Team:SoundBio/Model
Modeling
Click here to visit our GitHub!
The solution? Computational modeling! Computational models are used to predict the behavior of biological systems based on input conditions, so having a model of the BC-E.coli system would allow us to predict protein patterning given some light input. From there, determining input parameters given a desired output is simple--or, at least, far simpler than it would be without the model.
We also considered creating a model to predict bacterial cellulose production in our bioreactor design. This would be useful because such a model could be used to find the optimal operating conditions of the bioreactor. Ultimately we decided that we didn’t have the resources to pursue both paths, but we did create an information sheet for anybody interested in creating such a model.
Variables:
Equations:
∂c/∂t = Tc - Mc(𝜙, c) - (Dc)(c)
dp/dt = P(u, c) - (Do)(p)
du/dt = Tu - P(u, c) - (Do)(u)
dg/dt = Tg(p) - (Dg)(g)
Constants:
Functions:
Near the end of August, as we were thinking about what to do next, we stumbled upon this paper. Essentially, it describes an empirically validated, comprehensive model for gene expression given input light levels over time in Cph8-based systems--exactly what we needed. This model is described below.
Constants:
Ki =∫𝜎i · nlight dλ - photoconversion rate per unit light intensity
Left: LED setup with Raspberry Pi for measuring light intensity
Right: 3D printed Light Plate Apparatus
Unfortunately, due to difficulties Wetlab had in cloning the aforementioned Red Light Circuit, we weren’t able to execute the data-collection experiments we would need to train our model. However, as we were fully prepared to do so, we believe that we could have built a successful model if Wetlab had successfully cloned the RLC.
Importance
Our project, optogenetic circuit design for spatially controllable bacterial cellulose modification, could ideally be implemented for any desired patterning of a finished BC sheet with any CBD-bound protein. For this to be practical, however, one needs to be able to reverse-engineer input conditions from results; in effect, given the protein concentrations desired in each region of the bacterial cellulose sheet, one would need to determine intensity (how much light) and time (how long to shine the light) parameters for each part of the sheet.The solution? Computational modeling! Computational models are used to predict the behavior of biological systems based on input conditions, so having a model of the BC-E.coli system would allow us to predict protein patterning given some light input. From there, determining input parameters given a desired output is simple--or, at least, far simpler than it would be without the model.
Goal
Because of our time and resource constraints, we decided to focus on the E.coli part of our BC-E.coli system. Our goal for this season was to create a model that could predict, for E.coli transformed with Wetlab’s Red Light Circuit, the amount of sfGFP+dCBD produced by a single cell given the system’s input light intensity over time.We also considered creating a model to predict bacterial cellulose production in our bioreactor design. This would be useful because such a model could be used to find the optimal operating conditions of the bioreactor. Ultimately we decided that we didn’t have the resources to pursue both paths, but we did create an information sheet for anybody interested in creating such a model.
Click here for the information sheet!
Learning
We began this season with minimal knowledge, let alone experience, in computational/mathematical modeling, so we spent the first part of the season changing that. Our awesome advisor, Yoshi, helped us get up to speed on Markdown and version control, become familiar with the math underlying biomodeling, learn how to write models, and more!Model #1
After a short period of research, brainstorming, and discussion, we decided to build a gene expression model using both Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) conforming to the math below:Variables:
- Time: t
- Photon flux: 𝜙
- Cph8 concentration: c
- Mutilated cph8 concentration: m
- Phosphorylated OmpR concentration: p
- Unphosphorylated OmpR concentration: u
- Generic OmpR: o
- sfGFP + dCBD concentration: g
Equations:
∂c/∂t = Tc - Mc(𝜙, c) - (Dc)(c)
dp/dt = P(u, c) - (Do)(p)
du/dt = Tu - P(u, c) - (Do)(u)
dg/dt = Tg(p) - (Dg)(g)
Constants:
- Tn: translation constant for any protein n
- Dn: degradation constant for any protein n
- Other Constants:
- K (rate of phosphorylation): 1.5 sec^-1
- C (rate of translation of fusion protein): 0.012 min^-1
- L (rate of mutilation of cph8)
Functions:
- P(u, c) = Kuc: rate of phosphorylation of OmpR, directly proportional to u
- Tg(p) = Cp: rate of translation of sfGFP + dCBD, directly proportional to p
- Mc(𝜙, c) = L𝜙c: rate of mutilation/dissociation of cph8 due to red light; directly proportional to 𝜙 and c
Pivot: Tabor Model
Unfortunately, we didn’t end up building the model constructed above, since finding its parameters proved to be a greater challenge than we expected. By the time we knew what experiments we’d have needed to do to determine them, we didn’t have the time or resources those experiments required. Luckily, we found another way.Near the end of August, as we were thinking about what to do next, we stumbled upon this paper. Essentially, it describes an empirically validated, comprehensive model for gene expression given input light levels over time in Cph8-based systems--exactly what we needed. This model is described below.
Tabor Model
Variables:- Ground-state photoreceptors (sensors): Sg
- Active-state photoreceptors (sensors): Sa
- Photoconversion rates: k1 and k2
- Dark reversion rate: kdr
- Dilution rate: kdil
Constants:
Ki =∫𝜎i · nlight dλ - photoconversion rate per unit light intensity
Data Collection
After exchanging a few emails with Dr. Jeffrey Tabor, the PI of the lab that constructed the above model, we figured that we’d have to run some experiments to gather training data for the model (the parameters were fitted using linear regression). To prepare for these experiments, we built a device to control the intensities of red LEDs shone on 24-well plates, with each LED corresponding to a single well. This was based on the Tabor Lab’s Light Plate Apparatus, but significantly cheaper, simpler, and specialized for our needs. We also prepared for the experiment by securing access to a flow cytometer, reviewing and editing the data collection protocols contained in the paper (Appendices 1&2), and acquiring the necessary reagents.
Left: LED setup with Raspberry Pi for measuring light intensity
Right: 3D printed Light Plate Apparatus
Unfortunately, due to difficulties Wetlab had in cloning the aforementioned Red Light Circuit, we weren’t able to execute the data-collection experiments we would need to train our model. However, as we were fully prepared to do so, we believe that we could have built a successful model if Wetlab had successfully cloned the RLC.
Results
If given more time, we would likely have been able to complete our model. But even though we weren’t able to do so this year, we made a fair amount of progress and learned a lot about biological modeling. We look forward to using this experience next year!