Estimate the time between different residues?

Question

Imagine now, I have 5 structures, and I want to estimate the time when the 5 structures are closer to each other at the same time. I thought I could extract the distance between the different structures and structure number 1 (i.e., the distance between structure 1 and 2, the distance between 1 and 3, 1 and 4, etc.). At the end, I will have 4 files that contain the time and distance between these structures with respect to structure number 1. But when I plotted these different files, I couldn't know when the 5 structures were closer to each other at the same time.

Does anyone have any suggestions?

Answer 1

Let the centre of mass of each residue be denoted as $r_i$ and is evaluated at every frame. Let the centre of mass of the combined system be $r_c$ where c denotes combined. You can evaluate the distance between each $r_i$ and $r_c$ at every frame. This will give you 5 distance values for each frame. Now the task is to minimize the function $f(d_i) = \Sigma d_i$. If you evaluate that function at every frame, you should get the lowest values when all your residues are close to one another.

Here is a Tcl script that can do that

set psf adenine.psf
set dcd adenine.dcd
set output  [open distance.dat w]

mol load psf $psf
mol addfile type dcd $dcd waitfor all

set numframes [molinfo top get numframes]

for { set framecounter 0 } { $framecounter < $numframes } { incr framecounter } {
    molinfo top set frame $framecounter 
set total [atomselect top "resname ADE"]            # selects all the adenine molecules
set tcom [measure center $total weight mass]        # gets the centre of mass for the combined adenine system
    set segnames [lsort -unique [$total get segname]]   # gets the segnames for each adenine molecule
set dist {}
foreach segname $segnames {
        set sel [atomselect top "resname ADE and segname $segname"]
    set rcom [measure center $sel weight mass]
        set distance [veclength [vecsub $rcom $tcom]]   # calculate the distance between each residue COM and total COM
        lappend dist $distance                  # append it to a list
    }
    
    set totaldistance 0
    foreach distance $dist {
    set totaldistance [expr $totaldistance + $distance]
}
puts $output "$totaldistance"
}

close $output
mol delete all
exit