Toroidal Bioreactor

Making synthetic biology easier

• Theoretically, our bioreactor could scale up quite well as it is a modular, simple design.
• High customisability lends itself to wide range of applications in synthetic biology
• Continuous culturing method reduced high labour and time costs of manually refreshing media

Making synthetic biology more accessible

Accessibility has been a recurring element in our project. We put in effort to ensure that our bioreactor is operable and meaningful to as many people as possible. Our decisions are based on the criteria stated underneath each section below.

Materials Selection

• Everyone must be able to order the same materials or components wherever they are based
• The total cost of materials must be under 200 GBP
• Everyone must be able to handle these materials safely without the requirement of being in a laboratory or a machine workspace

Typically, bioreactors used in industries are made from steel and glass. Many open-source bioreactors used in laboratories are made from glass or 3D printed parts. The main issue with using these materials is that the technique used to modify them into the desired shape requires specific technique which is not accessible by everyone. Moreover, there is a higher risk of getting cuts and injuries from using these materials as opposed to plastic. As a result, our bioreactor vessel and container is made solely from clear extruded acrylic material.

Clear extruded acrylic are available as sheets and tubes in varying sizes and costs as low as 0.73 GBP. Moreover, acrylic is well known for being highly durable over a wide temperature range and weather conditions as well as being significantly lighter than glass. In case acrylic shatters under high stress, they form “large, dull edges”, making them safe to work with for everyone with basic health and safety training.

One of our initial concerns is maintaining sterile conditions in the vessel as autoclaving plastic would reduce its strength and therefore is not ideal. Our solution is to use Virkon between cultures to clean the bioreactor. Another advantage of using this technique over conventional autoclaving is that virkon solution can be pumped using a peristaltic pump, simultaneously sterilising the inlet tube.

Construction

• Everyone must be able to assemble the bioreactor with tools that can be purchased or service that is generally available
• Everyone must be able to build the bioreactor without the requirement of being in a laboratory
• Everyone must be able to understand and adapt the code to suit their purpose of culturing microorganisms

Although we obstructed our bioreactor in the University of Sheffield’s iForge, the university’s makerspace, considerations have been made for alternative techniques that can be done from home.

For our vessel construction, we used bandsaw to cut the extruded acrylic tube into desired height and sanded the edges with belt sander. Alternatively, a tenon saw or any other wood saws can be used to cut the acrylic tubes. The edges can be finished using sandpaper or file if belt sanders are not available. We then used a laser cutter for other parts of the bioreactor vessel and container. Although this is not necessary, as a coping saw will be able to achieve the same results, we highly recommend sourcing a laser cut service as this will save time and offer a more accurate finished piece. After all the acrylic has been cut to shape, they are assembled using acrylic cement which is again easily sourced online in many areas.

In terms of systems we incorporated, we only use standard electronic equipment which are available on Amazon and PiHut and control them using Raspberry Pi Pico. Arduino has long been the primary microcontroller for open-source projects, but coding similar to C++ language is more complicated and therefore only restricts the audience to engineers or people with coding basics. By using Raspberry Pi Pico, we have eliminated these restrictions and their overall advantage over Arduino is listed below:

• Cheaper than Arduino
• Code in micropython, which is easier to learn and code than C++ language
• Huge library available on the Raspberry Pi website to help guide people through
• Large online community, plenty of forums for at-home troubleshooting
• Smaller in size, so take up less space in the container
• Greater number of pins

Operation

• The bioreactor should be compatible for most laboratory chassis microorganisms
• The bioreactor should be compatible for growing microorganisms for any purpose
• The bioreactor should be able to run without causing any disturbance to the public i.e. noise, light, etc.
• Everyone should be able to run the bioreactor without a degree requirement, but should educated in safety awareness

Although our bioreactor is built for in vivo directed evolution of E. coli and V. natriegens, the same principle can be applied for growth of most laboratory chassis microorganisms with the exception of extremophiles, anaerobic, and photosynthetic microorganisms. The reason behind this is that extremophiles would require too high or too low temperature which will not be achievable by heating coil and PID controller, and potentially could be beyond the glass transition temperature of perspex. With our current testing results, we are unable to confirm that the bioreactor is suitable for anaerobic or photosynthetic microorganisms and this is one of the aspects we will be focusing on in the future.

With automated and continuous OD measurement and dilution, the design can be applied to a wide range of applications. Currently, bioreactors used in industries and laboratories rely on taking aliquots out of the culture to measure OD using a spectrophotometer. Lab technicians in the university, who we have been in contact with, have confirmed that this new functionality will be applicable to their experiments.

During the testing phase of the bioreactor, we found out that the rotating sound of the servo motor is very loud and causes disturbance towards other people sharing the same workspace. However, after incorporating the box which serves as both noise and heat insulation, our bioreactor is able to run smoothly without disturbing anyone surrounding it. It also has the added benefit of creating calmer airflow inside the space, minimising the chances of contamination from ambient eddies.

Basic health and safety awareness surrounding the use of microorganisms and bioreactors should be made known. However, no additional certification or accreditation is required to operate the bioreactor.

Design & Simulation

For the design and simulation of the bioreactor we took a pragmatic approach to build a functional reactor efficiently. This meant that we started from the simplest model and then relaxed some of the assumptions iteratively to make more educated modifications to our initial build. As the goal of the engineering team was primarily to make a functional build, the design and simulation of the bioreactor was guided by the following questions:

• What is the oxygen diffusion profile across the bioreactor?
• How can we avoid hot spots and maintain the temperature within the desired boundaries?
• How can we avoid overflows of the media?

Therefore, we made mathematical models of the bioreactor in order to gain analytical insights to answer these questions and understand not only the edge cases and limitations of the bioreactor but also to have a general model which could be used to drive future adaptations.

Conduction analysis

To decide on a heating system, we considered various heating configurations and derived models to select a configuration with a desirable temperature profile to start from

Configuration 1 Rod inside Reactor

To model the way heat will flow across the bioreactor we could model the reactor as a cylinder. The following diagram shows a differential shell representing the surface area being heated

Heat balance through a shell

The heat source can be the heating coil. As such, by ignoring the heat provided by the heating coil from the top and the bottom of the bioreactor by convection as it can be considered negligible

\[ \frac{\partial T}{\partial z} = \frac{\partial T}{\partial \theta } = 0 \]

Which turns Fourier's equation from

\[ q = - k\nabla T \]

to the following model for the conduction of heat through the cylinder

\[ \frac{d}{dr} (r \frac{dT}{dr} + \frac{q_v r}{k}) = 0 \]

Where r is the inner radius, \(q_v\) refers to the heat generated within the volume and k is the thermal conductivity, which can be a function of temperature. Assuming that no heat is generated

\[ \frac{d}{dr} (r \frac{dT}{dr}) = 0 \]

Therefore, the temperature within the cylinder can be modelled as a logarithmic functions of the radius

\[ T = C_1ln(r) + C_2\]

Where the constants of integration \(C_1\) and \(C_2\) can be derived from boundary condition

\[ C_1 = \frac{T_0 - T_i}{ln(\frac{r_0}{r_i})} = 3.3\]

\[ C_2 = T(r=0) \]

Assuming that at the core of the reactor temperature (r=0) is at 37 degrees and the temperature within the box is 25 degrees the following model can be obtained

\[ T = 37 + 3.3* ln(r) \]

Temperature profile (rod inside reactor)

Relaxing some assumptions

the first configuration of the system assumes that all the heat supplied to the bioreactor will come from a rod. As such, the following assumptions were made:

• heat is supplied at steady state \( \dot{Q_x} \approx C\)
• central rods heat the bioreactor evenly \( \therefore \dot{\phi} \approx 0 \)
• assuming that the thermal conductivity of the material used is not a strong function of temperature

As such the Governing equation becomes

\[ \frac{\partial^2 T}{\partial r^2} + \frac{1}{r}\frac{\partial T}{\partial r} + \frac{\partial ^2 T}{\partial Z^2} = 0\]

By applying the following boundary conditions B.C.

\[B.C.1 : T(R,z) = 0\] \[B.C. 2 : T(r,L) = 0\]

where R and L are the radius and the length of the bioreactor respectively and at z=0

\[B.C. 3 : T(r,0) = T_0\]

assuming that the required solution is of the form

\[ T(r,z) = R(r)Z(z)\]

then we can derive the following solutions

\[ T(r,z) = \sum_{n=1}^{\infty}{a_n sinh(sinh(\lambda_n L})) \times j_0(\lambda_n)r \]

And \(a_n\) is the following integral

\[ a_n = \frac{2}{sinh(\lambda_nL)r_0^2j_1^2(\lambda_nr_0)} \int_{0}^{r_0}{T_0j_0(\lambda_nr)rdr} \]

the following plot shows a slice of the temperature profile which seems to be worse than the other plot as it drops faster. However, by plotting the heatmap a better picture of the temperature profile could be observed

Temperature profile of bioreactor with gradients in r> and z> directions

Configuration 2 Heat supplied from the bottom

For the second configuration a rectangular shape was assumed in order to simplify the analysis of how heat flows around the bioreactor without focusing on the circulation. Assuming that the bioreactor is insulated on the sides the following diagram shows the model of the bioreactor tilted on its side, where z is in the direction of the height of the bioreactor. To simplify the analysis, the bioreactor radius and height were also assumed to be equal.

Diagram displaying bioreactor as a slab tilted on its side

The governing equation for the selected geometry (assuming that the thermal conductivity is not a strong function of temperature) is

\[ \nabla^2 T = 0\]

Since the bioreactor is insulated on the sides the governing equation becomes:

\[ \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial z^2} = 0\]

And the following boundary conditions can be applied

\[B.C.1 : T(0,z) = T_1\] \[B.C.2 : T(L,z) = T_1\] \[B.C.3 : T(x,0) = T_1\] \[B.C.4 : T(x,L) = T_2\]

A similar procedure can be implemented to solve the PDE by separating variables, and the following temperature profile model can be derived:

The following heat maps show the temperature profile of the plot after adding 1 term (a) and 69 terms (b):

Temperature profile of the bioreactor modelled as a slab

Configuration 3 Heat supplied from side wire

The following configuration involves the use of wires to heat the reactor from the side. The study was carried out using Fusion 360. The following set up settings were implemented:

Materials used:

Copper for wire

Acrylic clear for the body of the reactor

Thermal Loads

Heat source and internal heat generated is from the wire

Applied temperature is placed at the outer face of the larger cylinder

Convection of hot air moving slowly 10 W*m^-2*C^-1

Convection from internal fluid 15 W*m^-2*C^-1

As such the study generated the following results

Thermal Gradient

Oxygen diffusion profile

Knowledge of the oxygen diffusion profile is pertinent to the bioreactor design as we want the bioreactor to operate aerobically. This means that enough oxygen should be provided to V. natriegens to grow. As such,

• We derived a general model for diffusion of oxygen in media
• We applied reasonable boundary conditions to get an analytic solution

The intial simplest model of the diffusion of oxygen in media can rely on henry's law if we assume that the system is at equilibrium we can estimate the concentration of oxygen along the height of the bioreactor which we would expect to vary:

\[ p_{O_2}k_{O_2} = C_{O_2}\]

And since we know that pressure in a column of fluid can be expressed as a function of height

\[ p_{media} = p_{0} - \rho_{media}gz\]

Where:

• z refers to the height
• g is gravity
• k is henry's constant
• rho refers to the density of the liquid
• C is the concentration of oxygen
• y refers to the fraction of oxygen in the gas
• P media refers to the pressure at the bottom of the media
• P0 refers to the pressure at the top of the media or the pressure of the air which is on top of it

plotting the following function of C(z) assuming the following values

• concentration of oxygen in the gas 22%
• henry's constant of oxygen in media is 2.17*10^-7 (g/L*pa)
• g is 9.81
• the density of the media is approximately the same as water 1000 (Kg/m^3)

\[ C_{O_2} = p_0k -ky_{O_2}\rho gz \]

Oxygen diffusion model using henry's law

A more robust none linear model could be derived by solely considering the diffusion of oxygen through the media and apply our boundary conditions. Starting from Fick's law and a general material balance as displayed by the following two equations.

\[ \dot{J_{O_2}} = -\rho D_{O_2,media} \nabla w_{O_2} \]

Accumulation = flow in - flow out + net generation

• In this case \(\dot{J_{O_2}}\) refers to the molar flux of oxygen in the media
• rho refers to the average density of oxygen and the media
• \(D_{O_2,media}\) refers to the diffusivity coefficient of oxygen in media
• \(w_{O_2}\) refers to the mass fraction of oxygen in the media

By applying the mass balance considering oxygen our species of interest over the bioreactor we get:

\[ \frac{\partial\rho_{O_2}}{\partial t} = - (\nabla * J_{O_2}) + r_{O_2} \]

Where \(r_{O_2}\) refers to the amount of oxygen which has undergone reaction which was assumed to follow be roughly \( r_{O_2} \approx k_r C_{O_2} \)

• Assuming that at steady state the concentration of oxygen stays constant, therefore that there are no density changes over time
• Assuming that there are no gradients in the radial and the azimuthal direction since air will be able to enter the bioreactor from the top

The equation becomes

\[ -\frac{d}{dz}(-D_{O_{2,media}}\frac{dC_{O_2}}{dz}) + r_{O_2} = 0\]

\[ D_{O_{2,media}}\frac{d^2c_{O_2}}{dz^2} -k_rc_{O_2} = 0 \]

For our case can set two boundary conditions. A Dirichlet boundary condition which is given by the fact that at the top of the bioreactor the solubility is equal to the initial solubility and a Neumann boundary condition since oxygen cannot flux out of the bioreactor

\[B.C.1 : c_{O_2}(0) = C_{O_{20}} \] \[B.C.2 : \frac{dc_{O_2}}{dz}|z = L) = 0\]

The PDE can then be solved by making the variables dimensionless since a Sturm-Liouville equation can be derived

\[ \zeta = \frac{z}{L} \]

\[ \Gamma = \frac{f(c_{O_2})}{c^*_{O_2}} \]

By converting the PDE to this dimensionless values we obtain

\[ \frac{d^2\ \Gamma}{d\zeta} - \frac{k_rL^2}{D_{O_{2,media}}}\Gamma = 0 \]

We can lump the following constants into lambda to obtain a Sturm-Liouvile equation \(\lambda^2 = \frac{k_r L^2}{D_{O_{2,media}}}\). Therefore, the solution to our PDE after normalizing the boundary conditions is

\[ \Gamma(\zeta) = cosh(\lambda\zeta) - tansh(\lambda)sinh(\lambda\zeta)\]

Plotting the following equation:

Oxygen diffusion model using Fick's Law

Maintaining liquid level

In order to stop the liquid from overflowing we had to control its level. The Bernoulli's equation which relates the pressure, the height and the velocity of the fluid can be used to estimate the height of the fluid given a fluid velocity.

\[ \frac{P}{\rho g} + \frac{v^2}{2g} + h = C\]

Where:

• h is the height of the fluid
• P is it's pressure
• Rho refers to its density
• C is a constant

And g is the gravitational constant 9.81

Therefore, by controlling the speed of the fluid going into the bioreactor its height could be controlled. As show below

\[ h(v) = C - \frac{P}{\rho g} + \frac{v^2}{2g} \]

Nevertheless, this model was abandoned since we found that the size of the outlet aperture was a more important variable in controlling the fluid flow.

OD Measurements

To measure the turbidity through OD measurements we wanted to minimize the refraction scattering and distance that light would have to travel to be received. As such a combination of a phototransistor and an LED light was designed. The torouspherical shape of the bioreactor helped in the OD measurements too since the thin walls would reduce the distance between the light transmitter and the receiver. The following image shows an example of thr design and how it was intended to be used

Consequently, the OD measurement device was built and tested to measure turbidity at various level

Heating System

According to our analysis we knew that the heating system would preferably come from the bottom and wrap the bioreactor. This is because the configurations involving sources of heat from the bottom resulted having more desirable temperature profiles. Moreover, we did not want to make an intrusive heating system which would make the bioreactor harder to operate. Likewise, for controlling the temperature a sensor which would not obstruct the lid of the bioreactor whilst still Measuring the temperature of the bulk fluid adequately mass designed as shown below.

This was then built and implemented on the bioreactor by including holes on the lid.

Stirring System

For the stirring system our initial analysis suggested that by ensuring radial homogeneity of the media concentration the bioreactor should be able to operate aerobically at reasonable concentrations of oxygen since we found that the drop in concentration of oxygen along the length of the bioreactor was negligible. As such, the following stirring magnet was designed

Consequently, the following build was made

Finally the final bioreactor design was put together to understand which configuration would best fit all the designed components together. The following image shows the final design configuration and the final build of the bioreactor.