Modeling the Geometric Regularity in Proteus Mirabilis Colonies 公开

Zhang, Bin (2016)

Permanent URL: https://etd.library.emory.edu/concern/etds/zs25x859f?locale=zh
Published

Abstract

The colonies of Proteus Mirabilis exhibit a geometric regularity. There are three phases involved in the colony expansion, namely the lag phase, the swarming phase and the consolidation phase resulting in periodicity properties both in space and time domain. As the repetition of swarming and consolidation phases goes on, the pattern of the colony is concentric rings with higher and lower cell density alternately in space. The measurement of the repetition time of swarming and consolidation is periodic. We investigate this spatiotemporal regularity using a one-dimensional reaction-diffusion model. We analyze the influences of the thresholds in two categories, nutrient and cell density. The thresholds are added to the reaction-diffusion model as Heaviside functions. We found that the thresholds in these two categories together can provide the period of P. mirabilis colony expansion in the simulation. However, they are not sufficient to maintain an unchanged period in time as observed in the experiments.

Table of Contents

Contents

1. Introduction 1

1.1 Proteus Mirabilis 1

1.2 Regularity of the Growth in Proteus Mirabilis 2

1.3 Phases in the Growth of the Proteus Mirabilis 3

1.4 Controllable Parameters in the Experiment 6

2. Methods, Models and Discussion 9

2.1 General Diffusion and Growth Model 9

2.2 Influences of the Thresholds 10

2.3 Forward Time and Centered Space Method 11

2.4 Diffusion Reaction Model with One Threshold in Nutrient Cannot Generate Periodic Patterns 12

2.5 Diffusion Reaction Model with One Threshold in Nutrient and Two Thresholds on Cell Density Can Generate Periodic Pattern with Varying Period 14

2.6 Diffusion Reaction Model with Two Thresholds in Nutrient and Two Thresholds on Cell Density Can Generate Periodic Pattern with Varying Period 18

2.7 Diffusion Reaction Model with One Thresholds in Nutrient and Two Thresholds on Cell Density (for Diffusion Activation and Deactivation) Can Generate Periodic Pattern with Varying Period 21

2.8 Analysis of the Time Period 23

2.9 Modification of Growth Function and Rate 25

2.10 Conclusion 26

3. Future Work 28

3.1 Quorum Sensing 28

3.2 Modification of Growth Functions and Rates 30

List of Figures and Tables

Figures

Figure 1-1 Geometry Regularity of the P. Mirabilis Colony 2

Figure 1-2 Phases in the Growth of the P. Mirabilis Colony 4

Figure 2-1 Spatially Distributed Cell and Nutrient Density versus time 13

Figure 2-2 The cell number versus time at a certain point 15

Figure 2-3 The nutrient level versus time at a certain point 16

Figure 2-4 FFT of the cell number versus time at a certain point 16

Figure 2-5 Relationship between period and diffusion coefficient 18

Figure 2-6 The cell number versus time at a certain point 20

Figure 2-7 Relationship between period and diffusion coefficient 21

Figure 2-8 Spatiotemporal of the P. mirabilis colony modelling 23

Figure 2-9 Normalized Period versus Diffusion Coefficient 24

Figure 2-10 The Growth Rate Changes with Monod Form 26

Tables

Table 1 Parameters in the P. Mirabilis Colony Growth Experiment 8

Table 2 General Rules of Thresholds in Explored Scenarios 12

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