydrogen bond between donor D and acceptor A they were released. After equilibration, trajectories of 5 ns were obtained exists at t = 0, then it still exists at time t, even if the bond broke at some at 300 and 250 K with a Nosé–Hoover thermostat. Nonbonded interactions intermediate time (51). We adopt a standard criterion for hydrogen bonds were gradually brought to zero by a shift function for the electrostatics (i.e., a donor-acceptor distance of 3.5 Å and a D-H-A angle greater than as well as a switch function for van der Waals interactions between 10 and 12 Å. All simulations were carried out by integrating Newton’s equations of 150°) (51, 52). motion with the Verlet algorithm and 1-fs time steps. The system coordinates and velocities were stored every 10 fs. The velocity autocorrelation function ACKNOWLEDGMENTS. We thank E. Bründermann for the initial setup and was computed as C (t) =
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