Corpuscles

Introduction

1. Bending elasticity of lipip bilayer


2. Strain (both shear and strecth) elasticity of cytoskeleton


3. Viscosity of lipid membrane


4. Thermal fluctuations of lipid membrane


5. Constraint of reduced volume of a closed membrane surface


6. Constraint of total area of a closed membrane surface


7. Constratin of total volume of a closed membrane surface


8. Constratin of area difference between outer- and inner-surface

Install

$ cat conf.mk
CC = gcc
FC = gfortran

FCFLAGS = -O2 -g
FXFLAGS = -fallow-argument-mismatch

GSLCFLAGS = “ gsl-config --cflags“
GSL_LDFLAGS = “ gsl-config --libs“

CFLAGS = -O2 -g
LDFLAGS =
PREFIX = $(HOME)/.local
DATAPATH = $(HOME)/.co
MAXIMA_HOME = $(HOME)/.maxima

# prefix for commands
P = co

$ cat $HOME/.bashrc
PATH=”$HOME/.local/bin:$PATH”

$ MAKEFLAGS=-j4 make

$ make test

$ cat main.c
#include 

#include 
#include 

#define FMT CO_REAL_OUT

int
main(void)
{
    real A, a[] = { 0, 0, 0 }, b[] = { 2, 0, 0 }, c[] = { 0, 1, 0 };
    A = tri_area(a, b, c);
    printf(“Area of a triangle is : “ FMT “\n”, A);
}

$ cat Makefile
include ../../conf.mk
PREC = d
main: main.c
    $(CC) main.c $(CFLAGS)  co.conf --cflags --libs $(PREC) $(LDFLAGS) -o $@
clean:; rm -f main

$ ./main
Area of a triangle is : 0.9999999999999999

This program reads an OFF file from an input stream:

$ cat main.c
#include 
#include 
#include 
#include 
#include 
int
main(void)
{
    real *x, *y, *z, hi;
    He *he;
    int nv, nt;
    y_inif(stdin, &he, &x, &y, &z);
    nv = he_nv(he);
    nt = he_nt(he);
    hi = array_max(nv, x);
    printf("number of vertices is %d\n"
           "number of triangles is %d\n"
           "maximum x coordinate is " CO_REAL_OUT "\n", nv, nt, hi);
    y_fin(he, x, y, z);
}

$ make
$ ./main < `co.path`/regular/tetra.off
number of vertices is 4
number of triangles is 4
maximum x coordinate is 1
 

Write mesh file

Read off, compute area of every triangle, and output off file with
colors (example/off/write/area)

$ cat main.c
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
int main(void) {
    int nt;
    real *x, *y, *z, *a;
    He *he;
    y_inif(stdin, &he, &x, &y, &z);
    nt = he_nt(he);
    CALLOC(nt, &a);
    he_area_tri(he, x, y, z, a);
    boff_tri_fwrite(he, x, y, z, a, stdout);
    y_fin(he, x, y, z);
    FREE(a);
}

$ ./main < $(co.path)/rbc/laplace/0.off > out.off

To see the results

$ co.geomview -r 55.9195 -13.672 8.69021 -f 25.0389 out.off

Refine mesh

$ co.geomview -r 60 -40 10 -f 22 `co.path`/rbc/icosahedron/0.off
$ co.sqrt3 < `co.path`/rbc/icosahedron/0.off > a.off
$ co.geomview -r 60 -40 10 -f 22 a.off

Visualization

$ co.geomview -h
co.geomview [-t x y z] [-r x y z] [-a APPEARANCE] [-o FILE] [OFF]..
he geomview wrapper
-t x y z      translation
-r x y z      rotation in degree
-f zoom       field of view (default is 40)
-a APPEARANCE load appearance from a file
-o FILE       write FILE and exit
-O            write all PPM files and exit
-OO           write all oogl files and exit
-format    ppmscreen|ppm|ps|ppmosmesa|ppmosglx
-p command    process every off file by running  ‘command ‘ < IN.off > OUT.off
-n none|each|all|keep normalization status (see geomview manual)
-c command    run command on every file and write output to stderr, %f is replaced by a file name
-e command    if keys  ‘e ‘ is pressed runs
               ‘<OFF command -t x y z -r x y z -f zoom -i [index of a file] -n  [number of files]  ‘ or
               ‘<OFF command ‘ if -e  ‘|command ‘ is passed
-i command    run command on every image, %i replaced by input; %o — by output; %b —- by basename

Keys:
    q: quit
    s: save snap.ppm
    S: save every snapshot
    e: run command on OFF file (see -e option)
    p: panel
    j/k: switch between off files
    J: dump file name
    [SPC]: dump orientation and field of view

Environment variables:
WX, WY: resolution of the snapshot (default: 800x600)
BACKGROUND: default ( ‘1 1 1 ‘)
GEOMVIEW_ARGS: pass to geomview

Examples:
co.geomview -t 0.25 0.25 0     data/rbc.off
co.geomview -a data/appearance data/rbc.off
co.geomview -o snap.ppm        data/rbc.off
co.geomview                    data/rbc.off data/sph.off
co.geomview -p co.orient       data/rbc.off data/sph.off
co.geomview -c off.volume      data/rbc.off data/sph.off

Library

Floating point precision

prec/s/real.h, prec/d/real.h, prec/l/real.h
: single, double, long double

Math

vec.h, edg.h, tri.h, dih.h, ten.h
: vector, edges, triangels, dihidrals, tensors

dvec.h, dedg.h, dtri.h, ddih.h
: derivatives of vector edges, triagels, dihidrals

ring.h
: operation on the first ring of neighbors

Utility

array.h
: array related functions

argv.h
: read from argv and shift

err.h
: error handling

endian.h
: deal with endianess

macro.h
: macros

sum.h
: Kahan summation

memory.h
: memory related

util.h
: uncategorazed

Surface properties

area.h
: area

volume.h
: volume

laplace.h
: Laplace operator of coordinates

normal.h
: normal

“Forces”

bending.h
: generic interface to several bending forces

forces.h
: generic interface to forces

stretch.h
: stretching force

Surface transformation

equiangulate.h
: equlatirate triangles

orient.h
: orient surface in a direction of eigen values of momentum tensor

restore.h
: restore a volume of the surface

transformation.h
: translate, rotate, and and scale surface

remesh.h
: “edit” surfaces

Half-edg related

read.h
: read half-edg to intermediate structure HeRead, used to initialize half-edg

he.h
: half edg data structure (provides half-edg API)

hash.h
: stores an integer for a pair of integers

IO

gts.h,
obj.h,
off.h,
ply.h,
punto.h,
stl.h,
stl.h,
xdmf.h
: read/write GTS, OBJ, OFF, PLY, punto, STL, VTK, and XDMF files.

X and Y

x.h
: simple interface for one surface

y.h
: not so simple interface

Documentation

git pages
docs/index.html is generated from
README.md.m4. To update run

$ make html

requires pandoc.

Hacking

After adding new files to lib update depdendencies:

$ (cd lib && ./bootstrap)

Publications

Bian, X., Litvinov, S., & Koumoutsakos, P. (2020). Bending models of
lipid bilayer membranes: Spontaneous curvature and area-difference
elasticity. Computer Methods in Applied Mechanics and Engineering,
359, 112758.
doi:10.1016/j.cma.2019.112758