key operation for MD Simulation and studying Protein Interactions
- EMin is finding lowest energy form on a graph, like a regular math problem
- Central dogma: lowest energy structure is the ‘correct’ one
- This is where first derivative = 0
- If 2nd derivative > 0, it’s a minimum
- if 2nd derivative < 0, it’s a maximum
- If 2nd derivative = 0, it’s a saddle point
- So in this problem
- y is potential energy usually from force field equaitons
- Xi is coordinate, sometime cartesian but not usually
- This is where first derivative = 0
- We have to look for global minimum not local minima
- Newton’s method: most CPU intensive but accurate
- Approximate y locally using a Taylor series truncated to a parabola
- Newton-Raphson: generalization of newton to multiple dimensions
- **Steepest descent: **cheap on CPU works better when far away
- Draw bunch of lines and use 3 points to make parabolas
- calculate one with lowest point, go there. Repeat
- Good at getting in the area quickly on dramatic cliffs but struggles with shallow plains it will wander aimlessly
- Conjugate gradients: good general more expensive than steepest
- Use M steps where M is the number of variables
- Search in one, draw orthogonal vector for each one and proceed
- Strategy
- It’s advisable to start with a cheap one like steepest descent then refine search with a more expensive and accurate method
- Newton’s method: most CPU intensive but accurate