ONIOM calculations on 1W7S

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Using the created input file ONIOM calculations were submitted always using the DFT B3LYP 6-31G* : Amber scheme.

Minimal model

Optimisation started from the Amber optimization chk file, this was because we want to compare frequencies at the SAME minimum critical point for each level of theory.

The minimal model includes the planer portion of the chromophore residue (number 64 - CSY) and contains 16 heavy atoms and 8 hydrogens. The smaller the model region, the more efficient the ONIOM calculation becomes since only model is treated with the DFT costly theory. The exact input command line was - #p opt oniom(b3lyp/6-31g(d):amber=softfirst) geom=connectivity. The time taken to optimise was 2 hours 25 minutes 1.2 seconds and the final energy was -736.838427249468. This optimisation uses the Gaussian default Mechanical Embedding scheme where the MM charges are not included in the high level model - this is cheaper but not as accurate. Another calculation was started from the same inital structure but optimised using Electronic Embedding (polarisation of the wavefunction), this input line was - #p opt oniom(b3lyp/6-31g(d):amber=softfirst)=embed geom=connectivity. The time taken for optimisation was 7 hours 25 minutes 29.3 seconds and the final energy was -736.807010778592.

Frequency calculations were then run on the resulting geometries. For the inputs with water molecules 10A near the chromophore, 3N-6 frequencies were returned. When comparing these frequencies we used the C=O frequency which is discussed in detail in many papers. It involves a C=O stretch mixed with a C=C stretch in the chormophore and has been assigned experimentally to occur at 1680cm-1. Calculations on the HBDI molecule as a chromophore model gave the mode a frequency of 1802cm-1 using B3LYP 6-31G*. This is not good agreement with the experimental value, so something must be missing - the protein electrostatic environment (cf. ian gould saying electrostatics are by far most important term in forcefield)

The table below shows the C=O frequency for the 2 ONIOM calculations.

Calculation	Time	C=O Frequency
ONIOM with ME	4 hours 40 minutes 55.2 seconds	1804
ONIOM with EM	13 hours 10 minutes 50.4 seconds	1745

It is clear that not much changes in comparison to the HBDI model when using ME with the ONIOM scheme, this is to be expected since no real change has been made to the structure or wavefunction across the chromophore (except for the connections to the protein primary sequence). The C=O frequency occuring at 1804cm-1 in the ME scheme is thus to be expected and confirms the hypothesis that the protein provides an electrostatic environment which polarises the wavefunction over the chromophore and affects the frequencies.

Moving to the EE scheme, the MM charges are used to polarise the wavefunction over the DFT region, and results in a significant downshift of the C=O mode to 1745cm-1. This shows that the protein electrostatic environment has had a significant effect on the frequencies of the chromophore region. This frequency is also converging on the experimental value (1680cm-1). It is also noted that 8 modes outline in the HBDI experiments were observed in the ONIOM calculations and all moved towards experimental values.

In conclusion the minimal model has provided an improvement on the frequency calculation of HBDI towards the experimental value calculated for GFP. The next step is to expand the model to include hydrogen bonding interactions from the surrounding protein (cf. hydrogen bonding by DFT, orbital interaction, directional, electrostatics more like a field)

An expanded Model

The next step is an expanded model region to include hydrogen bonding interactions between the chromophore and its surrounding residues (in space, not adjacent in sequence). The residues proximal to the chromophore which have some ability to hydrogen bond were detailed in the paper by Jasper van Thor:

Uncovering the hidden ground state of green fluorescent protein, John T. M. Kennis,†‡§ Delmar S. Larsen,†‡ Ivo H. M. van Stokkum,†‡ Mikas Vengris,† Jasper J. van Thor,¶ and Rienk van Grondelle†, Proc Natl Acad Sci U S A. 2004 December 28; 101(52): 17988–17993.

The diagram in this paper shows the interactions. A model was then built around this diagram, trying to keep the model system as small as possible. Residues surrounding the chromophrore with suggested interactions are:

Glu222
Ser202
Gln94
Arg96
Tyr148
Ala203

The parts of these residues that were of interest were added to the model system, along with crystalographic water molecule near the phenol hydrogen (with suggested H-bond network).