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BRIGHT - cis. DARK - trans. Highlights in Physics 2005 11–14 October 2005, Dipartimento di Fisica, Universit à di Milano Quantum methods in protein science C. Camilloni * , P. Cerri * , D. Provasi * † , G. Tiana * † and R. A. Broglia * † * Dipartimento di Fisica, Universit à di Milano
DARK - trans
Highlights in Physics 2005
11–14 October 2005, Dipartimento di Fisica, Università di Milano
Quantum methods in protein science
C. Camilloni*, P. Cerri*, D. Provasi*†, G. Tiana*†and R. A. Broglia*†
* Dipartimento di Fisica, Università di Milano
† INFN – Sezione di Milano
Binding affinity: Kb
Is a measure of the effectiveness of an inhibitor
F = -RT ln Kb
The protein can be in a fluorescent (BRIGHT) and non fluorescent (DARK) conformations, which can be switched by appropriate wavelength. The dark state corresponds to an absorption peak at 3.5 eV. To compute absorption we use the Time Dependent Density Functional Theory.
Metadynamics approachto quantum
molecular dynamics(A. Laio and M. Parrinello PNAS 2002 99:12562 ) :
History dependent (non markovian)
Metadynamics allows the exploration of free energy
surface as a function of a selected set of collective
variables (CV). A fictitious time-dependent potential acting on the CVs is added to the Lagrangian in order to escape free energy minima.
In an ideal (infinite time) metdynamics simulation, after filling free energy wells, collective variables evolve in time with brownian motion. Keeping track of the hills allows the reconstruction of the free energy surface
δ(t) perturbation to the potential;
evolution and the density n(t);
From the density we find the time-dependent dipole moment;
With a Fourier transform we find the dynamic polarizability in frequency domain and the the absorption cross section.
Free energy F(s)
We have observed the absorption peak at 3.5 eV and identified the
dark state of the protein with the trans conformation of the chromophore
Collective variable (s)
O – N distance (bohr)
Our unbound state has negligible
translational entropy if
compared to the translational
entropy of the ligand in bulk
solvent. This is a consequence of
CV confinement, which we required
for computational reasons.
We have improved the degree of approximation, considering: 1) the amino acids close to the chromophore, in particular the hydrogens bond network, 2) the chromophore and the Coulombian field of the whole protein, showing that the two effects are complementary on the absorption spectrum prediction and must be accounted in a realistic description of the optical properties of the system.
Zn – N distance (bohr)
We assumed that F = F(unbound)-F(bound) = F0 - TSfree + TSunbound
From our calculations
Results for HCAII with trifluoromethane-sulfonamide :
F0~ 21.1 kcal/mol
TS ~ 15.5 kcal/mol at room temperature (300 K)
F~ 5.5 kcal/mol
Finkelstein Prot. Eng. vol. 3 no. 1:1-3
Experimental values of F are on the order of 5 kcal/mol
(A. V. Ishchenko, and E. Shakhnovich, J. Med. Chem., 45:2770)
These results are obtained including effects due to the electrostatic field generated by the part of theprotein not included in our ab-initio calculations. We observed that neglecting these effects yields wrong results