BJRS

Model

Hypothesis

Hypothesis 1：VHb has linear influence on available oxygen

Hypothesis 2：the gaining effect of available oxygen is orthogonal to the burden of producing VHb

Formulas

We assumed that VHb has an additional positive effect on the surrounding oxygen concentration. The adsorption coefficient of VHb which shows the relationship between incremental oxygen concentration and VHb protein concentration in the bacteria is designated as K₁, whose value is determined by the efficiency of VHb; And the conversion coefficient which convert the percentage of VHb into concentration of VHb is designated as K₂. Therefore, K₁K₂pVHb will denote the incremental oxygen concentration surrounding the bacteria. The total oxygen available will be the original oxygen concentration plus the incremental oxygen adsorbed by VHb as shown in Formula 1.

Previous researches have reported that the growth rate of bacteria is affected by both the oxygen concentration and protein expression. Stolper et al. (2010) showed the positive relationship between oxygen concentration and growth rate; Scott et al. (2010) reported the negative effect of gene expression on growth rate since protein expression is an energy-consuming process. Given an unchanged level of total energy, additional protein expression will reduce the energy available for cell growth. Based on these two researches we got the relationship between growth rate and VHb concentration as shown in Formula 2.

Since the original growth rate r was measured under the original oxygen concentration, we made a correction using Formula 3 to remove the influence of the oxygen concentration, and the corrected r_c was applied to Formula 2.

symbol	description
r	Original growth rate^[2]
r_c	Corrected r removing the effect of original oxygen concentration
k	The slope constant^[2]
K_s	Half saturation constant with respect to growth
pVHb	The percentage of VHb in total bacterial protein
μ	Growth rate of the bacteria
μ_max	The maximum growth rate of the bacteria under the adjustion of oxygen concentration
O_2ori	The original oxygen concentration surrounding the bacteria
O_2useful	The total amount of oxygen available to the bacteria
K₂	The conversion coefficient of VHb concentration
K₁	The oxygen adsorption coefficient of VHb

Explaination of parameter

	Value	Reference
K_s	121nM	R^[1]
μ_max	2h^-1	Supposed from R^[1]
r	1.7h^-1	R^[2]
k	0.034	R^[2]
K₁	0.5	hypothesis
K₂	100	hypothesis
O_2ori	100nM	hypothesis

Result

**Figure 1** Prediction of the influence of VHb expression on the growth rate of bacteria under different gathering rate of oxygen.

Team:BJRS China/Model

Model