ENTREVISTA DE LA EVALUACIÓN

The calculation of the frequency and collective motion of vibrational modes for a system is achieved through performing a normal mode analysis (NMA). A non-linear system has 3N-6 normal modes, where N is the number of atoms. The first 6 modes are removed because they detail translational and rotational motions that do not report on the internal dynamics of the molecule. Modes do not interact with each other: each mode is independent of all others. The lowest frequency modes involve global motions with many atoms undergoing larger displacements. The highest frequency modes involve localised motions with displacement of smaller numbers of atoms. For proteins, a well-defined native state necessitates that the protein is in an energy basin, allowing the energy potential to be assumed as harmonic when the native structure is thoroughly minimised; the harmonic oscillations around the minimum are the normal modes. Neutron scattering and THz spectroscopy measurements reveal a ‘dynamical transition’ whereby protein fluctuations start to deviate from harmonicity above 180 K.146,147 _{This limit has been recently shown to extend down to 110 K in}

temperatures the harmonic approximation of NMA is unsuitable. However, due to the 110 K operating temperature of the new THz system, NMA is suitable to model the harmonic oscillations of MUP.

In NMA, a Taylor expansion of the MD potential energy function around the minimum is performed. The second-order partial derivatives of the potential energy function, the force constants for the harmonic oscillations, are placed in a mass- weighted matrix. Diagonalisation of this matrix results in the eigenvalues and eigenvectors corresponding to the collective atomic displacements and frequencies that define the modes.149 _{The procedure is quick, taking only a few hours on modern}

computers. Collective motions can be analysed for a single mode or superposition of multiple modes. The relative amplitudes of the collective motions are independent of temperature: the absolute amplitudes of the motions, sometimes useful for experimental comparisons, can be scaled using a temperature factor. In this work the amplitude of the modes is not considered, as only the frequencies in difference spectra are necessary to identify affected modes.

The structure and the hydration level used both affect the NMA, and therefore these two factors need to be considered carefully. The native well of an energy landscape contains multiple sub-minima, each of which can be approximated harmonically, Figure 5.3. Consequently, traditional single-structure NMA (SS NMA) results in some modes idiosyncratic to a single minimum in the native well. However, averaging NMA from multiple sub-minima in the native well has been shown to diminish idiosyncratic modes whilst enhancing the modes common to sub-minima, thus generating a more representative picture of native vibrational fluctuations.122,150 _The

speed of NMA is not greatly undermined because short trajectories are sufficient to generate the non-identical poses required.122 _{This refinement, native ensemble NMA}

(NE NMA), is used herein for the first time with THz spectroscopy. All-atom explicitly solvated MD trajectories were generated to sample the native basin, at both the THz and NMR experimental temperatures of 110 K and 298 K. Additionally, SS NMA is performed using the crystal structures. NE NMA trajectories simulating the crystal asymmetric unit are currently being developed, and trajectories of the crystal unit cell are being considered.

Figure 5.3 A protein energy landscape with detail of the native state energy well. Traditional single-structure NMA (SS NMA) results in some modes idiosyncratic to a single minimum in the native well. However, averaging NMA from multiple minima in the native well diminishes idiosyncratic modes whilst enhancing common modes. Multiple minima are sampled by generating a short MD trajectory.

Water molecules are included firstly to avoid the collapse of protein surface elements during the thorough minimisation procedure. Secondly, the hydration dependence of THz spectra, whereby increasing water increases absorbance, demonstrates that hydration water contribute to vibrational modes.142 _Likewise,

increasing hydration increases normal mode densities at lower frequencies. Therefore a realistic hydration level must be applied in NMA. This reveals another benefit of the new THz system, wherein accurate (i.e. closer to experimental) NMA hydration is simpler to achieve than for previous systems. This is because the unit cell hydration is known from the crystal structure, and remains consistent across the experiment due to low temperature. Accordingly, for SS NMA, the protein was hydrated to replicate the asymmetric unit water density observed in the crystal. This resulted in asymmetric hydration due to the structure of the asymmetric unit, with a depth of water molecules extending between 2 and 10 Å from the protein surface. Consequently, for this preliminary investigation, structures from the explicitly solvated MD trajectories

used for NE NMA were edited to only contain water molecules within 5 Å of the protein surface, approximately the middle of this range.

Importantly for this work, the qualitative correspondence of fluctuations described by NMA and NMR S2 _{values has been described}151,152_{. Therefore using NMR}

S2 _{as benchmark data for this preliminary investigation is justified. Herein NMA is used}

as a method of interpreting the frequencies in THz difference spectra in terms of changes in collective vibrational modes, and thus site-specific dynamics, upon ligand binding. Additionally, the capacity of NMA to predict ligand-induced site-specific RMSF changes without the use of THz difference spectra is considered, alongside the effect on mode densities of the different NMA approaches.

5.1.5 Work undertaken

This work is a preliminary investigation into the combination of two complementary and developing techniques to comprise a novel probe of site-specific dynamic changes upon ligand binding, namely NMA-interpreted THz difference spectra. ‘Gold standard’ NMR S2 _{data are used as a benchmark for site-specific changes in protein dynamics}

upon ligand binding to MUP. Protein, crystals and ligand solutions were produced for THz spectroscopy. Dr Kasia Tych acquired THz difference spectra for the binding of both IBMP and hexanol to MUP. The THz system acquires spectra at 110 K, thus NMA’s harmonic approximation of protein fluctuations is justified. MD trajectories are generated to provide conformational samples for NE NMA at temperatures corresponding to the THz and NMR experiments, 110 K and 298 K, and are checked for unexpected behaviour before being analysed. NE NMA is compared to traditional SS NMA with regards to the agreement of THz difference spectra-derived predictions with NMR S2 _{data. The capacity of NMA to predict ligand-induced changes without the}

use of THz difference spectra, and the effect on mode densities of the different NMA techniques are also considered.

5.2 Materials and Methods