Team:IISc-Bangalore/Model

  1. Gas Vesicle Structure
  2. Mathematical Model
  3. Experimental Data
  4. Results
  5. References

Gas Vesicle Structure

Gas vesicles are proteineceous nano-structures that are utilized by many aquatic micro-organisms like halo-bacteria and some algae to provide buoyancy. The structure and arrangement is highly conserved between organisms with width being almost the only widely varying parameter. They contain gases which diffuse in during formation and are kept localised by the hydrophobicity of the inner membrane. Unlike true vesicles, these are made of proteins instead of phospholipids and are hence of considerable interest. Each gas vesicle is composed of two primary protein monomers, the gas vesicle forming proteins A (GvpA) and C (GvpC). The entire structure will be discussed in the following sections.

Verification of presence of Gas Vesicles

The easiest way to assay presence of gas vesicles is their disappearance under high pressure under a microscope. This was observed even during normal experiments. Fully filled micro-centrifuge tubes containing dilute gas vesicle suspensions lost their faint opalescence when the tube was closed (this did lead to a loss of samples). A more strict assay was done using DLS (See Dynamic Light Scattering) and SEM Imaging to pinpoint the exact size of the nano-particles. It was found that these gas vesicles have an effective hydrodynamic radius of around 230nm. This estimate was particularly valuable in the development of our model.

GvpA

The gas vesicle forming protein A (~8kDa) forms the main ribbed structure of the gas vesicle. The 3-Dimensional structural model of the protein was recently decoded by Strunk et.al ([1]). As was noted, the best probable docking pattern in a vesicle involves formation of a dimer and their consequent stacking. We intended to re-create the whole gas vesicle structure from this data and try to explain the growth pattern noticed during their formation. It is interesting to note that the hydrophobicity of the internally exposed part of GvpA is what keeps the gases from diffusing out.

GvpC

The gas vesicle forming protein C is the second most abundant protein found in the nanostructure. It is still far rarer compared to GvpA (1:25 molar ratio, [2]) and does not contribute to the structure but rather to the integrity of the gas vesicle. The vesicles used in the various experiments were stripped of GvpC before use and hence were much more sensitive compared to wild type gas vesicles. The critical pressure for the gas vesicles was found to reduce drastically on the removal of this protein.

Stacking of proteins in a GV nanoparticle

3-Dimensional structure of the nanoparticle

Effective buoyant density

Most of the physical properties of the gas vesicles were uncovered by Walsby et al. In their groundbreaking review ([3]). They calculated the average buoyant density of a gas vesicle to be around 120kgm-3. Note that while this density if much less than that of water, it doesn’t necessarily imply a flotation advantage due to the presence of diffusive forces in a suspension. The smaller the particle, higher is the magnitude of these diffusive interactions and more is the deviation from the ideal concentration profile in a column. The mathematical model part of our project deals with finding how these profiles evolve for overtime and how this evolution changes when we purposefully make them flocculate using agents like chitosan and biotin-streptavidin.

Mathematical Model

The following sections detail the development of our model which deals with the dynamics of gas vesicle motion in a medium and how their concentration profiles change over time.

Terminal Velocity

A floating particle in a media experiences multiple types of forces, some of which are more prominent than others. Given the buoyant density of the particle, we can find the terminal velocity by equating all the upward forces to the downward ones and solving for velocity from the stokes’ drag term.

[SCHEMATIC OF A GAS VESICLE]

Assuming the gas vesicle to be of the shape given above, its volume in terms of length l, half angle θ and radius r is given by,

[EQUATION 1.1]

So, the buoyant force on the gas vesicle is given by,

[EQUATION 1.2]

Where ρ is the density of the media.

Similarly, the force due to gravity is,

[EQUATION 1.3]

Where ρgv is the buoyant density of the gas vesicle.

When the particle reaches its terminal velocity, all the forces are balanced. Thus we can equate,

[EQUATION 1.4]

The viscous drag is usually a complex function of particle shape and size, in our case however, the DLS experiment directly gives the hydrodynamic radius of the particle. Hence we can use the well known expression for drag on a spherical particle given by,

[EQUATION 1.5]

Where vt is the terminal velocity and r the hydrodynamic radius.

Solving for vt, we get

[EQUATION 1.6]

The various parameters can be modified to find the terminal velocity for a particular kind of nanoparticle after measuring the hydrodynamic size with a DLS system.

For a normal H. Salinarium gas vesicle, the terminal velocity comes out to be,

[CALCULATE]