Overview ​

Application to Coral Conservation ​

In the application of our circuit to coral conservation efforts, it is evident that the progressive expression of the chromoprotein aeBlue leads to a reduction in light intensity within the coral's microenvironment. This effectively mitigates the coral bleaching process and improves the overall condition of the coral.

Coordinated Regulation ​

At the cellular and molecular levels, we utilize an AND gate to connect the light sensor and thermosensor components, allowing for coordinated regulation of aeBlue expression. Both quantitative analyses and qualitative simulations serve as essential tools in this context; we employ mathematical modeling to analyze the stability of the circuit's expression, aiming to provide necessary support and supplementation for experimental laboratory work.

Development of CircuitFlow ​

Consequently, our dry lab modeling team developed a Python program that utilizes ordinary differential equations (ODEs) to simulate the stability of circuit expression, named CircuitFlow.

Model Formulation ​

Limitations of Light as an Indicator ​

As thoroughly discussed in the engineering cycle, relying solely on excessive light as a singular indicator of coral bleaching for assessing circuit activation is inadequate—there exist numerous instances in nature of corals thriving under high light exposure. Consequently, after a comprehensive literature review, we decided to incorporate elevated temperature as an additional indicator for detecting coral bleaching and regulating circuit activation.

Mathematical Articulation of Expression Characteristics ​

This led to the central question of our modeling endeavor: how to mathematically articulate the expression characteristics of the AND gate connecting the thermosensor and lightsensor, along with the expression of the downstream-regulated chromoprotein.

Modeling Approach ​

In order to address the challenge of clearly describing the expression characteristics of the AND gate that connects the thermosensor and lightsensor, as well as the expression of the downstream-regulated chromoprotein using mathematical formulations, our modeling approach is as follows: We utilize the fundamental expression equations for mRNA transcription and protein translation to simulate the characteristics of the thermosensor component, since its expression within the circuit is not directly regulated until the temperature reaches the threshold. Given that the aeBlue connected to the AND gate absorbs light intensity, the modeling equations for the lightsensor component require appropriate modifications to incorporate its dependency on light intensity. The downstream regulation of the AND gate is influenced synergistically by both the lightsensor and thermosensor; hence, we employ various binding constants to simulate this co-regulation process. Finally, for the chromoprotein's absorption of light intensity, we opt to use the Michaelis-Menten equation to model this process.

Focus on Sensor System Sensitivity ​

The primary focus of our work in the dry lab is to simulate the sensitivity of the two sensor systems using ordinary differential equations (ODEs). Within the time frame of coral bleaching, we assume that temperature remains constant; however, light intensity diminishes in accordance with the expression of the circuit. Consequently, we have:

$\frac{dm_L}{dt} = a_{p_L} \cdot \frac{I^n}{K_D^n + I^n} - r_{m_L} m_L$

$\frac{dp_L}{dt} = m_L b_{p_L} - r_{p_L} p_L$

$m_L$: The quantity of mRNA produced by the transcription of the light sensor gene.

$p_L$: The mass of protein generated by the light sensor.

$a_{p_L}$: The transcription rate of the light sensor gene.

$b_{p_L}$: The translation rate of the light sensor protein.

$r_{m_L}$: The degradation rate of the light sensor mRNA.

$r_{p_L}$: The degradation rate of the light sensor protein.

$I$: Light intensity (subject to simulation).

$n$: Hill coefficient, describing the influence of light intensity on transcription.

$K_D$: The half-saturation constant for light intensity.

There are the formulas of lightsensor part.And for thermosensor,we have:

$\frac{dm_T}{dt} = a_{p_T} - r_{m_T} m_T$

$\frac{dp_T}{dt} = m_T b_{p_T} - r_{p_T} p_T$

$m_T$: The amount of mRNA produced by the transcription of the heat sensor gene.

$p_T$: The amount of protein produced by the heat sensor.

$a_{p_T}$: The transcription rate of the heat sensor gene.

$b_{p_T}$: The translation rate of the thermosensor protein.

$r_{m_T}$: The degradation rate of the thermosensor mRNA.

$r_{p_T}$: The degradation rate of the thermosensor protein.

For AND gate(chromoprotein):

$\frac{dm_A}{dt} = P - r_{m_A} m_A$

$\frac{dp_A}{dt} = m_A b_{p_A} - r_{p_A} p_A$

$P = K_r \left( \frac{K_1 + \frac{K_2}{K_{AC}} P_L^2 P_T^2}{1 + K_1 + \frac{K_2}{K_{AC}} P_L^2 P_T^2} \right)$

$m_A$: The amount of mRNA produced by the transcription of the chromoprotein gene.

$p_A$: The amount of protein produced by the chromoprotein.

$b_{p_A}$: The translation rate of the chromoprotein.

$r_{m_A}$: The degradation rate of the chromoprotein mRNA.

$r_{p_A}$: The degradation rate of the chromoprotein.

$K_r$: The maximum transcription rate.

$K_1$: The basal transcription level.

$K_2$: The binding constant of the activator.

$K_{AC}$: The dissociation constant of the activator.

$\frac{dI}{dt} = - \frac{V_{max} \cdot I}{K_m + I} \cdot p_A$

Practical Assumptions for the Model ​

Considering the practical circumstances in the context of preventing coral bleaching, along with the operational adjustments made during parameter calibration, our model is based on the following assumptions:

Observational Changes in Light Intensity ​

1. Only the changes in values associated with light intensity within the light sensor will be observed; theoretically, the expression of the light sensor and thermosensor should remain independent of one another.

Adjustments for Real-World Conditions ​

2. Given the various disturbances that the circuit may encounter in real-world environments, it is advisable to increase the degradation rates of proteins and mRNA while concurrently reducing their synthesis rates. Furthermore, the binding affinity of the AND gate component is presumed to be relatively weak, indicated by a small binding constant.

Gene Expression Parameters ​

3. All gene expression parameters, with the exception of light intensity—which is measured in lux—are represented as normalized relative values.

Parameter Estimation ​

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The rationale behind setting the initial value of I at 6000 lux has been thoroughly articulated in our engineering cycle, and thus will not be reiterated here. Below are the values of our other parameters:[1][2][3]:

Upon inputting these parameters into our CircuitFlow model, the transcription and translation outcomes of the lightsensor, thermosensor, and the AND gate are illustrated in the following figure: The results presented in these figures indicate that both the aeBlue linked to the light sensor and the genes connected to the thermosensor can achieve stability within 120 minutes under the regulation of the AND gate, with expression levels remaining within a reasonable range. The light intensity is observed to consistently decline over the duration indicated in the figure captions. This observation suggests that our AND gate-regulated circuit will effectively mitigate the impact of light-related factors on coral bleaching.

It is noteworthy that in the final circuit model, both temperature and light intensity are simultaneously employed as inputs to regulate the expression of the entire AND gate circuit. Consequently, we further explored the use of heatmaps as a powerful tool to represent gene expression data in relation to the numerical values of temperature and light intensity. The results are illustrated in the figure below:

Reference ​

1. Li, X., Zhang, C., Xu, X., Miao, J., Yao, J., Liu, R., Zhao, Y., Chen, X., & Yang, Y. (2020). A single-component light sensor system allows highly tunable and direct activation of gene expression in bacterial cells. Nucleic acids research, 48(6), e33.

2. Tamayo-Nuñez, J., de la Mora, J., Padilla-Vaca, F., Vargas-Maya, N. I., Rangel-Serrano, Á., Anaya-Velázquez, F., Páramo-Pérez, I., Reyes-Martínez, J. E., España-Sánchez, B. L., & Franco, B. (2020). aeBlue Chromoprotein Color is Temperature Dependent. Protein and peptide letters, 27(1), 74–84.

3. CIE. (n.d.). Homepage. Retrieved August 15, 2024

4. Sari, Y., Sousa Rosa, S., Jeffries, J., & Marques, M. P. C. (2024). Comprehensive evaluation of T7 promoter for enhanced yield and quality in mRNA production. Scientific reports, 14(1), 9655.

5. Conrad, T., Plumbom, I., Alcobendas, M., Vidal, R., & Sauer, S. (2020). Maximizing transcription of nucleic acids with efficient T7 promoters. Communications biology, 3(1), 439.