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Dispersion Forces and the Molecular Origin of Internal Friction in Protein Sashikantha Reddy Pulikallu, Dasari Ramakrishna, and Abani K Bhuyan Biochemistry, Just Accepted Manuscript • DOI: 10.1021/acs.biochem.6b00500 • Publication Date (Web): 01 Aug 2016 Downloaded from http://pubs.acs.org on August 2, 2016
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Biochemistry
Dispersion Forces and the Molecular Origin of Internal Friction in Protein
Reddy Pulikallu Sashikantha, Dasari Ramakrishna, and Abani K. Bhuyan School of Chemistry, University of Hyderabad, Hyderabad 500 046, India
Corresponding author:
Abani K. Bhuyan School of Chemistry, University of Hyderabad Hyderabad 500 046, India
[email protected] Phone: 91-40-2313-4810 Fax: 91-40-2301-2460
Running title: Molecular Origin of Internal Friction
Keywords:
internal friction; dispersion forces; aromatic ring-flip; collective motion; volume fluctuation
ABSTRACT
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Internal friction in macromolecules is one of the curious phenomena that control conformational changes and reaction rates. It is held here that dispersion interactions and London-van der Waals forces between nonbonded atoms are major contributors to internal friction. To demonstrate so, the flipping motion of aromatic rings of F10 and Y97 amino acid residues of cytochrome c have been studied in glycerol-water mixtures by cross relaxationsuppressed exchange NMR spectroscopy. The ring-flip rate is highly overdamped by glycerol, but this is not due to the effect of protein-solvent interactions on the Brownian dynamics of the protein, because glycerol cannot penetrate into the protein to slow the internal collective motions. Sound velocity in the protein under matching solvent conditions show that glycerol exerts its effect by rather smothering the protein interior to produce reduced molecular compressibility and root-mean-square volume fluctuation (δVRMS), implying increased dispersion interactions of nonbonded atoms. Hence, δVRMS can be used as a proxy for internal friction. By using the ansatz that internal friction is related to nonbonded interactions by f(n)=f0+f1n+f2n2+⋅⋅⋅, where the variable n is the extent of nonbonded interactions with fi coefficients, the barrier to aromatic ring rotation is found to be flat. Also interesting is the appearance of a turnover region in the δVRMS dependence of the ring-flip rate, suggesting anomalous internal diffusion. It is concluded that cohesive forces among nonbonded atoms are major contributors to the molecular origin of internal friction.
Keywords
internal friction, dispersion forces, aromatic ring-flip, volume fluctuation
INTRODUCTION 2 ACS Paragon Plus Environment
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Internal friction refers to a phenomenon by which the energy and momentum of intramolecular motion is dissipated into internal degrees of freedom. Although the existence of the phenomenon has been realized since early studies of polymer viscoelasticity,1−3 its definite meaning and manifestations in protein dynamics remain unclear. A large number of studies during the past 20 years have invoked internal friction to model kinetics and dynamics of the protein folding reaction. Earlier experimental work using viscogens have found folding rate damped either in excess of what Kramers equation would,4 indicating the presence of extrasolvent friction, or only in accord with the inverse relationship between rate and solvent friction.5,6 Theory and simulations have identified the front factor of the general transition state equation with inverse internal friction.7 This friction that arises from intersegmental hindrances to chain motion is thought to grow stronger with native-like conditions so as to limit the folding rate, a manifest of which is the chevron rollover observed for many proteins.7-9 Reports of brake on configurational reorganization due to energetics of intrachain interactions,10 and the correspondence of energy landscape roughness and internal friction11-13 have appeared. Structurally, internal friction is suggested to originate from misdocking of preformed structural elements12 or intersegmental nonnative interactions which slow diffusive motion over the folding transition barrier.14 Some experimental studies have sought
to
understand
the relevance
of internal friction
in
early chain
reconfiguration,13,15-19 and its localization along the protein folding reaction path,20 and transition-path time.21 More recent reports from computer simulation and theory suggest that helix formation during protein folding that requires large changes in dihedral angle is associated with substantial viscosity dependence, attributing torsion angle isomerization to one of the structural sources of internal friction.15,16,22 It is also shown that the extent of 3 ACS Paragon Plus Environment
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internal friction varies from one protein to another, and the manifest within a given protein varies with solution and temperature variables.13,21,23 Such studies carried out in the perspective of the protein folding reaction establish that an extrasolvent friction, meaning not related to solvent-coupled diffusion of chain segments, critically sets the folding time of some proteins. The literature above largely report on manifestations in folding view rather than the meaning, mechanism, and the molecular origin of internal friction, and the effects thereof on intramolecular motions in native proteins. Because internal motions are inseparably linked with functional activities of proteins and enzymes,24-26 insight into the motion-friction relationship is clearly necessary. Such motions are generally referred to as collective motions involving movement in unison of a set of covalently or non-covalently bonded neighboring atoms, in contrast with fast and random atomic fluctuations that are presumably not relevant to functional activities.24 Collective motions are not random, not modeled by Brownian dynamics, and do not trigger large-scale conformational changes. The rapport of internal friction and intramolecular collective motion is analyzed here by monitoring the rate of aromatic ring flips in native cytochrome c placed in glycerol-water solutions. Ring isomerization in protein-like dense systems often engages parts of the chain backbone,27,28 offering a collective type of large-amplitude motion to studying the connection of intramolecular dynamics to internal friction. The rationale of using glycerol is to smother the protein so as to increase the interatomic cohesion strength, which we consider a scale for intramolecular friction.
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MATERIALS AND METHODS All experiments were done at 25ºC in 20 mM phosphate buffer. NMR determination of ringflip rate constants followed procedures detailed earlier,29,30 and are briefly described in Supporting Information. Solution density and velocity of sound wave at ~4.8 MHz were measured using a Anton paar vibrating tube densitometer. The details of the procedure and analysis of primary data are provided in the Supporting Information.
RESULTS AND DISCUSSION Implication of Internal Friction in Aromatic Ring Rotation in Glycerol-Water Mixture. The ring flip rate is determined to a high degree of accuracy by NMR exchange spectroscopy (EXSY), which is essentially the same as the transient nuclear Overhauser spectroscopy (NOESY), except that the mixing period in the latter is filled by a train of 90º pulses as described earlier.29,30 Cross relaxation of dipole-coupled spins is suppressed, and the exchange peaks associated with aromatic rings are quantified along with the corresponding diagonals in a series of EXSY spectrum of different mixing time.31 The process was repeated with the protein placed at different percent-glycerol in the solution. The NMR spectra and data used for the extraction of ring-flip rates are supplied in the Supporting Information (Figures S1 and S2). Observed changes in the ring-flip rate constants (kflip) for C2,6 and C3,5 ring protons of F10 and Y97 in the water-glycerol (Figure 1) might initially convey as though the bulk viscosity retards the flip motion. The results may indeed be treated with an empirical Kramers-type equation, for example,32,33 5 ACS Paragon Plus Environment
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flip ≈
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∆ exp − (1) +
where, η is solvent viscosity with viscosity exponent n, σ is interpreted as internal viscosity or internal friction, and ∆G is the transition barrier height. The σ-values of 1.0 and 2.9 cP obtained from fits to F10 and Y97 data, respectively, suggest the operation of a non-solvent internal viscosity, which is higher in the Y97 ring site. Values of n (3.8 and 4.5 for F10 and Y97 ring protons) also indicate exceedingly overdamped ring-flip motion, suggesting the presence of excessive solvent friction that slows the flip. However, the F10 and Y97 rings are only marginally solvent exposed (Figure 1), so the solvent friction should affect the ring isomerization little. While the C2,6 and C3,5 protons of F10 register only slight solvent accessibility, the corresponding protons of the Y97 ring are almost entirely shielded from the solvent (Figure 1). Thus, the interpretation of n is not straightforward here, and for that matter even σ is not a unique measure of internal reaction friction.10 All that one could make from the present results is excessive damping of ring rotation. It is also clear that a consideration of the effect of glycerol and bulk viscosity on the ring dynamics is of little help, because the flip motion under consideration is entirely intramolecular and glycerol cannot penetrate into the ring vicinity to produce direct frictional effect. It appears that overriding internal friction slows down the rotational motion of F10 and Y97 rings. This observation is consistent with the recognition for a long time that ring rotation dynamics are retarded by internal friction. In seminal studies of Weber and colleagues,
34-36
fluorescence polarization of aromatic side chain fluorophores in glycerol-water mixture was found to decrease with increasing temperature. They proposed that frictional resistance to ring rotation in proteins arises from a small number of protein atoms in the fluorophore
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proximity.36 This friction must originate internally because glycerol would have little access to fluorophore sites in the protein interior. Damped ring-flip motion has also been observed in several earlier high-pressure NMR studies,37-40 and the observations are consistent with results obtained here. Both pressure and glycerol decrease the compressibility of the protein causing an increase in internal friction, and hence damped ring rotation. The high-pressure results have also provided quantitative information about void spaces in the ring vicinity and activation volume of rotational motion.37,40
Compressibility of Cytochrome c in Glycerol-Water Mixture. The direct effect of glycerol in the protein-water-glycerol system is localized at the protein-water interface due to preferential hydration of protein and exclusion of glycerol.41,42 These surface interactions drive the ensemble of native protein structures to more ordered, compact, and less flexible states42 that exhibit higher intramolecular density and decreased compressibility.43-46 Because intramolecular motions such as ring rotation dynamics studied here are related to internal friction, it is useful to cast the influence of glycerol in terms of density and compressibility43 rather than considering the effect of external bulk viscosity itself. The idea here is to find a functional dependence of internal friction on volume fluctuation of the protein that can be obtained from compressibility measurements by the exact thermodynamic relation,47-49 < >= (2) where , VM, and βT are mean-square volume fluctuation, intrinsic volume,49 and bulk isothermal compressibility, respectively. The intrinsic volume obtained from the sum of van der Waals volume of all the protein atoms and intramolecular void spaces is approximately 7 ACS Paragon Plus Environment
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1.65×10-20 cc for cytochrome c. This value is close to the configurational average volume (1.56×10-20 cc) calculated by the use of apparent specific volume, which is directly determined from experimental data. Values of obtained by using 1.56×10-20 cc in calculations shown here are within 4% of the values yielded by 1.65×10-20 cc. Since the value of βT is closely approximated by the adiabatic compressibility of the protein solution (βs),48 we carried out compressibility measurement of the protein solution at glycerol concentrations matching those used for ring-flip experiments so as to obtain values of corresponding to ring-flip rates. A vibrating tube density meter was used to measure density of and sound velocity in water-protein-glycerol solutions prepared in 20 mM phosphate, 25ºC, the protein concentration being held uniform at 50 µM. Primary data, including solution density, and partial specific volume and molal adiabatic compressibility, are provided in the Supporting Information (Figure S3). The viscosity dependence of adiabatic compressibility determined for the solvent (βso), the solution (βs), and the protein (βsp) are shown in Figure 2. To calculate the value of βsp, the compressibility of the water hydrating the protein has been taken equal to 18×10−12 cm2 dyne−1, which is the compressibility of ice.48,50 This assumption may seem reasonable due to facts that waters in inner hydration shells are largely bound to the protein, generally denser than the bulk water,51,52 and have higher residence times.53 The compressibility decrease with glycerol viscosity that appears to follow a power law dependence (Figure 2) should have contributions from average compressional relaxation time of liquid glycerol, and its effect on water structure, and hydration and compressibility of the protein. The protein compressibility (βsp) is lower than that of the solvent (βso) by 3.6-
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fold uniformly across the glycerol viscosity scale (Figure 2a,c) which must be due to higher mean density of the protein. For the protein alone though, βsp decreases by 1.65-fold in the 060% range of glycerol (Figure 2c), which arises from glycerol-driven changes in both hydration48,54 and intrinsic protein compressibility. Because lower compressibility is related to diminished atom density fluctuations or constrained conformational freedom,55,56 the results suggest a smothering effect of glycerol on the protein molecule which now experiences greater interatomic interactions.
Increased London-van der Waals Bonding at Higher Glycerol. Contemplating on the results above, we look at the glycerol dependence of sound velocity in the protein molecule by using the values of βsp =
"ij 1 = (3) sp !sp !sp
where the equilibrium density ρsp~1.42 for a protein the size of cytochrome c,57 and eij is an average elasticity parameter for all i and j atom pairs. The significant increase in sound velocity across the glycerol range (Figure 3) must be due to higher elasticity in regions of diminished atom density fluctuations. For the non-bonded atoms, the elasticity may be thought to increase through rapid attraction and repulsion between atoms via high-frequency fluctuations of local multipoles. In essence, this promotes nonbonded atom interactions or non-covalent bonding by London-van der Waals dispersion forces.58
Nonbonded Atom Interaction and Internal Friction. The glycerol dependence of the two sets of results − ring-flip collective motions and adiabatic compressibility − are 9 ACS Paragon Plus Environment
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correlated in Figure 4, which plots the variation of the ring flip rate constants, kflip, for 2,6 and 3,5 ring protons of F10 and Y97 of cytochrome c with inverse root mean square volume fluctuation (δVRMS−1) determined by Equation 2. The value of kflip dampens 10-fold for a decrease of δVRMS by 5.4 cc mol-1, which must be due to a proportional decrease in molecular compressibility or an increase in mass density. This increased mass density can be phenomenologically viewed as the major contributor to internal friction that dampens the ring-flip rate. The rationale is the increase of dispersion interactions of nonbonded atoms in the highly dense molecule. We ansatz the dependence of internal friction on nonbonded atom interactions by the function59 -
&(') = &( + &) ' + & ' + ⋅⋅⋅= + &, ', (4) ,.(
where the variable n is a positive number representing the degree or the extent of nonbonded interactions, and the coefficients fi are real numbers with the stipulation that the last coefficient is positive. It is important to note that this n is completely unrelated with the n found in Equation 1, where it was used to denote solvent viscosity exponent. Equation 4 simply means that the extent of internal friction will increase with higher values of n. In the limit f1, f2, …=0, f(0)=f0, which would be the case if there were no nonbonded interaction (n=0). This limit holds when the protein is absolutely unfolded, where the chain density approaches zero and there is no internal friction. When the values of n becomes larger, lim→3 &(') = ∞, with the last coefficient positive. This limit would hold for protein native state, where large number of nonbonded interactions produces sizable internal friction. Now the volume fluctuation, internal diffusion coefficient (Dint), and the friction coefficient represented by the function f(n) are related as 10 ACS Paragon Plus Environment
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RMS ∝ 6int ~
(5) &(')
meaning that one is scaling the values of kflip with internal friction f(n)∝1/δVRMS in Figure 4a. Since reaction rate coefficients in general are expected to decrease due to friction, the dependence of kflip on internal friction could be evaluated by flip ≅
:( exp − (6) &(')
where the parameter C contains details of the potential energy surface, and E0 is the average barrier height separating the two rotamers of the ring. Because f(n)∝δVRMS-1 and kflip∝f(n), the equation relates kflip to δVRMS through f(n). Both kflip and δVRMS are experimentally determined, and the dependence of the latter on the extent of nonbonding interaction n is expressed by the f(n) function. In other words, n is a measure of δVRMS, and hence the experimental values of δVRMS serve for values of n. The data in Figure 4a are simulated by this equation, where values of C and E0 change little for truncation of the f(n) function after the second or the third term, although the sharpness of the curve increases with the degree of the polynomial. The fits shown in Figure 4a are obtained with f(n)=f0−f1n+f2n2, where the negative value for the coefficient f1 is data-driven. Interestingly, values of E0~10.5 kcal mol-1 and C~1×108 mol cc-1 s-1 indicate a fairly sizable but flat barrier (Figure 4b), which is a reflection of the fact that ring-flip dynamics are exceedingly overdamped. To provide a physical picture, the rate of ring rotation is proportional to δVRMS whose magnitude is inversely related to the extent of nonbonding interaction n, and thus the variable n enters into the ring-flip rate equation through the function f(n). Hence, δVRMS is a scale for internal friction. 11 ACS Paragon Plus Environment
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Is Internal Diffusion Anomalous? An interesting feature of the kflip vs δVRMS-1 curve is the appearance of a turnover region, on either side of which the kflip decreases nonlinearly (Figure 4). Since conditions required to producing bulk viscosity less than that of the aqueous solution is difficult to achieve, no data point is available for lower values of δVRMS-1 where kflip decreases. The turnover is a sign of anomalous diffusion, but has no connection with a similar turnover region that straddles the energy diffusion and activated diffusion-controlled regimes in Kramers reaction rate theory. The rollover may rather originate from statistical behavior of time-averaged mean square displacement (MSD) of group of atoms engaged in fluctuations.60 In our model, these are the same fluctuations, often referred to as anisotropic breathing motions that give rise to volume fluctuation.61 The linearity of MSD with fluctuation amplitude is valid only in the long-time limit; at short times, the behavior is anomalous.17,62,63 The turnover has also been observed very recently in a study of reconfiguration dynamics of polymer chain with internal friction at different levels of density.17 Anomalous diffusion in the form of subdiffusion in dynamic fluctuations inside the protein molecule has also been described.64 If internal friction in proteins has its origin in atom dispersion interactions that are constantly modulated by dynamic fluctuations, then the friction must be associated with nonBrownian diffusion, where MSD∼tα with 0
