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Study of recombinant micro-organism populations characterized by their plasmid content per cell using a segregated model

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Abstract

Numerous observations from recombinant systems have shown that properties such as the specific cell growth rate and the plasmid-free cell formation rate are related, not only to the average plasmid content per cell, but also to the plasmid distribution within a population. The plasmid distribution in recombinant cultures can have an effect on the culture productivity that cannot be modelled using average values of the overall culture. The prediction of the behaviour of a plasmid content distribution and its causes and effects can only be studied using segregated models. A segregated model that describes populations of recombinant cells characterized by their plasmid content distribution has been developed. This model includes critical causes of recombinant culture instability such as the plasmid partition mechanism at cell division, plasmid replication kinetics and the effect of the plasmid content on the specific growth rate. The segregated model allows investigation of the effect of each of these causes and that of the plasmid content distribution on the observable behaviour of a recombinant culture.

The effect of two partitioning mechanisms (Gaussian distribution and binomial distribution) on culture stability was investigated. The Gaussian distribution is slightly more stable. A small plasmid replication rate constant results in a very unstable culture even after short periods of time. This instability is dramatically improved for a larger value of this constant, hence improving protein synthesis. For a very narrow initial plasmid distribution, a given plasmid replication rate and partitioning mechanism can become broad even after a relatively short period of time. In contrast, a very "broad" initial distribution gave rise to a "Gamma-like" distribution profile. If we compare the results obtained in the simulations of the segregated model with those of the non-segregated one (average model), the latter model predicts much more stable behaviour, thus these average models cannot predict culture instability with the same precision.

When compared with the experimental results, the segregated model was able to predict the practical behaviour with accuracy even in a system with a high plasmid content per cell and a high rate of plasmid-free cell formation which could not be achieved with a non-segregated model.

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Abbreviations

A :

dimensionless number, defined in Table 2

D :

dilution rate, 1/h

E :

recombinant enzyme concentration, U/L

f(z,t):

probability density function

F :

fraction of plasmid-containing cells

H :

function defined in Table 4

h :

ratio Δt*/Δz*

I:

number of nodes in the z variable

k E :

recombinant enzyme rate constant, [g/(plasmid/cell)(cell/L)h]

K Eμ :

inhibition constant in Eq. (14), 1/h

K S :

Monod constant, g/L

K z :

inhibition constant in Eq. (7), (plasmid/cell)n

K zz :

plasmid replication rate constant Eq. (8), 1/h

K zμ :

inhibition constant in Eq. (8) and (9), 1/h

m :

power in Eq. (7)

n(t):

t)cell concentration, cell/L

p(z,z′):

partitioning probability function

r z :

plasmid replication kinetics, plasmid/h cell

R :

function defined in Table 4

S :

substrate concentration, g/L

t :

time, h

V 0 :

plasmid replication rate constant, Eq. (8), plasmid/cell h

V :

discretized v(z,t*) distribution function

w(z,t):

distribution of plasmid-containing cells

Y wS :

substrate yield coefficient, g/g

Z :

space of possible values of variable z

α,β :

parameters in Eq. (12)

Δt :

time step size, h

Δz :

plasmid content step size, plasmid/cell

ε :

standard deviation

Γ :

gamma function

μ :

specific growth rate, 1/h

θ :

probability of formation a plasmid-free cell

*:

dimensionless variables

av:

average

max:

maximum

F:

feed

0:

initial

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Acknowledgments

This research was supported by Conicyt (project Fondecyt 1950620) and the Millennium Institute for Advanced Studies in Cell Biology and Biotechnology (ICM P 99-031-F).

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Authors and Affiliations

  1. Center for Biochemical Engineering and Biotechnology, Department of Chemical Engineering, Millennium Institute for Advanced Studies in Cell Biology and Biotechnology, Universidad de Chile, Beaucheff 861, Santiago, Chile

    B. A. Andrews & J. A. Asenjo

  2. Department of Chemical Engineering, Universidad de La Frontera, Casilla 54-D, Temuco, Chile

    C. Shene

Authors
  1. C. Shene
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  2. B. A. Andrews
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  3. J. A. Asenjo
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Correspondence to J. A. Asenjo.

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Shene, C., Andrews, B.A. & Asenjo, J.A. Study of recombinant micro-organism populations characterized by their plasmid content per cell using a segregated model. Bioprocess Biosyst Eng 25, 333–340 (2003). https://doi.org/10.1007/s00449-002-0313-x

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