Science Buddies: "Ask an Expert"

Hello,

I'm trying to put together a docking package for virtual screening, and I have a question about them energy minimization step that is performed on the ligand and receptor prior to docking and after each pose is placed in the receptor (Metropolis Monte Carlo conformational search).

If I were to use a force-field based scoring function to determine how well the ligand binds to the receptor, I would use the same scoring function for energy minimization right? I'm a little confused by what the following algorithms are used for if a Stochastic search (like Monte Carlo) is used in conjunction for docking/scoring: How come these algorithms are not used during the conformational search and only for energy minimization?

Steepest Descent (SD)
Conjugate Gradient (CONJ)
Adopted Basis Newton-Raphson (ABNR)
Newton-Raphson (NRAP)
Powell (POWE)
Truncated Newton Method (TNPACK)

Thanks!

- Eric

don't mean to be a pest, but bump! anybody out there?

Hi Eric,

Sorry for the late reply. On top of that, perhaps I am not the most qualified to answer this (I'm sure you know more about this than I do), but I will certainly give it a shot.

My best understanding is that stochastic searches (Monte Carlo) are used for the conformational searching because it most closely mimics true biological function, since the ligand searches randomly for a docking site (as a side note, this may not be most accurate due to the globular intermediate folding structures hypothesis, but I suppose you already know about this). However, the energy minimization and scoring are not random but are instead functions defined across the whole surface of the receptor. I can't speak to the exact algorithms that you mention, but they all search in general for minima of surfaces, in this case of an energy functional surface defined by all possible binding conformations, whereas the force-field is the scoring itself that generates the energy functional surface. In simpler terms, the force-field scores to generate an energy surface for each conformation, then use a energy minimzation function on that surface to find the best conformation, within the stochastic paths given by the Monte Carlo.

I have only the most general knowledge about the molecular conformation problem, but perhaps the following is pertinent.

The Monte-Carlo methods search more or less randomly, and can search over an arbitrarily large parameter space. The other methods try to find the lowest point in a local "valley" of the target function. They never (unless by error) take the parameters outside the valley. If the parameters start off in the wrong valley, you never find out what's over the nearest hill.

A Monte-Carlo method hopefully can find the right valley, and the directed search methods can refine the conformation.

Hi Aaron Lin,

I think I understand what you mean but I just wanted to clarify:

So a scoring function doesn't generate a single number R, where R = binding affinity? Instead it produces an energy surface (i imagine the following picture, except the real thing has many more dimensions), whose lowest point is found by the minimization algorithm (steepest descent, conjugate gradient?) Then the lowest point should be the value R right?



Hm, before I always imagined force field scoring to be a equation that takes in a bunch of parameters (or at least iterates over them for pairs of atoms between the ligand) and spits out a value. I also thought that when the searching takes place, it goes something like this:

1. random position/rotation of ligand to receptor.
2. scoring function spits out a number R
3. repeat M.C. algorithm, using Metropolis to get closer to a better number R.

But I'm probably mistaken (and definitely confused now) - how can scoring generate a potential energy surface if the measurements between the ligand and receptor are determinate? Is it because you are accounting for degrees of freedom based on that stochastically-generated pose, and then using minimization to find the approximately closest one within the stochastic pose? Seems like sampling is still required to generate that surface from within a pose, and wouldn't that result in repeated samples (since potential energy surface probably has intersections with the hyperplane generated by the Monte Carlo)?

Why not just do more sampling from the Metropolis M.C. and use a function that spits out the number R without having to implement a minimization algorithm?

sorry for my confusion...

- Eric

Hi Eric,

Oops, I suppose that was a tad unclear. A scoring function is still a function, returning a single number, let's say S (for energy score) for a bunch of given parameters (based on some hypothetical binding position). Based on the random sampling, multiple (forming a surface) hypothetical binding positions could be iterated, and for each position the scoring function would assign that a unique S. Because the sample would be iterative, you would generate a surface with S as the dependent variable. Minimizing S on that surface would give you the best binding position (lowest energy, etc). I suspect that force-field scoring refers to the overall process rather than an actual particular function. In short, I am agreeing with your 1,2,3 method. Perhaps the MC algorithm is not that biologically accurate (again, refer to the intermediate globular structures hypothesis, but who knows?)

As to your last question, I think that is a big debate within the field. Protein folding more broadly has been debating this question (see the Levinthal sp? paradox). Minimization provides the most stable structure, but whether this is achieved (and under context-specific conditions), or if it is closer to an MC simulation, is very much under debate. There is certainly support for both sides, so I would choose one way to implement based on the literature that you have read.

Ahhh that enlightening feeling when you suddenly understand how things work and at the same time feel so ashamed for being ignorant before.

Thanks Aaron, I understand it know - before I thought that optimization has to be done on an explicit mathematical equation (like x^2-x+2), but I just learned from Stanford's ml-class that minimization/optimization can be performed on a data set or matrix that define the energy surface.

So minimization is used to guide the scoring function to the lowest value once enough S values have been calculated? So if minimization guides the scoring function to the lowest energy value S, then how does minimization integrate with the docking algorithm? Seems like docking algorithm (e.g. metropolis) also guides the conformational search, but if docking gets to guide the molecules, why is minimization required?

Hi Eric,

Good that it makes sense to you! I think some of my attempted help was unclear before, but hopefully it is helpful in some way.

I think the remaining confusion may just be semantics (or it might not). My understanding was that docking was the name for the whole algorithm (initial binding, searching, scoring, and minimization), but I could be totally wrong here. If so, let me know and maybe provide a bit more information about the type of docking algorithms that you are referring to.

Hi Aaron,

You are right in that docking is the whole algorithm. It was me that was confused - I think I am understanding it a little better now with regards to conformational search: technically the stochastic search I am using (Monte Carlo) could replace minimization but i think that some parameters are given to Monte Carlo to 'optimize' and others like bond length and angles are given to minimization algorithms:

"In MC implementations, the ligand is considered as a whole and random changes are made to change the translation and rotation of the ligand, as well as torsion angles. After each move, the structure is minimized, and the energy of the new structure is determined. Minimization before evaluating the Metropolis criterion increases convergence".

So in a sense I think we were talking about the same concept of using optimization (whether by monte carlo or one of the minimization algorithms), but the thing that confused me is that the metropolis criterion can actually be used to replace minimization (and thus MCMC can simply coupled with the scoring function).

- Eric