Review Session BS123A/MB223 UC-Irvine Ray Luo, MBB, BS

Math Requirements Differentiation (up to the 2 nd order) of 1-d, 2-d and 3-d functions Integration of 1-d functions Bring your calculator!!!

Theoretical Grounds Newtonian v.s. quantum mechanics Deterministic v.s. probabilistic descriptions Note that molecular events should be described by quantum mechanics in principle The pros and cons of both approaches

Representations of Molecules Sequence Bonding Fold Volume Surface Physical/Chemi cal properties

Molecular Mechanics Design principles Formalism of the simplistic molecular mechanics force fields (also explained in book) Significances of the parameters in the simplistic force fields Nonbonded interactions: Coulombic, van der Waals, hydrogen-bonding, polarization, and their scalings

Potential Energy Surface The importance of PES Descriptions of PES, maxima, minima, global minimum, saddle points, their mathematical definitions. Need to know how to obtain them for a given simple mathematical function Classifications of minimization methods

Minimization Methods Why we need conjugate directions, how are they defined? How steepest descent works? Ideas behind Newton-Raphson You are required to perform simple minimization on paper for simple mathematical functions Pros and cons of each minimization methods

Molecular Dynamics Simulations Space and time scales in biochemistry Formalism of molecular dynamics What physical properties are most important in molecular dynamics? Differences between dynamics and minimization

Applications in Thermodynamics Boltzmann’s law, and the example on atmosphere Microscopic events v.s. macroscopic measurements How to calculate observables given the Boltzmann’s law? How to calculate observables in molecular dynamics? The ergodic hypothesis

Applications in Kinetics The assumption for kinetics studies given that dynamics algorithm is chaotic Simply perform numerous independent runs for statistically meaningful conclusions – reproduction of a kinetics measurement in a test tube Need to know how to perform a kinetics analysis given sample data by following instructions

Practical Aspects of MD Starting a simulation Controlling the system (temp, press, density) Equilibrating Looking at the atoms Real simulation data will be given to test your knowledge.

Complexity of Biochemical Systems Complexity is the scaling with the number of particles. Number of terms in pair potential is N(N- 1)/2  O(N 2 ) For short range potential you can use neighbor tables to reduce it to O(N)

Tricks in MD How to make force calculation fast? It can use 99% of the computation time. Avoiding square root Table look-up and spline-fit potentials Multiple time-step methods Proper handling of long-range forces Cutting corner in solvating biomolecules

Monte Carlo Simulations Goal: Achieving an equilibrium distribution according to Boltzmann’s law R’ R E’E’ E

Monte Carlo: How It Works How it works? By definition, equilibrium means that probability of transition_(R A → R B ) = probability of transition_(R B → R A ). What is detailed balance condition? How is it derived? Design of a method to achieve Boltzmann distribution, i.e. P(A)/P(B) = exp[-(U A – U B )/k B T], and to satisfy the detailed balance, i.e. probability of transition_(A → B) = probability of transition_(B → A). Need to know how to use the detailed balance condition for acceptance.

Free Energy Simulations Basic idea of free energy perturbation Why is it only possible to calculate small free energy changes with this method? Practical usage of free energy perturbation usually needs a thermodynamics cycle. Need to know how to compute thermodynamics data with the thermodynamics cycle.

Simple Free Energy Simulations Docking, MMPBSA, and Predominant state concept