<<<<<<< HEAD

simulation.py:

the final version and go to output.txt to check output

npyReader.py

to heads.npy and furthest.npy generated in simulation.py

distance.png

ratio of cir and con with increasing distance and fixed DNA length

original.py:

the original version

previous.py:

a temporary file saving last edition

byGPT.py:

a very basic example generated by GPT with visualization

heads.npy. and furtherest.npy

positions of all heads and the furthest distance from head to tail for each molecule

output.txt is:

the output of simulation.py

Overview

This project is to simulate DNA circularization and concatemerization using mathematical model.

Circularization direcotry contains all models simulating circularization. Similarly, concatemerization directory
contains all models simulating concatemerization. Models in these two files consider circularization and
concatemerization independently, which might be a limitation.

Data directory contains all data for all models. Same for figure directory.

Circularization\

For circularization, we have several models.

Eventual Return Formula

It uses combinatorial formula to count number of returns of DNA to calculate probability of circularization. It is
counted as circularization as it reaches the origin. The limitation is that there is a big gap from reality.

Random Walk Model

We use a random package for choosing the next step, and let it walk for a certain number and count number of
circularization. We define circularization happens if the head of DNA is within a sphere with radius 1 length of
nucleotide created based on the position of tial of DNA.

There are many ways for randomly walk. For a fast method, one is for 6 directions, and another is 5 directions, which
does not include completely going back direction. We also have lattice grid with 360 * 180 directions and another way
that distribute directions based on Fibonacci sphere and it cannot go to directions too sharply curved from previous
direction.

We use numba to accelerate the speed of running.

Concatemerization\

For concatemerization, we use Monte Carlo method to get probability.

We defined concatemerization happens if, similarly from circularization, distance between head and tail is elss than 1. For comcatemerization_ranom.py, the DNA tails are randomly generated according to uniform distribution. Other files
assumed DNA tails are evenly distributed, which is far from reality.

Others

direction_functions.py contains all functions generating directions.

directionTest.py is to test functions in directions_functions.py.

simulation.py contains a model considering circularization and concatemerization together.

npyReader.py to heads.npy and furthest.npy generated in simulation.py

distance.png ratio of cir and con with increasing distance and fixed DNA length

original.py the original version

previous.py a temporary file saving last edition

byGPT.py a very basic example generated by GPT with visualization

heads.npy and furtherest.npy positions of all heads and the furthest distance from head to tail for each molecule

output.txt is the output of simulation.py

9521a518d321760724ecfba7f2e7810af0fb17be