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lecture7 - Molecular Dynamics Introduction Motivation Most...

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Molecular Dynamics Introduction Motivation Most questions in molecular biology are concerned with dynamic processes in macromolecules. Levinthal’s paradox: How does protein folding happen quickly on a high-dimensional energy landscape? How does protein structure change during a catalytic reaction? How do DNA bending and twisting a ff ect gene regulatory processes such as chromosome crosstalk? How do transcription factors find their target sequences? How are structure and stability related in RNA sequences? How can we design e ff ective drugs that bind to specific regions in proteins or nucleic acids? Jay Taylor (ASU) APM 530 - Lecture 7 Fall 2010 1 / 20
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Molecular Dynamics Introduction Quantitative Models of Molecular Dynamics Molecular dynamics attempts to address these kinds of questions by simulating the motion of individual molecules. MD can be used to study processes that cannot be observed directly. Representations can be atomistic or coarse-grained. Motion is usually modeled using Newtonian mechanics. Thermal fluctuations can be modeled using Langevin or Brownian dynamics. Example: Translocation of DNA through the α -hemolysin pore. (Math´ e et al. 2005) Jay Taylor (ASU) APM 530 - Lecture 7 Fall 2010 2 / 20
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Molecular Dynamics Introduction Newtonian Mechanics and Molecular Dynamics The potential energy function constructed in molecular mechanics can be incorporated into Newton’s equation of motion: M ˙ V ( t ) = −∇ U ( X ( t )) ˙ X ( t ) = V ( t ) where X ( t ) R 3 N is the position vector of the atoms; V ( t ) R 3 N is the velocity vector; M is the 3 N × 3 N diagonal matrix of atomic masses; F ( X ( t )) = −∇ U ( X ( t )) is the force. Jay Taylor (ASU) APM 530 - Lecture 7 Fall 2010 3 / 20
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Molecular Dynamics Introduction Initial Conditions: Positions The initial locations of the simulated particles can be assigned using a combination of empirical and theoretical evidence. The coordinates of the atoms in the macromolecule are often taken from a solved structure and then subjected to a round of energy minimization. Solvent and salt molecules are added next, using information about the charge distribution on the macromolecule, and the whole system is again refined by energy minimization. Caveat: MD simulations usually exhibit sensitive dependence to initial conditions. Jay Taylor (ASU) APM 530 - Lecture 7 Fall 2010 4 / 20
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Molecular Dynamics Introduction Initial Conditions: Velocities The initial velocities are usually sampled from the Maxwell-Boltzmann distribution : p ( V ) = N i =1 m i 2 π k B T 3 / 2 exp m i ( v 2 i , x + v 2 i , y + v 2 i , z ) 2 k B T where V i = ( v i , x , v i , y , v i , z ) is the velocity vector of the i
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