SolSim.jl

SolSim.jl simulates solute molecules, modeled as a union of hard spheres, in an implicitly modeled hard sphere solvent. The solvation free energy of the system is calculated by the so called morphometric approach.

The computationally difficult part of this approach is to calculate geometric measures of a union of 3d balls. We utilize a wrapped version of the AlphaMol program written by Patrice Koehl.

SolSim.jl is written in Julia.

To run SolSim.jl you will need to:

1. Install and run Julia 1.7.3 or later

2. Build the SolSim.jl package

Running the First Simulation

In the scripts folder you can find some useful helper functions to run simulations. To run a simulation for eight balls that has a helical configuration as the putative minimiser do:

    julia> include("scripts/hard_sphere_simulated_annealing_calls.jl")
    julia> single()  

Outputs are saved to "io/output/singles". See the function declaration for parameters you can adjust.

The file "scripts/reproduction_calls.jl" contains several functions that scan the parameter space given by solvent radius, packing fraction and number of dissolved particles. The data generated by these functions is discussed in this paper.

# Viusalization in Houdini

Look at generated output files in Houdini. A Houdini project for this is included in the repository under "externaltools/solsim_visualizer.hipnc". The following two renders give an example:

Hard Spheres Assembled into Helix	Corresponding Contact Graph

A bug and its implications

When generating the data presented in the publication: Exotic self-assembly of hard spheres in a morphometric solvent there was bug in the calculation of the geometric measures. The mean curvature can be decomposed into positive and negative parts, i.e. $C = C^+ + C^-$. The bug was that $C^-$ was counted twice. This led to the simulations being driven by the following energy:

$E = p{wb} V + \sigma{wb} A+ \kappa{wb} (C + C^-) + \overline{\kappa}{wb} X$,

where $p{wb}, \sigma{wb}, \kappa{wb}$ and $\overline{\kappa}{wb}$ are the white bear prefactors.

For a union of balls $\bigcup{i} Bi$ with radii $r_i > 0$, the mean curvature $C$ can be written as

$C = C^+ + C^- = \sum{i} \frac{Ai}{ri+rs} + C^- = \frac{1}{R+rs}\sum{i} Ai + C^- = \frac{A}{R+rs} + C^-$,

Therefor we can write $E$ as follows

$E = p{wb} V + (\sigma{wb} - \frac{\kappa{wb}}{R+rs}) A+ 2\kappa{wb} C + \overline{\kappa}{wb} X$,

which is the classic morphometric approach with a different set of prefactors.

The white bear prefactors are give by:

$\beta p{wb} = \frac{\eta}{rs^3} \frac{3}{4\pi}\left(\frac{1+\eta+\eta^2-\eta^3}{(1-\eta)^3}\right)$,

$\beta \sigma{wb} = \frac{\eta}{rs^2} \frac{3}{4\pi} \left( - \frac{1+2\eta+8\eta^2-5\eta^3}{3(1-\eta)^3} - \frac{\text{ln}(1-\eta)}{3\eta}\right)$,

$\beta \kappa{wb} = \frac{\eta}{rs} \frac{3}{4\pi} \left(\frac{4 -10\eta+20\eta^2-8\eta^3}{3(1-\eta)^3} + \frac{4\text{ln}(1-\eta)}{3\eta}\right)$,

$\beta \overline{\kappa}_{wb} = \eta \frac{3}{4\pi} \left(\frac{-4 + 11\eta -13 \eta^2+4\eta^3}{3(1-\eta)^3} - \frac{4\text{ln}(1-\eta)}{3\eta}\right)$.