1. Maximise rate.

A primary function of the beads is to maximise reaction rate per bead volume; halving the radius of a sphere doubles its surface area:volume ratio. Many, small, bacteria-embedded agarose beads (to a technical limit) are therefore optimal, as the average bacterium is closer to the surface of each bead and being ‘used’ efficiently. Assuming brownian motion, substrate molecules are more likely to collide with and be broken down by ‘outer’ bacteria. Product molecules, additionally, have a shorter path length to the surface and are likely to diffuse out faster:

Assuming ρ (a coefficient of bacterial density), to be independent of r (distance from bead center) and R (bead radius), avg. bacterium-surface distance =



Oxford iGEM 2014

2. Protect bacteria

For this system and others of its type, it is highly valuable to maximise local substrate concentration to the bacteria within the viable range of toxicity, especially while the viable concentration range to the strain remains a limitation to the breakdown rate (directly or indirectly).

In our case, the diffusion-limiting polymer chosen was cellulose acetate (as its synthesis from cellulose is straightforward and safe) for which we modeled diffusion data for variable polymer thickness (see below). Acylation stoichiometry or even polymer type entirely, polymer density and methods of bead coating are among many variables that can be further researched and optimised for desirable diffusion coefficients.

As bacteria need direct access to water, yet DCM is water-soluble only up to ~200mM, for limited water-solubility substrates, as part of future research, we propose suspending beads at the interface of a biphasic mixture of the two by exploiting differences in density. In such a system, the immediate substrate ‘reservoir’ is essentially maximised.

For the purposes of this project we opted to construct beads less dense than water, as the aqueous DCM concentration of the biphasic system is more reliable, and we had yet to establish the robustness of the diffusion-limiting system to external fluctuations in [DCM].

3. Physically containing bacteria.

Surrounding bacteria-embedded agarose beads in a diffusion limiting polymer acts as a secondary safeguard to an envisioned genetic killswitch.

It is for ease of use in practice, and this point, that macroscopic beads containing ~10^7 bacteria, rather than attempting to encapsulate individual cells, are conceptually preferred.

Acylation of cellulose was carried out via Acetyl Chloride esterification, based on methodology by Org. Lett., 2005, 7, 1805-1808. 1cm diameter agarose spheres were passed through a thin film of the polymer to coat. Thickness was then calculated by the difference in measured initial and final diameters (an average of 5 diameters, using 0.01 mm precision callipers).





The volatility and poor visible absorption of DCM posed a challenge in reliably measuring rates of diffusion though the polymer. We decided to base our modelling on the diffusion of indigo dye from within prepared beads, collecting the following spectrophotometric absorption data (calibrated to prepared concentration standards):

Alongside the experimental absorption data (red) we have plotted our theoretical lines of best fit. Because we predicted that system behaviour would be governed by Fick’s law, which states that:

i.e. that mass flux is proportional to a concentration gradient, we then predicted that the response of our system would follow the classic exponential asymptotic approach to a maximum value where the concentrations of dye both inside and outside the system were equal.

Thus our lines of best fit take the form:

φ = average concentration outside bead (g/ml)

A = equilibrium concentration (g/ml)

k = variable dictating rate of approach to equilibrium (min^-1)

t = time (min)

The value of k in each system was obtained through our parameter fitting algorithm.

Our results are tabulated below:

From these experiments we could conclude that the polymer coating was indeed diffusion limiting through two simultaneous effects. Firstly, the rate at which the system reaches equilibrium concentration i.e. defined by the variable k which is itself a function of bead surface area, polymer diffusivity and coating thickness, is reduced in each of the systems. Furthermore, the maximum concentration reachable at the equilibrium point is itself a function of the thickness of the coating and decreases as the polymer thickness increases.

Further analysis of polymer coating

To further explore coating thickness – diffusion rate relationship, we used analogous relationships developed for heat diffusion. This is done because the fundamental laws governing mass and heat diffusion are of a similar form; they are both driven by gradients – concentration and temperature respectively:

Because the system involves two-phase diffusion, we used an equivalent form derived from two-phase heat transfer.

This yielded:

Using this relationship alongside diffusion data for two given thicknesses, we can characterize the two phase system using two unknown diffusion constants- k and h. Because the system had not reached a steady state and the rate of change of concentration ̇was constantly varying, we used the conditions at the start of the diffusion process where C_0 = 0 and used the gradient at t = 0 as a starting value for C ̇.

Finding the mass transfer rate was done by matching the experimental data to an anticipated exponential response and calculating the initial gradient as described above.

Using this form, the initial gradient can be calculated:

By using the data gathered from the 1mm and 5mm tests, we could then calculate the two diffusion constants and plot a theoretical predicted relationship for initial concentration flux rate against coating thickness:



Oxford iGEM 2014

Given more time, we would then run the test for a range of other thicknesses and compare the data collected to the theoretical form established above. Once the accuracy of the above form could be established, the next step would then be to predict the theoretical maximum breakdown rate of DCM achievable by our bacterial systems and then calibrate the thickness of the biopolymer capsules such that the influx rate of DCM through the polymer is less than or equal to our breakdown rate. This would result in an approximate steady state [DCM], within the cells' limits of substrate toxicity.