Lateral interactions between protein molecules adsorbed onto a planar interface

Abstract

This paper seeks to express the chemical potential for proteins on a surface in terms of number surface densitiy. Generalized Van der Waals (GVdW) theory and Virial hard disk theory are explored and fitted to experimental data by varying the hard disk radius.
Additionnally Metropolis Monte Carlo simulations are used to simulate the interactions between proteins. Simulations are done on freely rotating proteins with the center of mass constrained to a 2D plane and employing the Widom insertion method to calculate the chemical potential. The theory, derivation and discussion of GVdW, Virial and Widom insertion are examined in this paper. Finally an interactive tool is included, which dynamically plots GVdW potentials. This tool is available online, both as source code and as a public web interface.

Popular Abstract

The surface of cells or the cell membrane contains proteins that are floating along the surface. How closely can you pack those proteins and how much energy would that cost?
Proteins like to be spread out across the surface. The proteins are anchored to the cell membrane, but can move along the surface. In this way, they behave similarly to the particles in a gas, except that they can only move in two dimensions. 

One can indeed quite accurately model the proteins on a cell surface as a two-dimensional gas. Even the most basic theory of gases—which models molecules as hard marbles that bounce off each other when they get to close works quite well. Even though the shape, charges and other interactions of the molecules have been ignored, the hard marbles theory which only model the volume of the proteins correctly is able to make some decent rough predictions for the chemical potential, where the chemical potential is defined as the amount of energy it takes to add a single particle to the system.
More than a century ago Dutch physicist Johannes van der Waals developed theories that describe the behavior of gases. The description of liquids and gases that he developed, is now called the “Van der Waals equation of state” and earned him the Nobel prize in physics in 1910. His theory is still relevant today and factors in two corrections to the ideal gas law: Firstly, molecules take up space, and their “excluded volume” limits the
movability of the other molecules, which increases the pressure. Secondly, molecules attract each other, which lowers the pressure, which is expressed with a value called the “binding constant”. 

An alternative way to study the properties of a gas is to simulate it: put some virtual molecules in a virtual box and let the computer move and rotate them such that this virtual system is representative of a physical system. Then this virtual gas can be analyzed by several methods. For example, the chemical potential can be analyzed by via a sampling algorithm. The chemical potential is defined as the amount of energy it takes to add a single particle to the system. In the virtual gas you can do just that: add a particle to your system and calculate how the energy changes. Remove the particle and repeat the process a hundred times so you can calculate an average. 

This thesis treats proteins on a surface as gas molecules in a plane in order to find physical properties about them, such as the chemical potential. The moleculer were modeled as “hard marbles”, then interactions were introduced by calculating the “binding energy constant”, and even more details were taken into account by simulating the proteins entirely on a computer.

• author: Kouwenhoven, Niels
• supervisor: Mikael Lund; Peter Jönsson
• organization: Department of Chemistry
• course: KEMN30 20171
• year: 2017
• type: H2 - Master's Degree (Two Years)
• subject: Chemistry
• keywords: Monte Carlo simulation 2D Van Der Waals, nanochemistry, nanokemi
• language: English
• id: 8927990
• date added to LUP: 2017-12-18 08:58:43
• date last changed: 2017-12-18 08:58:43