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| Home | Folding Submission Form | Pathway Submission Form | Folding Results Database | FAQ |
This page answers some frequently asked questions about our technique. Please see our research project webpages for more information about our technique and research.
A roadmap is what we call the graph approximating the protein's potential landscape that is generated by our technique. Roadmap vertices (sometimes called nodes) correspond to sampled protein conformations and roadmap edges correspond to transitions between protein conformations. The roadmap contains more samples near the user specified target conformations and hence better approximates the potential landscape in those regions. A roadmap contains of thousands of representative pathways to and between the user specified target conformations.
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The energy landscape associates every protein conformation with its potential energy. It is believed that the energy landscape is shaped like a funnel with the native state at the bottom (see Figure 1). Proteins fold by traveling along this landscape. The energy landscape theory explains how proteins can fold and re-fold so quickly to the native state despite the large degrees of freedom available. Different energy landscapes indicate different folding behaviors (e.g., smooth landscapes indicate a relatively quick folding, rough landscapes indicate relatively slow folding).
First, protein conformations are sampled by iteratively perturbing existing conformations, starting with the provide target conformations (usually one of which is the known native state). This yeilds denser coverage of the energy landscape near the target conformations. Then, neighboring conformations are connected together by some simple local planner (e.g., a straight line interpolation). These samples and connections together form the roadmap.
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Because the energy landscape is so large, simple uniform random sampling would take too long to provide sufficiently dense coverage of the area around the native state. Protein conformations are instead sampled by iteratively perturbing existing conformations, starting with the known native state. This biased sampling yields a denser coverage near the native state and a sparser coverage of unstructured regions (see Figure 2). There are numerous ways in which conformations can be generated from existing conformations and this is a matter of current research; please see the papers listed below and our research project webpages for specifics on sampling techniques.
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Each conformation q is kept baed on the following probability where E(q) is the energy of the conformation:
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For each conformation, we attempt to connect it with its k nearest neighbors on the energy landscape; typically k is a small constant, e.g., k=10. For each connection, we use a simple local planner (a straight line interpolation) to transition between the two conformations. We compute the energy E(ci) of each intermediate conformation ci along the connection. We then assign the following edge weight:
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We then compute the edge weight between conformations q1 and q2 as:
This gives low weight to more energetically feasible transitions and high weight to energetically unlikely transitions.
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We can use different ways to extract paths from a roadmap. One method is to use Dijkstra's single shortest path algorithm to extract the most energetically feasible path between the start and final conformations in the roadmap. Recall that the roadmap edge weights reflect the transition's energetic feasibility, so extracting the smallest weighted path corresponds to extracting the most energetically feasible path.
We also developed a new technique for path extraction called Map-Based Monte Carlo (MMC) simulation. MMC performs a random walk on the roadmap similar to traditional Monte Carlo simulation except that transition probabilities to neighboring conformations are a function of the out-going edge weights. Unlike shortest paths which are deterministic, this technique more closely mimics the stochastic folding process.
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We model the protein as an articulated linkage where each amino acid has 2 degrees of freedom, the phi and psi backbone torsional angles. We model these torsional angles as revolute (rotational) joints taking values in [0,2*pi). Side chains are modeled as spheres with 0 degrees of freedom. Figure 3 shows the model of 1 amino acid.
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We can use any potential function. For the server, we use a coarse potential based on a potential function developed by Levitt (see M. Levitt, "Protein folding by restrained energy minimization and molecular dynamics," J. Mol. Biol., vol. 170, pp. 723-764, 1983 for more details). Our potential function uses a step function approximation of the van der Waals component and only considers the contribution from the side chains. In our model, we treat each side chain as a single large "atom" R located at the Cbeta atom. Let rmin be the minimum distance between any two R atoms in the conformation c. Our potential is as follows:
Kd is 100KJ/Mol, d0 = dc = 2A, and di is the separation between a pair of atoms which form a hydrophobic bond or disulphide bond in the native state. For Ehydrophobic, when the R atoms of any two hydrophobic amino acids come within a distance dRh, the potential is decreased by Eh, where dRh = 6A and Eh = 20KJ/Mol.
Although this coarse potential is an approximation of an all atoms potential, we find it is accurate enough to produce similar results to an all atoms potential while reducing the program running time 50 to 100 fold.
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| If you have any questions or comments, please email proteinfolding@cs.tamu.edu. |
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