Matlab code to run simulations of a batch reactor , MATLAB Programming

Background Protein therapeutics are a major component of the biotechnology industry, with sales estimated in the range of ~$99bn annually (2011) and steady market growth. Many pharmaceutical companies have been acquiring/developing intellectual property and the physical capacity to produce protein therapeutics, to offset revenues lost as traditional 'small molecule' drug revenues decline. As the development of protein therapeutics was fueled by advances in recombinant DNA technology that occurred between the late 1970's and late 1980's, the patents for some such drugs have now expired or are soon expiring, opening the market to generic versions, called "Bio-generics" or more often "Biosimilars."

In this project Your company is considering moving into the Biosimilars market and you need to design a system of reactors to produce a generic form of FancyMAb, commonly known as MAbZ1, which is secreted from cells. Populations of cells (CHO cells in this case) are grown from "clones," or individual cells (Nn=1), through division. However, individual clones of cells vary widely in their ability to produce (secrete) MAbZ1, and scaling up from the lab (batch reactors) to pilot plant (fed-batch reactors) often reveals differences in secretion potential between clones in each setting. Thus, you must test 8 different clones to find the one that performs best. The process of growing up single cells in the lab to large scale bioreactors is time consuming, so you need to plan out your experiments carefully and provide your boss with an approximate timeline for when you will need the large scale bioreactor for your studies and how long you will need it for. They will have to stop production of their high-value patent protected product while you conduct these experiments in the 5000 L reactor. You also have other work you would like to get back to, so you want to be done with this as soon as possible.

Under ideal conditions, the rate of cell growth at low density is given by:

{1 cell/ 0.1 ml < N < 5x105 cells/ml} dNcells / dt = k1 Ncells     k1 = 0.4 day-1

N = number of cells per ml

Cells under these low-density conditions are fed (i.e. the cells are collected and the growth substrate is replaced in the batch reactor) more often than needed to ensure that adequate nutrition is always present.

Once cells reach a critical density, their growth rate increases, and at such densities they consume substrate from the medium more rapidly, such that it typically begins to become depleted in a batch reactor. The substrate for cell growth is actually a mixture of many different nutrients, including glucose, proteins, amino acids, and dissolved oxygen, among others, but we will lump these together as "S" for simplicity. Too much substrate (> 3 M) is toxic to cells, so a culture is usually started off with 1 M substrate.

{5 x 105 cells/ml < N < 5 x 106 cells/ml}: dNcells / dt = {k6 Ncells [S]} / { k5 +[S]}

                                                                        d [S] / dt = - kNcells  

k5 =0.05 M

k6 = 1/day

k7 = 2 x 10-7 (M-ml)/(cells-day)

Finally, cells don't grow if they are too sparse or too dense:

{N < 1 cell / 0.1 ml; N > 5x106 cells/ml}   dNcells / dt =  0

The average amount of functional MAbZ1 secreted per cell depends on the cellular density, the time in the reactor (due to degradation), and the substrate concentration.

dE / dt = {k2 Ncells [S]} / { k5 +[S]} - k3 Ncells 2 - k4 Et       (Units of E: ng/ml)

k2=0.21 ng/cell-day for a 'typical' clone

k3=4 x 108 10-8 ng-ml/cell2/day


You must first estimate the optimal cell density for secretion of MAbZ1 using a small batch reactor, in which substrate can not easily be manipulated and will be consumed by the cells. You may wish to examine the effect of varying the starting cell density on the rate of MAbZ1 secretion to aid you in this estimate. However, you will only collect product from the final, largest reactor (5000 L). This final reactor is run as a fed-batch, starting at 20% capacity and optimal cell density, with water added continuously to keep the cell density optimal as the cells grow and substrate added as it is consumed to maintain the value of 3 M. Assume that MAbZ1 is only secreted in the presence of an inducing agent, which can be added to the medium but is not consumed. In the fed-batch reactor, the inducing agent will be added at t=0, and no MAbZ1 is present initially: E(t=0) = 0

You will need to:

Design a system of batch reactors to grow CHO cells from a single clone to a large population and produce maximal amounts of product in the 5000 L reactor (batch reactors available to for you to purchase range in volume from 25 μL - 5000 L, and you will need several).

Describe the number, type, and volume of each reactor needed to generate sufficient cells in a Table. Use a table to describe the timeline by which the 8 clones will be tested in each reactor. You will want to minimize the number of reactors in your system. For analysis of a single clone, create a multi-panel graphic of the system of reactors, and the cellular density as a function of time in each reactor (in one Figure).

Using MATLAB, run simulations of a batch reactor at different starting cellular densities to help determine/illustrate ideal cellular density needed for production of MAbZ1. Make a multi-panel figure of N, S, and dE/dt as a function of time and starting cell density and describe how you identified the optimal cell density you chose. 

In a separate figure, show how much S and total liquid volume (water and S) will need to be added to the fed batch reactor as a function of time to maintain the optimal cell density and the total amount of MAbZ1 secreted for a 'typical' clone.

Describe the results you obtained in text. The text should stand alone as a document without the figures, describing results concisely.

Describe your conclusions, the number and size of reactors used and the total amount of MAbZ1 produced per day in the 5000 L reactor.

Include your MATLAB code in an appendix after all display items.

Posted Date: 3/21/2013 3:09:20 AM | Location : United States

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