K.A. Dill, A.T. Phillips, and J.B. Rosen, CGU: An Algorithm for Molecular Structure Prediction, IMA Volumes in Mathematics and its Applications, in press (1996).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....also been used in molecular dynamics simulations [145] An alternative method smoothes the energy hypersurface using local minima to construct separable quadratic underestimating functions. The local minima of these fitted functions are then used to initiate searches on the original energy surface [42, 142]. 3.5. Branch and Bound Methods. Typically, branch and bound methods have been associated with, and are efficient methods for, solving combinatorial global optimization problems [47, 49] The protein folding problem possesses inherently combinatorial aspects, and some explicit combinatorial ....

K. A. Dill, A. T. Phillips and J. B. Rosen, CGU : An algorithm for molecular structure prediction, In IMA Volumes in Mathematics and its Applications, 94, Springer-Verlag, (1997), 1-21.

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K.A. Dill, A.T. Phillips, and J.B. Rosen, CGU: An Algorithm for Molecular Structure Prediction, IMA Volumes in Mathematics and its Applications, in press (1996).

....minima are known exactly. 1. Introduction Unconstrained minimization of nonconvex functions with multiple minima plays a key role in computational biology problems such as protein docking [6] Although the problem is NP hard, computational approaches such as convex global underestimation (CGU) [1, 7, 9] have been quite promising. In these methods, the nonconvex function is successively bounded below by a strictly convex quadratic function whose minimum gives improved estimates of the global minimum of the nonconvex function. In the present approach we use instead a piecewise linear approximation ....

....written as: #(z) 11) The subgradient of #(z) with respect to z as defined in (10) is given by: ##(z) # # # # , i = 1, # i = 1, # #e # # # # . 12) where e #m and, for i = 1, #, k = 1, m: 1 if A i x b i 0 [ 1, 1] if A i x b i = 0 1 if A i x b i 0 . 13) We are ready now to state our algorithm. Algorithm 1 Successive Linearization Algorithm (SLA) Start with a random z 0 . Having z determine z as a vertex solution of the linear program: 14) Stop when ##(z ....

K. A. Dill, A. T. Phillips, and J. B. Rosen. CGU: An algorithm for molecular structure prediction. In L. T. Biegler et al, editor, IMA Volumes in Mathematics and its Applications: Large Scale Optimization with Applications III: Molecular Structure and Optimization, pages 1--22, 1997.

....as a basis for another quadratic underestimation over the reduced space. After several repetitions, the global minimum can be found with reasonable assurance. This CGU method, first described in [5] has previously been applied successfully to a simpler string of beads model as described in [2]. In this paper, we Figure 3.1 The Convex Global Underestimator (CGU) Figure 3.2 Defining the New Search Domain Energy Energy Figure 3.3 The New CGU Over the Reduced Search Domain 12 K.A. DILL, A.T. PHILLIPS, AND J.B. ROSEN apply the CGU algorithm to the more realistic polypeptide model ....

....Figure 4.2 The CGU Determined Native Structure for Met Enkephalin: Ribbon Representation Figure 4.3 The CGU Determined Native Structure for Bradykinin: Ball and Stick Representation 14 K.A. DILL, A.T. PHILLIPS, AND J.B. ROSEN fixed (and the CGU algorithm makes use of this property, see [2]) The global minimum energy obtained by the CGU algorithm in 445 seconds (7.4 minutes wall clock time) on the eight processor Dec Alpha workstation cluster was 119.01 kcal mol. The DME error for this structure (compared with pdb1xy1.ent from the Brookhaven Protein Database) was 0.338 Ang. ....

K.A. Dill, A.T. Phillips, and J.B. Rosen, CGU: An Algorithm for Molecular Structure Prediction, IMA Volumes in Mathematics and its Applications, in press (1996).

....basis for another quadratic underestimation over the reduced space. After several repetitions, the global minimum conformation f G and its associated global minimum energy F(f G ) can be found with reasonable assurance. For more specific details of the CGU method and its computational results, see [2], 3] 4] and [6] 3. Global Underestimation of the Energy Landscape As summarized in the previous section, the CGU algorithm will determine a global minimum backbone torsion angle vector f G and corresponding global minimum energy function value F G = F(f G ) As part of the CGU algorithm, a ....

K.A. Dill, A.T. Phillips, and J.B. Rosen, CGU: An Algorithm for Molecular Structure Prediction, IMA Volumes in Mathematics and its Applications 94, Large Scale Optimization with Applications, Part III: Molecular Structure and Optimization (1997), L.T. Biegler et al. (Eds), 1-22.

....simulation of real materials (with chemist John Weare, UCSD) and to particle methods. Ben Rosen, in conjunction with Ken Dill (Pharmaceutical Chemistry, UCSF) and Andy Phillips (CSci. USNA, and SDSC) are developing new parallel algorithms and software for computational biology applications [126][44] An example is predicting molecular structure by computing the global minimum of the molecular energy function. Keith Marzullo is working on fault tolerance in the Nile project [95] 104] 96] an NSF National Challenge project initiated at Cornell to build a wide area execution environment ....

J. B. Rosen, K. A. Dill and A. T. Phillips, "CGU:An Algorithm for Molecular Structure Prediction, " IMA Vols.in Mathematics and its Applications, Large Scale Optimization, Part III:Molecular Structure and Optimization, Springer-Verlag, 1997.

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