Combining Optimal Control Theory and Molecular Dynamics for Protein Folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the atoms. In turn, MD simulation provides an all-atom conformation whose positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization - MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages

Prediction of Optimal Folding Routes of Proteins That Satisfy the Principle of Lowest Entropy Loss: Dynamic Contact Maps and Optimal Control

An optimization model is introduced in which proteins try to evade high energy regions of the folding landscape, and prefer low entropy loss routes during folding. We make use of the framework of optimal control whose convenient solution provides practical and useful insight into the sequence of events during folding. We assume that the native state is available. As the protein folds, it makes different set of contacts at different folding steps. The dynamic contact map is constructed from these contacts. The topology of the dynamic contact map changes during the course of folding and this information is utilized in the dynamic optimization model. The solution is obtained using the optimal control theory. We show that the optimal solution can be cast into the form of a Gaussian Network that governs the optimal folding dynamics. Simulation results on three examples (CI2, Sso7d and Villin) show that folding starts by the formation of local clusters. Non-local clusters generally require the formation of several local clusters. Non-local clusters form cooperatively and not sequentially. We also observe that the optimal controller prefers “zipping” or small loop closure steps during folding. The folding routes predicted by the proposed method bear strong resemblance to the results in the literature

Sequential stabilization of decentralized control systems

Chemical Engineering Communications168187-206CEGC

Interaction measure for the selection of partially decentralized control structures

Industrial and Engineering Chemistry Research37124734-4739IECR

Extremely fast catalyst temperature pulsing : design of a prototype reactor

This paper discusses a novel principle of advanced process control strategy: the extremely fast and local pulsing of temperature. This strategy leads to some interesting potential applications, but there are no devices implementing it available yet. One such device currently under construction by the authors is introduced in this paper. It operates by converting electrical energy into heat by forcing a very high current through a very thin resistive element, which also acts as the catalyst for heterogeneous reactions. A design procedure for the key parameters is developed and a simulation of heat distribution in the design under construction is presented The simulation shows that it should be possible to get local temperature peaks of 500 K which exist for only about 20 µs

The level of quality of radiology services in Turkey: A sampling analysis

PubMed ID: 17160797Purpose: To determine the quality of radiographs, which have been referred from 40 different institutions for consultation, to discuss the causes of wasted resources; and to present possible solutions. Materials and methods: Five experienced radiology instructors determined the types of radiological examinations referred for consultation (conventional radiography, mammography, computed tomography and magnetic resonance imaging), the institutions at which they were performed (university or state hospital, private health center), and assessed the coverage area, field of vision (FOV), and dosage of x-ray. They also investigated problems in film processing, defects in sequence-printing windows, checked window levels, and checked the amount and timing of contrast material used. According to these criteria, the reviewers subjectively classified each radiograph as: 1. Poor, examination should be completely repeated, 2. Fair, examination should be partially repeated, 3. Good, accepted as adequate, no need for an additional examination, 4. Excellent, examination was as it should be. Results: We reviewed 120 radiological examinations from 40 different institutions in 4 reference centers. Frequency of problems determined for each category was as follows: coverage area 32.5% (39/120), FOV 16% (14/86), X-ray dosage 16% (15/94), film processing 31% (37/120), sequence or window 65% (53/81), window level 44% (36/81); contrast material 51% (25/49), timing of contrast material 61% (30/49). Only 22% of the examinations were classified as excellent, whereas 47% required complete or partial repetition. Conclusion: Approximately half of the radiological examinations in our sampling required partial or complete repetition. Health, ethical, and economic aspects of the problem necessitates the prompt application of measures to establish radiological quality control and standardization procedures. © Turkish Society of Radiology 2006