Nucleoids, Janus Particles,
and Active Matter

Wendell Smith

Topics

Flow through the Nucleoid

Janus Particle Propulsion

Active Particle Simulations

Flow through the Nucleoid

Hard Inner SpherocylinderSoft Potential
Spherocylinder Flow
Spherocylinder Flow
Spherocylinder Shape
Spherocylinder Shape

Flow through the Nucleoid

WigginsSoft Potential
Spherocylinder Flow
Spherocylinder Flow
Spherocylinder Shape
Spherocylinder Shape

Passive Model

If we combine the predicted drift velocity maps for the nucleoid exclusion and membrane confinement models, we see striking agreement with the qualitative shape and quantitative scale of the observed drift velocity map throughout the entire cell.
— Stylianidou, Kuwada, and Wiggins [3]

  • They use an entirely passive model, like ours, to predict the same nucleoid flow

Position Dependent Diffusion Constant

wiggins diffusion B
Fig. 4B from Wiggins

  • “The nucleoid-exclusion model would naively predict both decreased occupancy over the nucleoid as well as a decreased diffusion coefficient. Strikingly, our results show exactly the opposite phenomenology: comparison between the occupancy of MS2-mRNA (Fig. 2 A) and the position dependent diffusion coefficient (Fig. 4 B) reveals that the highest diffusion coefficients are observed in regions with the lowest MS2-mRNA occupancy and the highest nucleoid density.”

Position Dependent Diffusion Constant

Fig. 4B from WigginsSoft Potential
Spherocylinder Shape
Spherocylinder Shape

Diffusion constant calculated from

\[ D \sim \frac{\left< \Delta x^2 \right>}{\Delta t} \]

Step Size Distribution

WigginsSoft Potential
Spherocylinder Shape
Spherocylinder Shape

Janus Particle Propulsion

Janus Particle Flow

  • Half of each particle is coated with platinum, which catalyzes \(2 \mathrm{H_2 O_2 \rightarrow 2 H_2 O + O_2}\) on only one side

  • “The particles are being propelled by the local osmotic pressure gradient created by the asymmetric chemical reaction.” [2]

Note
Image is a modified diagram from a different paper [1].

Janus Particles

Janus Particle Trajectories
Janus Particle Trajectories in varying concentrations of H2O2

Janus Particles

Janus Particle MSDs

  • Particles in H2O2 move much farther

Active Particle Simulations

  • Metabolic activity does not significantly raise the temperature of the cell (right?)

  • ATP, the main energy source of metabolism, has energy \(E_\mathrm{ATP} \sim 20 k_B T\)

  • Metabolic activity would not have a rotational orientation

  • Individual events happen infrequently, relative to the diffusion coefficients

Simulating Metabolism

  • Langevin thermostat \[ \vec F = -\vec \nabla U - \gamma \vec v + \vec \Gamma_T + \vec \Gamma_k\left(t\right) \]

    • WCA potential / repulsive Lennard-Jones for \(U\)

    • Damping \(\gamma\) to simulate solution viscosity

    • Random, instantaneous "kicks" to the particles

      • \(\vec \Gamma_T\) for the thermostat; balanced by \(\gamma\), the drag force

      • \(\vec \Gamma_k\) for metabolism

Random Kicks

ThermostatMetabolism

  • \(\Gamma_T \sim \Delta t k_B T \sim {10}^{-5} k_B T\)

  • Every timestep

  • Mimic "bumping into water molecules"

    • Correlated: satisfy Fluctuation-Dissipation Theorem

    • Gaussian distribution

    • Balanced by the drag force \(-\gamma \vec v\)

  • \(0 \le E_k \le 20 k_B T\)

  • Instantaneous

  • Infrequent, ~100—1000 timesteps

  • Uncorrelated

  • Uniform distribution

Simulation

Without Activity

With Activity

Experimental MSDs

MSD of untreated vs. DNP+ cells

A factor of \(\sim 2-10 \)

MSDs

with \(20 k_B T\) Kicks

randkicktest MSD f0.60 R20 N100
randkicktest MSD f0.62 R20 N100
randkicktest MSD f0.64 R20 N100

MSDs

with \(200 k_B T\) Kicks

randkicktest MSD f0.60 R200 N100
randkicktest MSD f0.62 R200 N100
randkicktest MSD f0.64 R200 N100

MSD Comparison

randkicktest MSD f0.60 R20 N100
randkicktest MSD f0.62 R20 N100
MSD of untreated vs. DNP+ cells

Bibliography

  1. B. Feringa, Nat Chem 3, 915 (2011).

  2. J. R. Howse, R. A. L. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Phys. Rev. Lett. 99, 048102 (2007).

  3. S. Stylianidou, N. J. Kuwada, and P. A. Wiggins, Biophysical Journal 107, 2684 (2014).