1. Maximise rate.

A primary function of the beads is to maximise reaction rate per bead volume, since halving the radius of a sphere doubles its surface area:volume ratio. A large number of small, bacteria-embedded agarose beads (to a technical limit) are therefore optimal, as more bacteria will be closer to the surface of each bead and can metabolise DCM 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 as 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. This means our biopolymer beads can be adapted to restrict diffusion of a wide range of substrates.

Bacteria need direct access to water, yet DCM is only water-soluble up to ~200mM. Thus, for substrates that are not fully soluble in water, 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, since the aqueous DCM concentration of the biphasic system is more reliable. Furthermore, we had yet to establish the robustness of the diffusion-limiting system to external fluctuations in DCM concentrations.

3. Physically containing bacteria.

Surrounding bacteria-embedded agarose beads in a diffusion limiting polymer acts as a secondary safeguard to an envisioned genetic kill switch. Their physical confinement to the beads would ensure that, even if the beads are improperly disposed of, the bacteria have very little possibility of 'escaping into the wild'. This, together with considerations of practicality, is the reason we are using macroscopic beads that can contain ~10^7 bacteria.

Synthesis
1.5% agarose 'beads' were synthesised by dropping cooling (~40oC) 1.5% agarose solution through a 250 mL measuring cylinder of 0oC water, via 10mL Gilson pipette:



To coat the product with cellulose acetate, a modified biopolymer, the solidified agarose beads were passed through the following biphasic mixture, a thin organic layer consisting of cellulose acetate in ethyl acetate above an aqueous layer:






As of the wiki freeze, we had yet to perform polymer coating of bacteria-containing agarose beads, although have made arrangements within the Oxford's Biochemistry department to further research this, to be written as a scientific paper.

By collecting the resulting 'capsules' and repeating this procedure, polymer coat thicknesses were built up to 5mm, calculated by the difference in measured initial and final diameters (an average of 5 diameters, using 0.01 mm precision callipers). Polymer thicknesses are taken only to the nearest mm, reflecting the large uncertainty in thickness due to non-uniformity of both the 'bead' and 'capsules', and additionally non-uniformity of the polymer density.





Acylation of cellulose was achieved via Acetyl Chloride esterification, based on methodology by Org. Lett., 2005, 7, 1805-1808.

The volatility and poor visible absorption of DCM posed a challenge in reliably measuring rates of diffusion through the polymer. We decided, instead, 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. 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. Hence, we further 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:

Though these results is approximate, and intend to provide only an estimate of the diffusion kinetics, they demonstrate that the polymer coating is indeed diffusion limiting due 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 the relationship between coating thickness and diffusion rate, 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 concentration and temperature gradients, 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 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.