Protein Dynamics
5.2 Materials and Methods 1 THz spectroscopy
5.2.1.1 Production of crystals for THz spectroscopy
Proteins and crystals were produced as described in §2.2.1.1 and §3.2.2.1. IBMP was introduced to the crystals through addition to reservoir solution and overnight vapour-diffusion as described in reference 21. Hexanol was introduced by soaking
crystals in ligand-doped reservoir solution as described in §3.2.2.1. Soaking was performed by Dr Kasia Tych.
5.2.1.2 Generation of THz difference spectra
These experiments were performed by Dr Kasia Tych, with details summarised from reference 141. Crystals were transferred onto a pinhole aperture and excess solution
removed using a paper wick before being flash frozen using a nitrogen cryostream. The aperture is positioned at the focal point of the THz beam, such that the entire beam interacts with the sample. No diffraction effects were observed due to the use of the aperture. A time domain signal is measured from a broad-bandwidth THz frequency pulse applied to the sample, Fourier transformed and the absorption coefficient calculated using Equation 5.1 and parameters measured as detailed in reference 141. The
frequency components measured were from 0.3 up to 7.5 THz. All measurements were obtained at ~110 K. Reported absorption coefficients are from eight measurements of four crystals of each complex, and ten measurements of five crystals of the unbound protein, wherein each measurement itself is an average of five THz scans. Uncertainties in the THz absorption coefficients are propagated from uncertainties in the variables of Equation 5.1. Subtracting absorption coefficients and propagating their errors at each frequency resulted in difference spectra, Figure 5.6b. Frequencies at which the difference is zero within error were then discarded. Changes above error are displayed as absolute values minus the error, Figure 5.6c. A list of the accompanying frequencies was used with NMA as described in §5.2.2.3.
5.2.2 Normal mode analyses (NMA)
5.2.2.1 Single structure normal mode analysis (SS NMA)
The crystal structure of MUP (2ozq), MUP-IBMP (1qy1) and MUP-hexanol (Dr Caitriona Dennis, unpublished), were processed using CHARMM GUI ‘Quick MD Simulator’.118 A disulphide bridge was specified between residues 64 and 157 as
observed in the crystal structure. The structure was solvated to the density observed experimentally in the asymmetric unit and neutralised using Na+ placed using a distance
method. Protein parameters were taken from the CHARMM22 forcefield. The cadmium ion (from crystallisation solution) and ligand parameters for IBMP and hexanol were generated by CHARMM-GUI using the CHARMM Generalised Forcefield (CGENFF).47 These structures were then thoroughly minimised, to an
energy gradient lower than 10-12 kcal mol-1 Å-1, and subsequently analysed using the
VIBRAN module of CHARMM. RMSF values are obtained per mode or for all modes using scripts obtained from Dr Roland Stote (personal communication).
5.2.2.2 Equilibrium simulations and native ensemble normal mode analysis (NE NMA)
5.2.2.2.1 Generating trajectories
The crystal structure of MUP (2ozq), MUP-IBMP (1qy1) and MUP-hexanol (unpublished), were used as the starting structure for the simulation. The ‘Quick MD Simulator’ functionality of CHARMM-GUI was used to generate ligand parameters, neutralise and solvate the system, and set up periodic boundary conditions.118 Protein
parameters were taken from the CHARMM22 forcefield. The ligand parameters for IBMP and hexanol were generated by CHARMM-GUI using the CHARMM Generalised Forcefield (CGENFF).47 A disulphide bridge was specified between residues 64 and 157
as observed in the crystal structure. Sufficient K+ and Cl- were placed using a Monte-
Carlo method to achieve neutrality. The molecule was solvated in an octahedral box of ~7000 TIP3 water molecules with periodic boundary conditions. Long range electrostatic interactions were treated using the particle mesh Ewald method. SHAKE
was applied to constrain all hydrogen bonds, allowing a 2 fs timestep. Minimisation involved 1000 steps using the Steepest Descent algorithm followed by 100 steps using the Adopted Basis Newton-Raphson algorithm. The system was subsequently heated from 50 K to 298 K over 25000 steps, before performing 18 ns of equilibrium trajectory at constant temperature and pressure (298 K, 1 atm). Coordinates were saved every 1 ps.
5.2.2.2.2 Checking trajectories
Total energy and temperature as a function of time were obtained directly from CHARMM, Figure 5.4. RMSD and RMSF calculations, Figure 5.5 and Table 5.1 respectively, were performed using Wordom.48 The latter were calculated for three
subsets of atoms: alpha carbon (Cα), backbone nitrogen (N) or sidechain carbon
(Cβ,δ,γ), using trajectories wherein each frame was aligned using the same subset of
atoms.
5.2.2.3 Processing of normal mode analyses
Using Wordom48, 100 frames at equal spacing (1 per 180 ps, starting at frame 1) were
extracted from each trajectory, and reoriented and aligned with respect to the first frame of the trajectory. All TIP3 water not within 5 Å of protein were removed using CHARMM. These structures were then minimised and processed as detailed in §5.2.2.1.
The following procedures were performed on three datasets for both ligands: the single structure (§5.2.2.1) and the average over all 100 structures extracted from both 110 K and 298 K trajectories. RMSF values are obtained per mode or for all modes, averaged over all 100 structures, using scripts mentioned in §5.2.2.1. Heat maps in Figure 5.7 were generated using JColorGrid software.153
5.2.2.3.1 Mode density calculations
CHARMM reports the normal mode frequencies as wavenumbers. Equation 5.5 was used to convert wavenumbers to THz frequencies for comparison to difference spectra. Equation 5.5 is derived from Equation 4.4, which shows that frequency, ν equals the speed of light, c, divided by the wavelength, λ. Because the wavelength is the reciprocal of the wavenumber, Equation 5.4 becomes Equation 5.5.
ν = c / λ
Equation 5.4 ν = c * wavenumber
Equation 5.5