Transcript Highligh in Physics 2005

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
The study of phenomena taking place in proteins that can only be described by quantum mechanics is
particularly complicated, due to the large size of the system and the lack of symmetries. In these cases, a
possible approach is to describe quantum-mechanically only a part of the whole protein, accounting for
the rest of it in an approximated way.
• One example is the calculation of the binding free
energy of small ligands to the Carbonic Anhydrase
(HCAII), a protein involved in the glaucoma disorder. Due
to the presence of a zinc atom, standard methods based
on classical empirical potentials fail to predict correctly
the binding free energy. The use of density functional
theory, together with a novel conformational sampling
algorithm, allow a description of the interaction consistent
with the experimental data.
•The work is in collaboration with the groups of M.
Parrinello (ETH,
Lugano)
and
Binding
affinity:
KbE. Shakhnovich (Harvard)
Is a measure of the
effectiveness of an inhibitor
(A. Laio and M. Parrinello PNAS 2002 99:12562 ) :
 
1) δ(t) perturbation to the potential;
2) Calculate the
3) evolution and the density n(t);
4) From the density we find the time-dependent dipole moment;
5) With a Fourier transform we find the dynamic polarizability in

2


e
frequency domain and the the absorption
cross
section.
i t
3
 ( )  Im  ( )   e

 d rx n (t )  d t
0
 k

BRIGHT - cis
Chromophore alone:
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)
unbound
From our calculations
Results for HCAII with trifluoromethane-sulfonamide :
F0 ~ 21.1 kcal/mol
TS ~ 15.5
kcal/mol at room temperature (300 K)
F ~ 5.5
kcal/mol
Experimental values of F are on the order of 5 kcal/mol
(A. V. Ishchenko, and



r
,
t

i

r
,
t

t
   
 1 2



V
r
,
t
eff
 2
Our unbound state has negligible
bound
translational entropy if
compared to the translational
entropy of the ligand in bulk
solvent. This is a consequence of
CV confinement, which we required
Zn – N distance (bohr)
for computational reasons.
We assumed that F = F(unbound)-F(bound) = F0
- TSfree + TSunbound
Finkelstein Prot. Eng. vol. 3 no. 1:1-3
• The work is in collaboration with the experimental group
of G. Chirico (Bicocca), R. Nifosi’ (NEST, Pisa) and A.
Rubio (San Sebastian).
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 approach to quantum
molecular dynamics
 3/ 2 5 / 2  V  1 
RT ln  e   3 
N 

the fluorescence properties of the Green Fluorescent
Protein, a protein widely used in biology to detect the
expression of genes. Time dependent density functional
calculations highlight the mechanism which allows to
switch on and off the fluorescence by means of beams of
different wavelengths.
F = -RT ln Kb
Active site
Coarse grained
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 timedependent 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
F (Hartree)
brownian motion. Keeping track
of the hills allows the
reconstruction of the free energy
surface
• Another example of this procedure is the description of
E. Shakhnovich, J. Med. Chem., 45:2770)
These results are obtained including effects due to the electrostatic field generated by the part of the
protein not included in our ab-initio calculations. We observed that neglecting these effects yields
wrong results
DARK - trans
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.