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This page provides access to the neighbordependent Ramachandran distributions described in
Ting et al., PLOS Comp. Biol. (April, 2010).
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In
this work, Ramachandran probability distributions are presented for
residues in protein loops from a highresolution data set with
filtering based on calculated electron densities. Distributions for
all 20 amino acids (with cis and trans proline treated separately)
have been determined, as well as 420 leftneighbor and 420
rightneighbor dependent distributions. The neighborindependent and
neighbordependent probability densities have been accurately
estimated using Bayesian nonparametric statistical analysis based on
the Dirichlet process. In particular, we used hierarchical Dirichlet
process priors, which allow sharing of information between densities
for a particular residue type and different neighbor residue
types. The resulting distributions have been tested in a loop modeling
benchmark, and are shown to improve protein
loop conformation prediction significantly.
In the figure above, XXX.yyy indicates the Ramachandran distribution of residue type XXX with right neighbor yyy. In this file (35 MByte pdf, 43 pages), we show the Ramachandran distributions for the TCBIG set (Turns+Coil+Bridge+PiHelix+310Helix). yyy.XXX indicates the Ramachandran distribution of residue XXX with left neighbor yyy. The first page shows the neighborindependent distributions.
The paper has been published in PLOS Computational Biology. A reprint is available.
Please cite the paper: Daniel Ting, Guoli Wang,
Maxim Shapovalov, Rajib Mitra, Michael I. Jordan, Roland L. Dunbrack,
Jr. Neighbordependent Ramachandran probability distributions of amino acids developed from a hierarchical Dirichlet process model. PLOS Comp. Biol. (April 2010).
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Each file contains probabilities of phi,psi for specific residue
types given the residue type of a neighbor to the left or to the
right. "ALL" means all neighbor residues of the residue in question
were kept in the calculation. The format is this:
So for instance, here are some lines for LEUrightPRO Ramachandran distribution
Res Dir. Neigh phi psi Probability log(prob) Cumulative_sum
LEU right PRO 175 130 5.237406e08 16.76485 2.082167e04
LEU right PRO 175 125 4.726758e08 16.86744 2.082640e04
LEU right PRO 175 120 4.449988e08 16.92778 2.083085e04
LEU right PRO 175 115 4.332896e08 16.95444 2.083518e04
LEU right PRO 175 110 4.208621e08 16.98355 2.083939e04
LEU right PRO 175 105 3.898562e08 17.06007 2.084329e04
LEU right PRO 175 100 3.459067e08 17.17968 2.084675e04
Res = the residue type for the Ramachandran Distribution
Dir = the direction of the neighbor ("ALL" is ALL residue types at once)
phi and psi = the floors of 5x5 regions
Probability = the probability in the 5x5 regions with floor at that phi,psi (e.g. the point at 175,130 covers the range (175,130) to (170,125)
log(prob) = followed by the log probaility.
Cumulative_sum = the cumulative sum and can be used for drawing random values from the probability distributions. The sum is 1.0 for each neighbor map.
CPR is cis proline as a central amino acid
Note: the probabilities cover the regions above and to the right of the phi,psi point; e.g., at phi,psi = {60,0}, the probability is for the region {60,0} > {65,5}.
To calculate probabilies for triplets, use:
To calculate probabilies for triplets (center,left,right), use:
log p*(phi,psi  C,L,R) = log p(phi,psi C,L) + log p(phi,psi C,R)  log p(phi,psi C,R=ALL)
Once log p*(phi,psi  C,L,R) is calculated, calculate p*(phi,psi C,L,R) = exp(log(p*(phi,psi  C,L,R)))
Then sum them up for each Ramachandran map, and normalize the probabilities by dividing by the sum:
p(phi,psi,  C,L,R) = p*(phi,psi  C,L,R) / sum
There are four distribution files:
NDRD_TCBIG.txt = data from Turn, Coil, Bridge, PiHelix, and 310 Helix
NDRD_TCB.txt = data from Turn, Coil and Bridge
NDRD_Conly.txt = Coil only
NDRD_Tonly.txt = Turn only
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Roland Dunbrack