References
Jose Ignacion Garzón, Julio A. Kovacs, Ruben Abagyan, and P. Chacón.
Dfprot:A webtool for predicting local chain deformability Bioinformatics. 2007 Apr 1;23(7):901-2. 
J. Kovacs, P. Chacón and R. Abagyan. (2004) Predictions of Protein Flexibility:
First Order Measures. Proteins 56, 661-8.
References
Jose Ignacion Garzón, Julio A. Kovacs, Ruben Abagyan, and P. Chacón.
Dfprot:A webtool for predicting local chain deformability Bioinformatics. 2007 Apr 1;23(7):901-2.
J. Kovacs, P. Chacón and R. Abagyan. (2004) Predictions of Protein Flexibility:
First Order Measures. Proteins, 56, 661-8.
The concepts
DFprot underlying methodology is
detailed described elsewhere in Kovacs, et al., 2004. In a few words,
main-chain deformability is deduced by treating the normal modes as vector
fields over the molecule, and applying the conformal field theory.
Two successive calculations are carried out by DFprot. Initially, Normal Mode Analysis is performed over the target structure. Then deformability is calculated from the obtained NMA results. Here below the equations evolved in such calculations are commented in detail.
Normal Mode Analysis. We perform the Normal Mode
Analysis (NMA) on the Cα atoms, setting the mass mi
of each as the total mass of the corresponding ith residue. For a given protein
molecule, its Cα atoms are interconnected with harmonic springs of a
strength defined by:
where i,j denote residue numbers, rij
is the distance between the Cα atoms of residues i and j,
and r0 was set to 3.8 angstroms, which is approximately the mean
distance between consecutive Cα atoms.For
simplicity, we have removed the normalized residue contact area term from the
previous formulation found in Kovacs et al. 2004. This harmonic model of the molecule gives rise
to a potential energy function E (E
is just the sum of all harmonic springs). If H denotes the Hessian of E, we have
the classical secular equation:
where
M is the mass
matrix, which in our case is diagonal. In order to get a symmetric eigenvalue
problem, the secular equation is rewritten as:
Using the residue masses and the spring strengths
given above, the Hessian matrix is diagonalized, yielding
3N-6
eigenvalues λ
n and their corresponding eigenvectors
un
(the normal modes of vibration). Each of
these modified modes can be visualized as the velocity vectors that atoms have
when, while vibrating according to that mode, they pass through their initial
positions.
DFprot gives all modal information (eigenvalues + eigenvectors) in a downloadable raw ASCII file named nmac_ptraj.evec. It also provides access to the normal mode perturbed structures of the lowest 20 frequency normal modes. Both NMA outcomes are accesible from the results web page.
Deformability Functions
Since we consider the normal modes u as vector
fields over the molecule, we can define the corresponding "conformal
tensor" Su by:
where
k,l are indices of spatial
coordinates
,
δ denotes the Kronecker delta function and div
u
denotes the
divergence of
u:
It is important to notice that conformal tensor Sun
describes how the vector field u affects (locally) the shape
of the molecule.
The deformability is calculated using the following
formula:
This expression describes how much, in average, the
molecule can deform at each point (residue). Note that deformability is a
global parameter, since its value at a particular point depends on the global
structure of the molecule.
The method for the numerical computation of the
partial derivatives has been previously described (Kovacs et. al 2004).
Mobility. The mobility function is given by the classical
formula for atomic fluctuations (Brooks et al. 1995)
where the
are
the vibrational frequencies, related to the eigenvalues by 
. Note that deformability gives us a measure
of the flexibility of the protein, whereas the classical fluctuation formula is related to protein mobility (typically reflected in B-factors). Both measures
are complementary but distinct. The relation between them is akin to a relation between function and its derivative. The deformability is a measure of likelihood
to form a hinge in protein chain, whereas the protein mobility reflects amplitude of the atomic fluctuations.
Atomic B-factors can be easily obtained from mobility using:
DFprot server provides deformability/mobility analysis of a query structures. The users can view in 3D their structures colored by
predicted deformability or mobility. The display of the results are fully interactive thanks to the use of Jmol viewer (www.jmol.org)
or combination of the rich ICM-Browser (free at www.molsoft.com) with the iSee technology(Abagyan, et al., 2006). Please visit and enjoy
with our examples at the results tab of this web tool.
References
- Abagyan, R., Lee, W.H., Raush, E., Budagyan, L., Totrov, M., Sundstrom, M. and Marsden, B.D. (2006) Trends Biochem Sci, 31, 76-78.
- Brooks, B. R.; Janezic, D.; Karplus, M. J. Comput. Chem. 1995, 16, 1522-1542.
- Kovacs, J. A.; Chacón, P.; Abagyan, R. Proteins: Struct., Funct., Bioinf. 2004, 56, 661-668.
- Cavasotto, C.N., Kovacs, J.A. and Abagyan, R.A. (2005) Representing receptor flexi-bility in ligand docking through relevant normal modes, J Am Chem Soc, 127, 9632-9640.
*is the 8-digit number provided when you run DFprot.
Download and Installation
Instead of using our web service you can download the program and run it in your machine.
By the moment, only Linux executables are provided. The use of the program is very friendly;
just one input PDB file is required (use -help option for advance options). Of course,
only raw data will be generated: deformability/mobility tabulated data, all NMA data,
and the displayed structures in PDB format.
Dfprot executable depends on standard linear algebra LAPACK/BLAS libraries. These libraries are available from all Linux distributions or can be obtained from original LAPACK site (available here).Moreover, two main optimized versions are available i) ATLAS (open source), and ii) INTEL MKL (free 30 day evaluation). We provide a specific version for each type of library, please do not confuse. Please uncompress the corresponding file and remember that either LAPACK-ATLAS or MKL should be properly installed.
| Filename |
Size (Kbytes) |
Architecture |
Release (Date) |
Notes |
| DFprot_MKL.gz |
552KB |
Linux - Intel MKL(32bits) |
1.0 (1/7/2006) |
 |
| DFprot_lx.gz |
734KB |
Linux - LAPACK/BLAS(32bits) |
1.0 (1/7/2006) |
|
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