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Research Papers

A Continuous Protein Design Model Using Artificial Power Law in Topology Optimization

[+] Author and Article Information
Sung K. Koh

Department of Aerospace Engineering, Ryerson University, Toronto, ON, M5B 2K3, Canadasungkoh@ryerson.ca

Guangjun Liu

Department of Aerospace Engineering, Ryerson University, Toronto, ON, M5B 2K3, Canadagjliu@ryerson.ca

Wen-Hong Zhu

 Canadian Space Agency, Saint-Hubert, QC, J3Y 8Y9, Canada; Department of Aerospace Engineering, Ryerson University, Toronto, ON, M5B 2K3, Canadawenhong.zhu@asc-csa.gc.ca

J. Mech. Des 131(4), 041001 (Mar 20, 2009) (13 pages) doi:10.1115/1.3086790 History: Received November 22, 2007; Revised December 03, 2008; Published March 20, 2009

A continuous protein synthesis formulation based on the design principles applied to topology optimization problems is proposed in this paper. In contrast to conventional continuous protein design methods, the power law (PL) protein design formulation proposed in this paper can handle any number of residue types to accomplish the goal of protein synthesis, and hence provides a general continuous formulation for protein synthesis. Moreover, a discrete sequence with minimum energy can be determined by the PL design method as it inherits the feature of material penalization used in designing a structural topology. Since a continuous optimization method is implemented to solve the PL design formulation, the entire design process is more efficient and robust than conventional design methods employing stochastic or enumerative search methods. The performance of the proposed PL design formulation is explored by designing simple lattice protein models, for which an exhaustive search can be carried out to identify a sequence with minimum energy. We used residue probabilities as an initial guess for the design optimization to enhance the capability and efficiency of the PL design formulation. The comparison with the exchange replica method indicates that the PL design method is millions of times more efficient than the conventional stochastic protein design method.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Schematic illustration of a chain of amino acid residues (1), and (b) folded conformation and sequence of 1SRL in the native state

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Figure 2

Lattice protein models: (a) 2D HP lattice protein in an irregular lattice, (b) 3D lattice protein in a 3×3×3 regular lattice composed of multiple types of residues

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Figure 3

(a) Discretized design domain for the design of structural topologies, (b) optimal distribution of a given amount of material (31)

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Figure 4

Material state interpolation by the artificial power law. As the power tends to increase, intermediate material states tend to be penalized (24).

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Figure 5

Interpolation of discrete residue states by the artificial power law: (a) the ith site interacting with the residue at the jth site, (b) a residue state interpolation by the artificial power law: an intermediate monomer state tends to be penalized as the power tends to increase

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Figure 6

(a) Schematic illustration of the most designable 6×6 lattice protein model, (b) uniform intermediate residues provided for the first stage optimization, (c) sequence synthesized for p=1 in Stage I, and (d) sequence synthesized for p=2 in Stage II

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Figure 7

The energy level of synthesized sequences; ○: energy level of the sequences synthesized by the PL design method and ●: minimum energy in the discrete sequence space

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Figure 8

◼: Alanine, ●: aspartic acid, ▲:cystine, and ▼:serine; (a) schematic illustration of the most designable 4×4 lattice protein model, (b) sequence synthesized by the PL design formulation for p=1 in Stage I, and (c) sequence synthesized for p=2 in Stage II using the sequence determined in Stage I as an initial guess

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Figure 9

(a) Schematic illustration of 4ICB, (b) sequence synthesized for p=1 in Stage I using a uniform initial guess, and (c) sequence synthesized for p=2 in Stage II using the sequence determined in Stage I as an initial guess

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Figure 10

(a) Schematic illustration of 1SRL, (b) sequence synthesized for p=1 in Stage I using a uniform initial guess, and (c) sequence synthesized for p=2 in Stage II using the sequence determined in Stage I as an initial guess

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