Lubricating bacteria model for the growth of bacterial colonies exposed to ultraviolet radiation

In this paper, we study the morphological transition of bacterial colonies exposed to ultraviolet radiation by modifying the bacteria model proposed by Delprato et al. Our model considers four factors: the lubricant fluid generated by bacterial colonies, a chemotaxis initiated by the ultraviolet radiation, the intensity of the ultraviolet radiation, and the bacteria’s two-stage destruction rate with given radiation intensities. Using this modified model, we simulate the ringlike pattern formation of the bacterial colony exposed to uniform ultraviolet radiation. The following is shown. (1) Without the UV radiation the colony forms a disklike pattern and reaches a constant front velocity. (2) After the radiation is switched on, the bacterial population migrates to the edge of the colony and forms a ringlike pattern. As the intensity of the UV radiation is increased the ring forms faster and the outer velocity of the colony decreases. (3) For higher radiation intensities the total population decreases, while for lower intensities the total population increases initially at a small rate and then decreases. (4) After the UV radiation is switched off, the bacterial population grows both outward as well as into the inner region, and the colony’s outer front velocity recovers to a constant value. All these results agree well with the experimental observations [Phys. Rev. Lett. 87, 158102 (2001)]. Along with the chemotaxis, we find that lubricant fluid and the two-stage destruction rate are critical to the dynamics of the growth of the bacterial colony when exposed to UV radiation, and these were not previously considered.

Figure 1

(Color online) The bacterial population density $b\left(r\right)$ as a function of distance $r$ from the center point of the colony at different times for $I=0.95$ [in (a), this is equal to $f=0.05$]. (a) The results of model I. (b) The results of model II, which have modified destruction rate and chemoattrctant flux. The parameters are $D_b=D_c=D_w=1$, ${\xi }_c=80$, $K_c=100$, $\mu =0.02$, $A=50000$, $B=10$. (c) The results of the model III, which is our final model. The parameters are $D_b=D_l=D_w=D_c=2$, $\gamma =\nu =1$, $\mu =0.1$, $\Gamma =5$, ${\xi }_c=80$, $K_c=100$, $A=50000$, $B=10$. Unless otherwise indicated, the results using models II and III use the same parameter values as those in (b) and (c).

Figure 2

The total population of the colony vs time for different UV radiation intensities. (a) The results from model I. (b) The results from model II. (c) The results from model III.

Figure 3

(Color online) The bacterial population density $b\left(r\right)$ as a function of distance $r$ from the center point of the colony at different UV intensities for $t_{\mathrm{UV}}=90$. (a), (b), and (c) are the numeric simulations of the models I, II, and III, respectively. In (a) and (b) there are obvious wide apexes.

Figure 4

The radius of the colony as a function of time from the point of inoculation. Three growth periods are considered: the initial growth period, the UV radiation exposure period, and the recovery period. The outer edge of the colony is plotted using (●), and the inner edge using (×). (a) The results of model I, the initial period is for $0<t<25$ and $I=0$; the exposure period is for $25<t<155$ and $I=0.95$; the recovery period is for $155<t<175$ and $I=0$. (b) The results of model II, the three periods are the same as (a). (c) The results of model III, the initial period is for $0<t<40$ and $I=0$; the exposure period is for $40<t<170$ and $I=0.95$; the recovery period is for $170<t<210$ and $I=0$.

Figure 5

The spatiotemporal response of the whole bacterial colony under UV radiation. (a)–(c) The images of the bacterial colony as a function of time $t_{\mathrm{UV}}$ under UV radiation. (a) $t_{\mathrm{UV}}=0$, (b) $t_{\mathrm{UV}}=30$, and (c) $t_{\mathrm{UV}}=90$. The UV radiation parameter $I=0.95$. (d)–(f) Recovery period of the bacterial population as a function of time $t_r$ after the UV radiation is switched off. The bacterial colony was allowed to recover for (d) $t_r=10$, and (e) $t_r=20$, (f) $t_r=30$. The bacterial population is observed to grow both outward as well as into the vacated inner region.

Figure 6

The bacterial colony’s front velocity $v_f$ vs the UV radiation intensity $I$.

Figure 7

The bacterial colony’s initial front velocity $v_i$ vs the diffusion coefficients $D_w$, $D_b$, and $D_l$, respectively. The solid circles (●) are the $v_i$ vs $D_b$ with the other two parameters $D_w=D_l=2$. The open squares (◇) are the $v_i$ vs $D_l$ with the other two parameters $D_b=D_w=2$. The symbols (×) are the $v_i$ vs $D_w$ with the other two parameters $D_b=D_l=2$.

Figure 8

The bacterial colony’s initial front velocity $v_i$ as a function of $\gamma$ and $\nu$, respectively. Obviously, $\gamma$ has a lager effect than $\nu$.