Physicist and data scientist. This is a collection of my research & projects.
In this post I will investigate the sequencing data from The Cancer Genome Atlas (TCGA) in order to familiarize myself with handling sequencing data. Specifically, I will focus on a dataset which is a subset of somatic mutations found...
Our study of multicellular chemotaxis was recently published in Physical Review Letters. The work compares two typical methods of collective chemotaxis in order to determine which one is more accurate in tracking chemical gradients.
Random walks have been used to study many phenomena in biology and ecology. Here I present a model of a biased and persistent random walk with the goal of using it to study cell chemotaxis.
In...
Research I conducted in conjunction with Prof. Andrew Mugler and Prof. Bumsoo Han has been published today in Biophysical Journal. The paper, Collective Chemotaxis through Noisy Multicellular Gradient Sensing , examines how cell-cell communication can enable a...
Prof. Andrew Mugler and I wrote a review on cancer metastasis from a physics perspective. By using simple physical models the limits to metastatic cells’ sensory capabilities can be understood, and experimental evidence that cells operate near these...
As previously discussed cell sensing and communication is modelled using the LEGI framework. The polarization vector →p is updated based on the downstream output of the LEGI model and the repulsion vector →q.
\[\frac{d\vec{p}}{dt} =...We vary the parameters β and ϵ and observe the resulting mean first passage time. Other parameters are left fixed unless otherwise noted, all plots are of groups of 4 cells.
Cells in a group communicate with one another in order to sense a gradient. We use a minimal adaptive model based on local excitation and global inhibition (LEGI). The network looks...
Simulation Parameters:
3x3x3 cubes.The simulation ran for 100 different instances each for a maximum of 60 Monte Carlo (MC) time steps.
From the simulations we were able to get statistics on the mean square...
We will continue our discussion on adaptation from the last lecture. We want to answer the question of what causes the sharp decrease (response) in activity A due to an increase in ligand concentration l.
As previously discussed, most bacteria use flagella in order to achieve forward motion. Bacteria then tumble in order to change direction. Experiments have shown that bacteria in environments of high concentration of some attractant...
The goal is to simulate a connected, one-dimensional chain of freely diffusing cells. We model the chain of cells by only worrying ourselves with the edges of each cell since we are interested...
Competance is a state in which bacteria can take in DNA from the environment and add it to their own. It is a desperate action in attempt to speed up evolution in order to survive.
We...
A repressilator is a feedback loop in which each gene suppresses the next one. The following diagram shows an implementation of a repressilator.
Questions about the repressilator
Recall the different types of feedforward loops. Last lecture we discussed the behavior of the C1 loop. The advantage of the C1 loop is that it protects Z from turning on due to fluctuations in X. This...
We have already examined the one node motif of auto-regulation, let’s now explore 3 node motifs.
Let n be the number of nodes and g be the number of edges. For a 3 node motif n=3 and...
A simple check that the simulations are working is to see how the cell volume Vj changes as α changes.
We expect that for large...
Can we say something quantitative about…
Last lecture we came up with an expression for the steady-state probability distribution for an autoregulating protein, but the expression was...
We will continue our discussion of autoregulating genetic networks. Specifically, we will continue talking about autorepression.
Recall that there are two advantages of autorepression.
In this lecture we will broaden our scope to a whole genetic network.
We define a motif as a pattern that is over-represented in a network. A pattern is considered to be over-represented by comparing it with...
We will continue our discussion of noise in gene activation from the previous lecture.
Last lecture we made a simple model for gene activation and the intrinsic noise in the system. Next we...
In the previous lecture we discussed a simple model of protein production with an activator.
X+D⇌k+k−Ck→Y+X+DNow lets consider a more involved model.
Starting with this lecture we will shift our attention in this course. Instead of focusing on physical characteristics of biological systems we will focus on functional control of biological systems.
Here is a simple example of a...
There are three cases that the code handles.
The single cell case is treated as a simple random walk. The edge cases and the...
Experimentally, the speed and the force on a loaded motor were calculated.
Fload=6.5 pNvmotor≈150 nm/sIn the case of an unloaded motor there is no force.
\[v \approx...
amazing picture. (source)
All motors rectify thermal motion. To make a molecular motor its potential energy U(x) needs to have one of the two following properties.
A good guess would be that it depends only on the two rates which we are aware of - the attach and detach rates.
\[\tau \approx...The probability density for cell location given a time t should look like a normal distribution. As time increases this prediction becomes less accurate since more...
Unlike microtubules, actin does not have the same critical concentration for both ends. The “+” end is the side where the filament grows and...
We are interested in calculating the efficiency of the flagellum as a means of propulsion for the bacteria. Efficiency is defined as the following:
\[\mathcal{E}...How do bacteria achieve forward motion?
Bacteria have flagella that drive their propulsion. Bacteria flagella move in a corkscrew pattern. Flagella do not flap back and forth like a paddle....
We will start be continuing in our answer to the question:
What shapes emerge from beinding energy considerations alone?
A pancake is a cylinder with rounded sides.
Let the rounded sides have height...
What determines the shape of grouped lipids?
A good guess is that conical shaped lipids are more likely to form micelles. Let a cone-shaped lipid have a length l, circular...
Consider a polymer where one end is fixed while the other end is free.
Now we apply a force, →f, to the free...
