Modelling for a biofactory
As part of our project, we decided that it would be interesting to see how many of plants it would require to give a single treatment to a person with severe Graves disease/ophthalmopathy, and how many to treat a less-severely affected patient. Initially we attempted to model this using data from N. benthamiana from various scientific papers that have used this as an expression system. In doing so, we created a simple equation that theoretically can be applied to any plant biofactory company, that ultimately calculates how many plants would be needed to create a single effective dose of medicine for a person with a disease/condition of interest. The benefit of this equation is that any one or all of the variables can be substituted to fit a new purpose, so that future teams/companies may be able to use this model and change or improve it, to estimate how many plants they would need to create a significant amount of product. To demonstrate this flexibility, we changed some of the variables ourselves and plotted some of the results gained from modelling using MatLab.The variables we changed showed the potential production using different plant vectors/systems, specifically using N. tabacum cultivars TI-95, and I-64, and the newer 'HyperTrans' and PVX expression systems, which boast up to 30% of total soluble protein (TSP) being recombinant protein! Finally, we estimated the number of people in the US that suffer from Graves disease, calculated the mean severity of the disease, and then ran the model to estimate how many plants we would need to give every sufferer of Graves disease in the US a single dose of effective (90% reduction in TSI-created cAMP) treatment. The simple equation is shown directly below, with the breakdown of how we applied this equation using our own variables below that. At the bottom of this page or using this link, you can find a PDF of all the variables and statistics that were used to model our theoretical biofactory, with some tables showing the key information that we turned into graphs.
Where:
N = The number of plants needed to create a single dose of antagonist for a single person.
D = The dose multiplier (How much protein product you need in relation to the molecule you are trying to inhibit (I)). This can be changed depending on studies carried out on a different antagonist/therapeutic. For example you may have an antagonist that has most effect at 2x the concentration of the molecule you are trying to inhibit, and thus 'D' would be 2.
I = The concentration of the molecule you are trying to inhibit. In our model, this is the concentration of Thyroid Stimulating Immunoglobulin (TSI) measured in µU/ml. This can be changed for any other molecule you are trying to inhibit, and the units can therefore be changed to.
V = The mean volume of blood serum in a patient, which is approximately 2850ml (between 2700 - 3000). This was used to estimate the total concentration of TSI in a patient, but should only be used when trying to calculate the total number of units of 'I' in a given volume of liquid.
P = The amount of the antagonist a single plant can create. Most production platforms measure this in mg, but out antagonist is measured in international units (IU), and needed to be converted to International µU per plant. This value and its units can change depending on the expression system you are using. We have demonstrated this by modelling different plant species, cultivars, and expression systems, changing the value of 'P'.
These are the factors that make up the simple interchangeable equation. However, for our model specifically, we needed several calculations to calculate the above variables. Thus, a breakdown of the equations that we used to create this model are shown below. These equations are not interchangeable, but are provided to show how we created these final models and graphs. Every made assumption is stated below in the breakdown too, with all the references to the papers/articles that these values were taken from.
The breakdown
This section will show what value was used for each of the variables in the simple model, the equations that were used to calculate the variables, and references to papers whose data we used in the calculations.
The amount of antagonist (µU) needed for every µU of TSI was calculated to be 0.2666667x. Fares et al. (2000) reported that the TSH antagonist had a maximal effect (reducing TSI-related cAMP production by 90%) in vitro when there was 200µU/ml of antagonist for every 750µU/ml TSI. Here in our equation, 'An' represents antagonist concentration (200µU/ml), and 'Ag' represents agonist concentration (750µU/ml). Thus, we calculate that we need the antagonist concentration 0.2666667x the amount of TSI in a patients body - both measured in µU/ml. Here, we make the assumption that the in vitro study by Fares et al. can be directly applied to patients in vitro .
The amount of TSI in a patient was calculated using two independent papers. The first paper, by Gerding et al. (2000), measured cAMP levels per 40,000 CHO cells, transfected with the hTSH-receptor, grown in IgG fractions (containing TSI) taken from patients with Graves' ophthalmopathy (GO) (a form of Graves' disease that is also caused by elevated TSI levels) , and divided these into two classes of severity (S). The more severe class was determined to have an average of 42pmol of cAMP, and the less severe class to have 35pmol. Thus, we use the left-half of this equation to deduce how much cAMP is present, on average, in patients with either more-severe or less-severe GO. This is measured in cAMP/cell, and was calculated to be 0.000875pmol of cAMP/cell for in a less-severe case, and 0.00105pmol of cAMP/cell. The right-half of the equation is taken from Kraiem et al. (1987), which used in vitro cell cultures of 25,000 cells, and measured 6.5pmol of cAMP produced in the surrounding solution when 250µU/ml of TSI was added. Using this, we can calculate how much cAMP is produced per cell per µU of TSI, which was calculated to be 0.00000104pmol cAMP/cell/µU/ml. Together, assuming that these in vitro studies reflect in vivo , and that the growth medium for these experiments does not influence cAMP production, we can estimate that a patient with less-severe Graves' disease has 841.35 µU of TSI/ml of serum, and a patient with more-severe Graves' disease has 1009.62 µU of TSI/ml of serum. Thus, these are the two units for 'I' that we used in the model. For the average, we took the mean of these values (925.485µU of TSI/ml) which was used to calculate the number of plants needed to treat the everyone in the US who has Graves' disease.
In our equation, 'V' is a constant which is simply the volume of blood serum, which is roughly the volume of blood plasma. Here we have used a value of 2850ml (the mean between the lower estimate of 2700ml, and the higher estimate of 3000ml), but clinically this would not be a constant, and would vary per patient. Generally, blood plasma makes up ~55% of total blood volume, so this would need to be calculated per patient.
