Team:Peking/CellularBurden

Introduction

In most iGEM projects and synthetic biology research, complex genetic circuits are imported into bacteria to achieve variable functions. Such plenty of extra proteins, however, brings out serious burden to the host. Numerous research reported this burden profoundly influence the general physiological state of the cell reflected by growth rate variation in steady state conditions^[1]. (Fig. 1) This negative effect might lead to serious result, for example, unexpected performance of genetic circuits which needs strict parameters to function, but rarely attracts enough attention. Precise description to evaluate the actual influence of this phenomenon is expected.

In addition, this year Peking strives for greater efficiency of killing algae, thus pursues maximum gross production of killing proteins. Gross production of proteins relies on both expression level of each cell and the number of cells, and generally the two items are usually contradictive, that is, increasing expression level may lade cells and slow down the growth rate, and eventually the population size. (Fig. 2) Therefore, it is necessary to establish a balance between them to optimize the whole production.

In this part, aiming at the two questions, we focus on experimentally constructing and verifying the relationship between cell cost and growth rate, which is similar with previous reported results^[2], and finally calculating the optimal expression level. Furthermore, we also explore the growth rate under different nutritional conditions, representing the different capability to afford protein burden. Combining these two parameters, we would establish a mathematical model based on partial differential equations to analysis the process of our project.(Fig. 3).

Gene Expression Effects

Considering the low toxicity of mRFP, a serial of high-copy plasmids containing mRFP under gradient intensity of promoters is transformed into E. coli, and the growth curve of different strains are characterized. (Fig. 4a) We use the fluorescence intensity provided by iGEM Registry BBa_J23100 to evaluate the different expression levels. According to our result, we successfully verify the empirical relationship between cell cost and growth rate. (Fig. 4b).

Nutritional Condition

The nutritional condition is also a limitation on growth rate. We measured corresponding growth rate λ and the maximum environmental capacity N_K under different concentration nutrient, realized by diluting the medium. It is shown that the growth rates in different nutrition condition follow the equations:

Combined the unnecessary gene expression and nutritional condition effects, we drive a phenomenological relationship:

The function α still needs to verified. Gradient diluted standard LB medium is used as medium to quantify the growth curve. (Fig. 6a) We can see the exponential relationship between the nutrition condition and growth rate λ.(Fig. 6)

Analytical Analysisl

Based on previous experiments and equations, the accumulated protein amount A could be represented by a multiplication between the current population of bacteria N(t) and expression level ϕ. The former is the integral of growth rate λ to time. The complete formula has the following form:

A=ϕ∫_0^t▒〖N(t)dt〗= Numerical simulation provides the extremum of this function in different nutritional condition. (Fig. 6)

Proliferation Model

In our design, almost all of nutrition comes from algae lysed by lysozyme. Thus the nutrition condition is related to the lysozyme production. Consider this relation, a proliferation model has been constructed to find a optimal expression in natural environment.

From result we can deduce that cyanobacteria are eliminated most quickly in a specific concentration, while too high or low expression level significantly dampens the killing efficiency (Fig. 7). Consequently we could choose an appropriate intensity of the lysozyme based on this model.

Discussion

In this part, we originally investigate the potential negative influence of cell physiological state on synthetic biology design and propose a method to quantitatively evaluate this effect based on growth rate. Actually, this phenomenon is not rare in experiments, for example, strains carrying high-copy plasmids usually has slower growth rate than that carrying low-copy plasmids in same growth condition. Unfavorable physiological state caused by excess burden influence on expression of promoters and proliferation rate, therefore might block the function of circuits relying on this key parameters. Our model provides a choice to describe this unknown effect. In process of network design, this factor would be considered a priori and thus be repressed, which enhance the robustness of circuits.

Moreover, similar with that in our project, industry which produces protein by engineered bacteria could also use this model to obtain maximum producing efficiency through adjusting expression intensity of target protein and nutrition condition of medium. At the time that accumulation of product needs to be controlled to prevent toxicity, it is a feasible measure to make engineered bacteria devote more resource into proliferation, and vice versa.

In general, this kind of questions should be paid more attention on, and our model provides a simple attempt to solve them. We hope that more sophisticated models would be proposed in the future, which would make the evaluation more precise and reliable.

References

[1] Scott, M., Hwa, T. (2011). Bacterial growth laws and their applications.Current opinion in biotechnology, 22(4), 559-565.

[2] Scott, M., Gunderson, C. W., Mateescu, E. M., Zhang, Z., Hwa, T. (2010). Interdependence of cell growth and gene expression: origins and consequences. Science, 330(6007), 1099-1102.