羅放,俞易,陳銘哲,楊以清,魏垠
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外源基因表達造成的群體感應(yīng)細菌生存壓力的建模分析
羅放,俞易,陳銘哲,楊以清,魏垠
上海科技大學(xué) 生命科學(xué)與技術(shù)學(xué)院,上海 201210
羅放, 俞易, 陳銘哲, 等. 外源基因表達造成的群體感應(yīng)細菌生存壓力的建模分析. 生物工程學(xué)報, 2018, 34(12): 1895–1905.Luo F, Yu Y, ChenMZ, et al. Model for fitness burden imposed by exogenous gene expression in quorum sensing bacteria. Chin J Biotech, 2018, 34(12): 1895–1905.
外源基因的表達及其對細菌種群的影響對于群體感應(yīng)系統(tǒng)和合成生物學(xué)產(chǎn)業(yè)的研究具有重要意義。然而,人們對于表達外源蛋白的細菌本身的行為模式仍然知之甚少。為了研究菌落生長和外源基因表達的過程究竟受到哪些因素的影響,文中測量了受Lux類受體調(diào)控的外源基因在N-酰基高絲氨酸內(nèi)酯(-acyl homoserine lactone,-AHL) 信號分子誘導(dǎo)下的表達,并模擬了其對細菌種群動態(tài)的影響。文中建立了一個假設(shè)性的數(shù)學(xué)模型,對信號分子誘導(dǎo)表達下細菌種群生長受影響的現(xiàn)象進行了分析。先前的研究通常將細菌種群生長受群體感應(yīng)系統(tǒng)影響的現(xiàn)象歸咎于合成群體感應(yīng)信號分子的消耗與-AHL信號分子的毒性,文中提供了對于這種生存壓力的另一種可能的解釋。
群體感應(yīng),細菌生長,基因表達,轉(zhuǎn)錄因子,生存壓力
Quorum sensing system makes it possible for bacteria to switch between their genetic expression repertoires under low cell density (LCD) or high cell density (HCD) situations and adjust their behavior according to the size of population. Many biological processes, including virulence[1], biofilm formation[2-4], bioluminescence[5-6]and sporulation[7-8]are closely related to quorum sensing[9](Fig. 1).
In the well-studied Lux-type quorum sensing system of Gram-negative bacteria, cells use LuxI-like synthase to produce-Acyl homoserine lactone (-AHL) signaling molecules.-AHLs are 4 to 18 carbon lipophilic molecules and able to pass through the cellular membrane.-AHLs from different species vary in the C3-carbonyl and the length of acyl chain[2]. The receptor of-AHL is LuxR-type signaling molecule receptor, a transcription factor that could active gene expression downstream its cognate pLux-type promoter(Fig. 1A).
The well understood mechanisms of Lux-type quorum sensing systems enable researches about expression activation induced by-AHL signaling molecules by mathematical modeling[10-13]. These models had greatly helped the understanding of Lux-type quorum sensing system and further synthetic system design.
In this study, we measured the gene expression level regulated by LuxR-type signaling molecule receptor and bacterial population growth after the induction by-AHL signaling molecules.
It is noticed that with a rising concentration of-AHL signaling molecules, both the carrying capacity and growth rate of bacteria is decreased. Though many models were suggested for how Lux-type receptor-controlled gene expression is regulated in response to-AHL signal concentration, and the decrease of carrying capacity and growth rate is also been reported[14]. However, most of these works explained such observation by the cost of synthesizing signaling molecule[14], or toxicity of quorum sensing elements[15].
To better explain this phenomenon, we set up a mathematical model considering input signaling molecule concentration and distribution to simulate the induced gene expression process. We further offered a hypothetical model for gene expressing and population dynamics under such circumstance and could partially explain the fitness burden independent of synthesis cost of signal molecule.
In our gene circuit, expression of Lux-type signaling molecule receptor (LasR) is regulated by the constitutive promoter BBaJ23100 and expression of GFP is regulated by a cognate pLas promoter. All gene expression is driven by RBS (BBaB0034)[12]and double terminator (BBa_B0015), All genetic circuits were constructed to pSB1C3, achloramphenicol-resistant high copy number plasmid following BioBrick RFC[10]standard (Fig. 2).
The sequence of all the expression vectors are available at parts.igem.org (BBa_K2315011, BBa_K2315030, BBa_K2315024, BBa_K2315014, BBa_K2315020) (Fig.2).
圖1 在N-AHL誘導(dǎo)下的基因表達和細菌種群動態(tài)變化示意圖
圖2 表達元件設(shè)計
.DH5α chemical competent cell (CWbio CW0808S) was used. For each transformation, 100 ng of the plasmid was transformed into 50 μL of competent cells, held on ice for 30 min, heat shock at 42℃ for 45 s, 1 mL of LB added following a 30 min incubation, and 200 μL bacteria culture was spread onto selection plate. Our DH5α cells had displayed a typical transformation efficiency of around 1×108CFU/μL pUC19.
Bacteria cultures was diluted to an optical density of600=0.5 and distributed to a 96-well plate in an amount of 200 μL per well. The pre-generated-AHLs gradient working solution(1μL, in DMSO) was then added with a multichannel pipette to reduce the duration of the process.-AHLs signaling molecule concentration gradients was prepared in a DMSO solution by serial dilution. The working solution needed for all experiments was prepared simultaneously to ensure the repeatability. After the-AHLs was added, the 96-well plate was transferred to a microplate reader (SpectraMax i3x, Molecular Devices and Synergy H1, BioTek) for fluorescence measurement with the parameters below:Mode: kinetic; read1: fluorescence, Ex: 485/20, Em: 528/20; read2: absorbance, Wavelength: 600nm. A 5s linear shaking was applied before every read.
With a constitutively expressed LuxR-type signaling molecule receptor and GFP gene controlled by its cognate promoter, we are able to qualitatively measure the induction efficiency of Lux-type expression vectors (see section 2.2 for details) by measuring the fluorescent readout corresponding to the expression level of GFP and trace the population density simultaneously by recording the optical density of the bacterial culture(Fig.3). For a better understanding of mechanisms and observed phenomenon, a model has been established based on the observed expression response and population change. The symbols used in this work are listed below in Table 1.
2.1.1 Basic model of gene expression
We use a general equation to describe how one substance is generated and existed in a bio-system:
表1 本文公式推導(dǎo)中所用的符號
To build a more precise model for gene expression, we introduced three factors involved in the basic physiological process to our refined model: growth of bacteria, diffusion of signal molecule at initial time and degradation of signal molecule.
2.1.2 Growth of bacteria
We first consider about the growth of, which can not only fluctuate both reactant and product concentration, but also act as an important variable in calculating the final concentration of products. Considering that the model is based on two fundamental relation below. The total amount of substance, the concentration of substance and volume of the chamber where contains the substance are denoted as Total, Concentration, and Volume in the equation, respectively:
Put These relations back to equation (1), we have:
Anrefers to growth rate ofandmaxrefers to the limits ofpopulation. SincemaxandN=0are constants, so we define the following parameter:
圖3 細菌對信號分子的響應(yīng)曲線
Fig. 3 Bacterial responses for the signaling molecules. (A) Time trace from expression of pCon-LasR-pLas-GFP across a range of 3OC12-AHL concentrations (B) Response curve of final gene expression level of corresponding to 3OC12-AHL signal molecule concentration. The response curve was fitted using a sigmoidal function and a half response1/2=1.9×10–10mol/L.
We are familiar with Linear Differential Equation of the First Order and its solution. If we have:
The solution should be:
We combine this solution with our equation, and then we get
Use lemma 1, 2 that will be explained in the supplementary materials to simplify the solution of mRNA concentration and protein concentration. Then:
In which:
Apply lemma 2 we have:
2.1.3 Diffusion of signaling molecule
We suppose the initial concentration difference between inside and outside ofis, so we will know that the time forto balance this difference is:
Approximately we have:
We can rewrite the equation into a simplified form as below:
Finally we have:
And the concentration of target protein is:
2.1.4 Degradation of signaling molecule
In the basic model, we neglected the degradation of signaling molecules. However, the degradation is a factor should be taken into consideration in our refined model:
So the degradation of signaling molecules can be shown as the following equation:
We used a linear form of decay function because the exponential fitting of degradation is so slow that it can be treated as a first-order expansion of an exponential function.
Andgeneratetends to be:
Combining the result above with the basic model, finally we have:
In which,Δ=
Combining these refinements, the improved mathematical model could better simulate the process of gene expression. Fig. 4 shows the gene expression pattern with the parameters followed: degradation rate=0.0388 mol/s, diffusion parameter=0.958 s, concentration of signaling molecule=0.538 mol/L.
We have noticed that with the rise of concentration of-AHL signaling molecules(-AHLs), the carrying capacity for the bacterial population is correspondingly decreased. Groups with higher-AHL concentration grows slower compared to those who are treated with lower-AHL concentration (Fig.5). In this part, we will discuss an interesting model on how the signal molecule affect the growth and population.
圖4 對基因表達的模擬結(jié)果
Two hypotheses could be proposed to explain the phenomenon that higher-AHL concentration treated bacteria grows slower:
1. The signal molecule is toxic to, so the population will decrease related to the increase of concentration linearly.
2. The signal molecule induces the synthesis of GFP which occupy the substance that is originally used for growth. If the GFP is produced, the population will be at a low level, otherwise the population will be at normal level.
2.2.1 Assumptions
We analyzed the experiments result and give a comprehensive model which combines these two hypothesis based on the following assumptions:
1.cells under the induction of signaling molecules are either in the state: A, proliferate or B, producing exogenous protein but not proliferate.
2. The influence of toxicity will be acted on the bacteria with a time delay.
2.2.2 Model
could transform between two states by the probability equals to:
The refined model of population size at timepointbased on these assumptions (Fig. 6) will be:
圖5 pCon-RpaR-pRpa-GFP細菌種群在不同濃度N-AHL誘導(dǎo)下的生長情況
圖6 細菌種群生長曲線的預(yù)測結(jié)果
Our experiment result shows that even without the existence of signaling molecule synthase, the bacterial population still suffers from decreased growth rate and carrying capacity. This result suggests that the synthesis cost alone cannot completely explain the observed fitness burden phenomenon and there should be some vector other than the cost of synthesizing signaling molecules which could affect the population dynamics of the exogenous gene expressing quorum sensing bacteria.
As is shown in Fig.5 and Fig. 6, this refined population model well reproduces the shape of growth curves observed in the experiment. It shows a possible way to explain the unknown factor behind the fitness burden in the non-signal molecule producing bacterial population.
As we concluded in the previous section, signaling molecule synthesis cannot alone explain the fitness burden in the quorum sensing systems. However, due to the difficulty to synchronize the population size and bacterial status between different bacterial cultures for simultaneous measurement, the model we developed could not convincingly rule out the role of the toxicity of-AHL. Therefore, further study might be able to target the major factor of fitness burden through solving or bypassing this paradox.
In the logistic model of microbial population, the birth rate is usually considered as a constant which shows the proliferation ability of individuals in species. In the classical model, the main factor responsible for growth rate changing is the competition between the population and carrying capacity which is a measure of the available resources. Therefore, to simplify the calculation burden, generally, we take birth rate as a constant in limited generations. It is indeed a strong assumption for the model and is required additional experiments to measure the actual proliferation rate for every individual in the population as well as the cell division limits.
In a previous study about calibration of microbial growth measurement, Stevensonsuggested that theobtained is proportional to the cell number until starvation when cell size is no longer constant[13]. In our experiment results, we have not observed any phenomenon indicating such change in cell size (i.e. sudden change points intime trace curve). Also, the maximumwe observed has an equivalent of 0.4 in 1 cm optical path length, so we assume that thevalue we observed could properly indicate the cell number in the culture.
Here we give two lemmas to simplify calculation.
Lemma 1:
Proof:
Also we have:
Lemma 2:
Proof:
According to lemma1, we have:
Do some transformation onN(), which helps us solve this problem partly according to this fact:
So we suppose:
From the biological perspective, this indicates the initial population ofhas been more than the half of maximum population, this assumption roughly fits our experiments. This condition promises following equation:
So we will have:
Apply to the solution of [mRNA]:
We thank the ShanghaiTech University Undergraduate Lab Training Facility, Molecular & Cell Biology Core Facility, Wei L. Shen Lab, Min Zhuang Lab, Chao Zhong Lab and Zhi Li Lab for their equipments and reagents. We would also thank other 2017 ShanghaiTech iGEM team members for their supporting works.
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團隊簡介:
我們是來自于上??萍即髮W(xué)的iGEM隊伍ShanghaiTech,此次比賽是上??萍即髮W(xué)所參加的第二屆iGEM比賽。我們的隊伍中有著許多來自不同學(xué)科背景、掌握著不同知識與技能的同學(xué)。在本次課題中,我們致力于使用群體感應(yīng)系統(tǒng)構(gòu)建基礎(chǔ)邏輯元件模塊和與之配套的軟硬件設(shè)備,使得非生物學(xué)背景人員也能夠利用我們提供的軟硬件設(shè)施設(shè)計自己的生物回路。在生物工程學(xué)領(lǐng)域,群體感應(yīng)系統(tǒng)在同步群體行為,設(shè)計復(fù)雜回路方面有著廣泛的應(yīng)用,而表征群體感應(yīng)系統(tǒng)的種種特性對于生物工程學(xué)領(lǐng)域的研究相當(dāng)有價值。故此,文中主要介紹了我們在去年的課題中所表征的不同的群體感應(yīng)系統(tǒng)對相應(yīng)的信號分子的響應(yīng)曲線,以及在表達群體感應(yīng)外源蛋白的情況下宿主菌生長曲線的特征。如果想要了解我們項目在社會活動與硬件設(shè)計方面的工作,歡迎訪問我們的主頁:http://2017.igem.org/Team:Shanghaitech。
(本文責(zé)編 陳宏宇)
Model for fitness burden imposed by exogenous gene expression in quorum sensing bacteria
Fang Luo, Yi Yu, Mingzhe Chen, Yiqing Yang, and Yin Wei
School of Life Science and Technology, Shanghai Tech University, Shanghai 201210, China
The exogenous gene expression and its impacts on the bacterial population are important to study quorum sensing systems and synthetic biology industry. However, the behavior of exogenous protein expressing bacteria remains poorly understood. To find out which factors are playing a critical role in the growth of population and exogenous gene expression, we measured Lux-type receptor-regulated exogenous gene expression under the induction of-acyl homoserine lactone (-AHL) signaling molecules and impacts on the bacterial population dynamics after such stimulation. To analyze the cause of fitness burden of bacteria, we set up a hypothetical mathematical model. Previous studies often arrogate this phenomenon to the synthesis cost and the toxicity of-AHL signaling molecule. However, we suggested another possible cause of the fitness burden.
quorum sensing, bacterial growth, gene expression, transcription factor, fitness burden
July13, 2018;
November29, 2018
Fang Luo. Tel: +1-269-4689259; E-mail: luofang@shanghaitech.edu.cn
2018-12-10
10.13345/j.cjb.180293
http://kns.cnki.net/kcms/detail/11.1998.q.20181207.1139.003.html