The change in the vibrational density of states of a protein (dihydrofolate reductase) on binding a ligand (methotrexate) is determined using inelastic neutron scattering. The vibrations of the complex soften significantly relative to the unbound protein. The resulting free-energy change, which is directly determined by the density of states change, is found to contribute significantly to the binding equilibrium. DOI: 10.1103/PhysRevLett.93.028103 PACS numbers: 87.15.He An understanding of how ligands bind to proteins is of fundamental importance in biology and medicine [1][2][3][4][5][6]. Protein:ligand association has been assumed to be dominated by factors such as the hydrophobic effect, hydrogen bonding, electrostatic, and van der Waals interactions. However, as early as 1963 it was suggested that an additional mechanism might exist, due to increased flexibility in the protein:ligand complex manifested by a change in the spectrum of vibrations due to formation in the complex of new, intermolecular interactions [7][8][9][10][11][12][13]. Theoretical normal mode analyses, used to estimate this vibrational change on insulin dimerization [12] and on water binding to bovine pancreatic trypsin inhibitor [13], have suggested that the effect is likely to be thermodynamically important. However, experimental determination of the vibrational change has been lacking.Inelastic neutron scattering, in which the dynamic structure factor Sq; ! is measured as a function of the scattering wave vector q and energy transfer h! (where ! is the angular frequency), has been used to determine the vibrational density of states (frequency distribution) g! for several proteins [14 -16]. Here we present an experimental determination of the change in g! on binding a ligand to a protein. This determination allows thermodynamic quantities associated with the vibrational change to be derived. The enzyme chosen is dihydrofolate reductase (DHFR), an important target for anticancer and antibacterial drugs [17][18][19][20][21]. DHFR catalyzes the reduction of dihydrofolate to tetrahydrofolate in the presence of the nicotinamide adenine dinucleotide phosphate (NADPH) cofactor. The ligand used is methotrexate (MTX), a folate antagonist of DHFR that has been used effectively as a cytotoxic agent in the treatment of cancers [22].To minimize scattering from solvent molecules, the system was exchanged with D 2 O. To do this, lyophilized DHFR from E.coli was dissolved in D 2 O equilibrated at 4 C overnight and freeze dried. NADPH and NADPH MTX were added in equimolar ratios to the enzyme. As the dissociation constants of DHFR with NADPH and MTX are low (K For the neutron experiments, the samples were contained in an aluminum sample holder. Sample amounts were 98.1 mg (uncomplexed) and 108.6 mg (complexed). The measurements were performed on the time-of-flight spectrometer IN6 at the Institut Laue-Langevin (ILL), Grenoble, with an incident neutron beam wavelength of 5.12 Å . The scattering experiments were performed at 120 K to ensure that all dyn...

Proteins undergo an apparent dynamical transition on temperature variation that has been correlated with the onset of function. The transition in the mean-square displacement, AEDr 2 ae, that is observed using a spectrometer or computer simulation, depends on the relationship between the timescales of the relaxation processes activated and the timescale accessible to the instrument or simulation. Models are described of two extreme situations-an ''equilibrium'' model, in which the long-time dynamics changes with temperature and all motions are resolved by the instrument used; and a ''frequency window'' model, in which there is no change in the long-time dynamics but as the temperature increases, the relaxation frequencies move into the instrumental range. Here we demonstrate that the latter, frequency-window model can describe the temperature and timescale dependences of both the intermediate neutron scattering function and AEDr 2 ae derived from molecular dynamics simulations of a small protein in a cryosolution. The frequency-window model also describes the energy-resolution and temperature-dependences of AEDr 2 ae obtained from experimental neutron scattering on glutamate dehydrogenase in the same solvent. Although equilibrium effects should also contribute to dynamical transitions in proteins, the present results suggests that frequency-window effects can play a role in the simulations and experiments examined. Finally, misquotations of previous findings are discussed in the context of solvent activation of protein dynamics and the possible relationship of this to activity.

Incoherent neutron scattering is widely used to probe picosecond-nanosecond time scale dynamics of molecular systems. In systems of spatially confined atoms the relatively high intensity of elastic incoherent neutron scattering is often used to obtain a first estimate of the dynamics present. For many complex systems, however, experimental elastic scattering is difficult to interpret unambiguously using analytical dynamical models that go beyond the determination of an average mean-square displacement. To circumvent this problem a description of the scattering is derived here that encompasses a variety of analytical models in a common framework. The framework describes the time-converged part of the dynamic structure factor [the elastic incoherent scattering function (EISF)] and lends itself to practical use by explicitly incorporating effects due to the finite energy resolution of the instrument used. The dependence of the elastic scattering on wave vector is examined, and it is shown how heterogeneity in the distribution of mean-square displacements can be related to deviations of the scattering from Gaussian behavior. In this case, a correction to fourth order in the scattering vector can be used to extract the variance of the distribution of mean-square displacements. The formalism is used in a discussion of measurements on dynamics accompanying the glass transition in molecular systems. By fitting to experimental data obtained on a protein solution the present methodology is used to show how the existence of a temperature-dependent relaxation frequency can lead to a transition in the measured mean-square displacement in the absence of an EISF change.

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