Team:USTC/Model/5

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Introduction


A wide range of bacteria species are known to communicate with each other through the so called quorum sensing (QS) mechanism by means of which the produce a small molecule that can freely diffuse in environment and among the cells.[1] Acyl-Homoserine lactone (AHL) and a family of N-acylhomoserine lactones (AHLs) is an important class of “quormones,” or autoinducers.[5] We use external AHL to stimulate the expression of CysDes protein, and choose arabinose to stimulate the expression of CmCR protein.

For the first part, we build an ODE (Ordinary Differential Equations) model by using MATLAB code to simulate the protein expression process. By solving ODEs, we can predict the expression rate(d[P]/dt) and the concentration of target protein([P]) during the several hours after the inducer was added to the medium. To identify the stability and reliability of our QS system, we also add some noise to our ODEs, which correspond to the disturbance in biology system. The result proved that our QS system can run stably in a quite high disturbance environment.

For the second part, we introduce a Universal Protein Expression Platform(UPEP) to model the process of gene transcription and translation switching on or off quantitatively and output the suitable inducer concentration and induction time, which helps us obtain a best induction condition and guide our experiment.

By using this platform, you need to input the type of QS system or inducer type used in your system, and some other information about your plasmid, including target gene sequence length and self-degradation rate of the target protein. By solving ODE based on biochemical reaction process, the platform returns a figure shows the time cost in induction process with different inducer concentrations. You can choose a maximum time cost that accepted in your wet-lab experiment, then decide the concentration of inducer added to the medium. What's more, once you determine your inducer concentration, our platform will output two figures showing the product concentration([P]) at steady state and product generate rate(d[P]/dt) at a different time.


ODE simulation


Acyl-Homoserine lactone(AHL) is an important class of “quormones,” or autoinducers widely used in bacterial quorum sensing(QS) systems.[5] And the mechanism of AHL inducer are studied clearly in the previous reserch. Firstly, we summarize the chemical process of reactions shown in appendix A, then we can write down the ODEs in appendix B. By solving these ODEs in MATLAB, result of the express rate(d[P]/dt) and the concentration of target protein([P]) - time curve are shown in Fig.1 below.

Fig. 1 | [P]-time and d[P]/d[t]-time curve of CysDes


Then we choose the function to fit the [P]-time curve, and fit the result shown in Fig.2. By fitting curve, we can define 2 parameters to characterize the protein expression process. The first one is ym, which means the balance concentration of protein. And the second one is t90, which means the time cost to reach 90% amount of expression of protein.

Fig. 2 | fit curve of [P] time

For the result of simulation are closely related to the copy number of plasmid and the concentration of inducers added, we change these two numbers and simulate respectively to each number, and find different ym and t90 under different conditions, shown in Fig.3 and Fig.4.

Fig. 3 | ym result with inducer added and [DNA]

Fig. 4 | t90 result with inducer added and [DNA]


Furthermore, to identify the stability and reliability of our QS system, we also add some noise to our ODEs, which means we add a random disturbance to ODE solver of each chemicals' concentration. Result of [P]-t curve was shown in Fig.5 below. Black curve is the ODE's solution at noise = 0, and 4 other curves are other solutions when noise is added. When we try to solve ODE in a loop code, and count the possibility of route to obtain the probability density on the curve, result is shown in Fig.6.

Fig. 5 | [P]-time curve after noise added

Fig. 6 | Probability Density of [P]-time curve



Universal Platform


Although QS system is widely used in the control of bacterial artificial chromosome expression for decades, but the research on the QS system is mostly qualitative, which reveal the process of transcription and translation switch on or off, and always have no accurate measurement of the biochemical reaction process. For this reason, most of the experiment with QS system used in bacteria is using experienced data or protocol to guide, such as the inducer concentration and induced time. But when we face different plasmid or different product, it always has different response to same inducer, so that it not still easy to decide the inducer dose or which protocol to utilize in the experiment.

To solve this problem, we introduced a Universal Protein Expression Platform(UPEP) to modeling the process of gene transcription and translation switch on or off quantitively and output the suitable inducer concentration and induced time, which helps us obtain a best induced result and guide our experiment. With the help of MATLAB App Designer introduced in 2016, we built this platform shown in Fig.7 below.

Fig.7 | Universal Protein Expression Platform screenshot

By using this platform, you need to input the type of QS system or inducer type used in your system, and some other information about your plasmid, include target gene sequence length and self-degradation rate of the target protein. By solving ODE based on biochemical reaction process, the platform returns a figure shows the time cost in induce process with different inducer concentration. You can choose a maximum time cost that accepted in your wet-lab experiment, then decide the concentration of inducer adds to the medium. What's more, once you decide your inducer concentration, our platform will output two figures show the product concentration([P]) and product generate rate(d[P]/dt) at a different time.



Reference


  1. Weber, M. & Buceta, J. Dynamics of the quorum sensing switch: stochastic and non-stationary effects. Bmc Systems Biology 7, doi:10.1186/1752-0509-7-6 (2013).

  2. Urbanowski, M. L., Lostroh, C. P. & Greenberg, E. P. Reversible acyl-homoserine lactone binding to purified Vibrio fischeri LuxR protein. Journal of bacteriology 186, 631-637, doi:10.1128/jb.186.3.631-637.2004 (2004).

  3. Roberts, C. et al. Characterizing the effect of the Staphylococcus aureus virulence factor regulator, SarA, on log-phase mRNA half-lives. Journal of Bacteriology 188, 2593-2603, doi:10.1128/jb.188.7.2593-2603.2006 (2006).

  4. Fukamachi, H., Nakano, Y., Yoshimura, M. & Koga, T. Cloning and characterization of the L-cysteine desulfhydrase gene of Fusobacterium nucleatum. Fems Microbiology Letters 215, 75-80, doi:10.1016/s0378-1097(02)00916-3 (2002).

  5. Kaufmann, G. F. et al. Revisiting quorum sensing: Discovery of additional chemical and biological functions for 3-oxo-N-acylhomoserine lactones. Proceedings of the National Academy of Sciences of the United States of America 102, 309-314, doi:10.1073/pnas.0408639102 (2005).

  6. Kaplan, H. B. & Greenberg, E. P. DIFFUSION OF AUTOINDUCER IS INVOLVED IN REGULATION OF THE VIBRIO-FISCHERI LUMINESCENCE SYSTEM. Journal of Bacteriology 163, 1210-1214 (1985).

  7. Bernstein, Jonathan A., et al. "Global analysis of Escherichia coli RNA degradosome function using DNA microarrays." Proceedings of the National Academy of Sciences of the United States of America 101.9 (2004): 2758-2763.

  8. Medina-Martinez, M. S., et al. (2007). "Degradation of N-acyl-L-homoserine lactones by Bacillus cereus in culture media and pork extract." Applied and Environmental Microbiology 73(7): 2329-2332.


Appendix


Appendix A | Biochemical reaction equations of AHL induced QS system




Appendix B | ODEs of AHL induced QS system




Appendix C | Biochemical Reaction constant of AHL induced QS system




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