Why We Made This Model
We designed models using the Hill's Equation to validate our biosensor system's design. The biosensor detects inflammation related to acne through responding to NO and H2O2 through an AND logic gate system with two plasmids. The promoter behavior / expression was predicted through the mathematical model. The model also allowed us to establish a proof of concept for our mechanism.
The Hill's Equation can be represented as follows:
Where L is the concentration of the ligand, Kd is the concentration for the promoter, n is the Hill's constant, and θ is the percent expression of the promoter.
The equation describes the cooperative binding between a ligand and its respective receptor. It is ideal for modeling the interactions between transcription factors and promoters. We simulated PnorV (NO-responsive), PoxyS (H₂O₂-responsive), and Plux (LuxR-AHL responsive) promoters to predict the sensitivity and dynamic range of the system as well as the functionality of the logic gate.
System Architecture
The biosensor has three components:
Plasmid 1: the PnorV promoter which drives LuxR expression once it's transcriptional factor, NorR, detects Nitric Oxide.
Plasmid 2: the PoxyS promoter which drives LuxI expression (producing 3OC6HSL) in response once the OxyR transcriptional factor is activated by H₂O₂
AND logic gate system: the Plux promoter requires both 3OC6-HSL and LuxR to produce the output signal
The AND gate design ensures that the biosensor is activated only when both NO and H₂O₂ are present at the same time to make sure we only attempt to reduce excessive inflammation.
Parameter Selection and Literature Sources
| Parameter | PnorV | PoxyS | Plux (for LuxR-HSL) |
|---|---|---|---|
| Dissociation Constant (Kd) | 0.5 µM | 2.0 µM | 1.0 µM |
| Hill's Coefficient (n) | 3 | 2.5 | 2 |
PnorV Promoter (NO-Responsive)
The PnorV promoter is activated by the NorR transcription factor in response to NO. We selected a Kd value of 0.5 µM because literature values show that although value could be as low as 0.05 µM, standard values are around 0.5 µM. The Hill's coefficient of 3 is due to the structure of the NorR transcriptional factor, which has a hexadimer structure. The maximum value for the Hill’s coefficient is dependent on the number of binding sites on the subunit, which is 6. We chose a value in between.
PoxyS Promoter (H₂O₂-Responsive)
The PoxyS promoter is activated by the OxyR transcription factor in response to H₂O₂. We selected a Kd value of 2.0 µM as it is the recommended value for extracellular addition of H₂O₂, which is what we were planning to do with our bacterial system. The Hill's coefficient of 2.5 is due to the tetramer structure of the OxyR transcriptional factor, which grants a maximum possible coefficient of 4. Here as well, we chose a value in between the minimum and maximum for optimal reliability.
Plux Promoter (Output)
The Plux promoter requires the LuxR-HSL complex for activation.
Since the expression of Plux is dependent on two ligands (LuxR and HSL), and those ligands are regulated based on NO and H₂O₂, it is not possible to use the standard Hill's Equation to model the interaction. Instead, we use a modified version that accounts for both ligands.
In this modified equation, the percent expressions of PnorV and PoxyS (given their ligand concentrations) are multiplied, and a baseline expression level is added to give us the total percent expression:
Where RAND is the final proportional expression of the reporter gene, RMax is the theoretical maximum GFP expression, and RBasal is the leaky GFP expression when inducers are absent.
Model Implementation
PnorV Response to Nitric Oxide
Key Findings: The model predicts that PnorV reaches 50% activation at 0.5 µM NO and approaches its maximal response by 2 µM. The steep response curve (n=3) indicates the promoter is a sensitive switch and minimizes basal expression while providing a strong activation above threshold (see Figure 1).
Figure 1: PnorV promoter activation curve showing response to varying NO concentrations
PoxyS Response to Hydrogen Peroxide
Key Findings: The model predicts that PoxyS reaches 50% activation at 2.0 µM H₂O₂ and approaches its maximal response by 8 µM. The broader curve in comparison to PnorV demonstrates the sensitivity provided across H₂O₂ concentrations that are found in acne lesions (see Figure 2).
Figure 2: PoxyS promoter activation curve showing response to varying H₂O₂ concentrations
Plux AND Gate Response
Key Findings: The AND gate model demonstrates that significant Plux output only occurs when both NO and H₂O₂ exceed threshold concentrations. At low H₂O₂ (< 0.1 µM), output remains minimal regardless of NO levels. This validates our circuit design for specificity: the biosensor should not activate in healthy skin where only one inflammatory marker may be transiently elevated (see Figure 3).
Figure 3: Plux promoter AND gate response showing activation patterns dependent on NO and H₂O₂ concentrations
Dark purple shading indicates the region of lowest Plux output and bright yellow shading indicates the region with highest Plux output. Even at high concentrations of one input, the output remains low unless the other input is also elevated.
Biological Relevance and Validation
Literature reports the following concentrations in acne lesions:
NO: 0.1-5 µM (elevated due to iNOS/NOS2 expression)
H₂O₂: 1-10 µM (produced by inflammatory cells and bacteria)
The model places both PnorV and PoxyS in detection ranges that are physiologically relevant, which ensures that the biosensor responds properly to inflammatory conditions.
Our model demonstrates that nitric oxide and hydrogen peroxide will be detected by our system. The results of the heat map graph show that unless both signals cross the threshold concentration, Plux will not be activated and IAA (GFP as of now) will not be produced, which prevents our system from de-activating inflammation that is necessary to the body. We hope to implement IAA downstream of Plux so that once the inflammation signals are detected by the system, our plasmids will be able to provide a response (IAA), which will be able to enter and mitigate inflammation by blocking nuclear translocation of the p65 subunit, which will help prevent the activation of NF-kB, the regulator of many acne inflammatory genes.
Model Predictions and Design Optimization
Sensitivity Analysis: PnorV's steep response (n=3) shows that this promoter has binary-like switching, while PoxyS's moderate cooperativity (n=2.5) demonstrates a broader detection window.
Dynamic Range: The difference between these graph shapes is important: NO is the primary inflammatory signal while H₂O₂ provides confirmatory evidence across a range of oxidative stress levels.
AND Gate Stringency: The multiplicative nature of the AND gate (LuxR × PoxyS) ensures output is proportional to the product of both inputs. This creates a stricter activation requirement than additive logic, reducing false positives from single-marker elevation.
Conclusion
These Hill's Equation models provide proof-of-concept for our acne biosensor design. By simulating PnorV, PoxyS, and Plux promoter responses, we demonstrated that:
Both inflammatory markers (NO and H₂O₂) can be detected at physiologically relevant concentrations. The AND gate logic ensures specific activation only when both markers are present. System parameters align with computational predictions from our ML inflammation model. By validating our design computationally before wet lab work, we increase the probability of successful implementation and demonstrate how mathematical modeling serves as a critical bridge between computational biology and synthetic biology applications.
References
Balasiny, Basema, et al. “Release of Nitric Oxide by the Escherichia Coli YtfE (RIC) Protein and Its Reduction by the Hybrid Cluster Protein in an Integrated Pathway to Minimize Cytoplasmic Nitrosative Stress.” Microbiology, vol. 164, no. 4, 1 Apr. 2018, pp. 563–575, https://doi.org/10.1099/mic.0.000629.
D'Autreaux, Benoît, et al. "Characterization of the Nitric Oxide-Reactive Transcriptional Activator NorR." Methods in Enzymology, vol. 437, Feb. 2008, pp. 235–251, https://doi.org/10.1016/S0076-6879(07)37013-4.
Why We Made This Model
We developed this regression model to find out what drives acne-related inflammation, focusing on the NF-κB pathway. This pathway is important as it plays a crucial role in controlling immune signaling and producing NO and H2O2, which are both inflammatory molecules. Our therapeutic molecule, IAA, works by inhibiting NF-κB activation, which makes understanding these pathways crucial for validating our approach. Analyzing gene expression data allowed us to determine which genes are the ones that most strongly predict inflammatory states.
We used an unbiased feature selection in this model to discover which genes help to predict inflammation. Our model revealed that IL1B and NOS2, two inflammation-related genes, are among the topmost predictors. NO and H2O2 are produced downstream of this inflammatory signaling, which proves that these findings are biologically significant. Our model therefore proves IL1B and NOS2's roles in inflammation and also validates the relevance of our biosensor system.
Data Acquisition and Labeling
To gather data, we obtained the dataset from GSE54456 on the Gene Expression Omnibus (GEO). This dataset contains 13,000+ expression values (RPKM) across samples of both normal and psoriatic skin. Although our project focuses on acne, this psoriasis dataset works well since both conditions have reasonably similar biological pathways involving NF-κB for inflammation.
Each sample ID was then mapped to either psoriasis_skin or normal_skin for inflamed
or healthy samples, respectively. A series matrix file was provided along with the dataset which allowed us to
do
this. We then used these accurately labeled samples to train our classification model.
Data Cleaning and Transformation
To reduce noise in the dataset, any genes with a mean RPKM below 1.0 were removed. This is because genes with an RPKM below this number typically represent technical noise instead of biologically relevant signals. The missing values were then filled with median expression values per gene.
To validate this threshold, we performed a variance analysis to compare gene expression levels across all samples. Genes below the 1.0 threshold are shown in red, and they cluster in the low-variance region (around 10-6 to 100). In contrast, genes above the 1.0 threshold are shown in green, and they demonstrate a much higher variance (around 100 to 106). Since our model relies on identifying genes that vary between inflammatory and normal states, it is important to understand that low-variance genes contribute mostly to noise rather than to a predictive signal (see Figure 1). The threshold successfully removes about 35.4% of genes that do not support accurate inflammation prediction.
Figure 1: Mean Expression vs. Variance of Genes in GSE54456
The dataset was then normalized using a log_2(x + 1) transformation, which stabilized variance
and
enhanced
the model's convergence.
Pipeline Implementation
We then implemented a proper ML pipeline. Our first version of this model included data leakage and provided inflated results, so we made sure to implement a proper pipeline in the next iteration. The pipeline is as follows:
- 1. Split up the data using a 70/30 split for training and testing, respectively, stratifying by class (this ratio was used to balance having sufficient data for the model while reserving enough test data to reliably evaluate performance)
- 2. Calculate the variance based solely on the training data
- 3. Select the top 500 most variable genes from the training set
- 4. Apply this same feature selection to the test set
Model Training and Evaluation
Next, we trained a logistic regression classifier with L2 regularization (C value of 0.05). We got relatively strong performance metrics from this model:
Training Accuracy: ~95%
Testing Accuracy: ~90%
ROC-AUC Score: 0.904
The training accuracy is slightly high, but the small difference between training and testing accuracy (5%) indicates there is minimal overfitting and robust generalization to unseen data.
SHAP Feature Importance Analysis
Using SHAP (SHapley Additive exPlanations), each gene's contributions to predicting inflammation was analyzed. Upon logging the top 500 genes, we see that IL1B and NOS2 are in the dataset and are ranked #164 and #311, respectively:
🧬 TOP 500 INFLAMMATION-PREDICTIVE GENES (by SHAP): ---------------------------------------------------------------------- # 1. HLA-J SHAP: 0.1113 # 2. TNNT1 SHAP: 0.1005 # 3. MUCL1 SHAP: 0.0817 ... #164. IL1B SHAP: 0.0265 ... #311. NOS2 SHAP: 0.0120 ...
Biological Significance
IL1B ranked #164 out of the top 500 most variable genes with a SHAP score of 0.0265. Interleukin-1 beta is a pro-inflammatory cytokine that activates NF-κB signalling in acne lesions. This signaling cascade is particularly relevant since IAA, our therapeutic molecule, can help reduce NF-κB activation and downstream inflammatory effects in acne.
NOS2 ranked #311 out of the top 500 most variable genes with a SHAP score of 0.0120. iNOS is directly responsible for producing NO during acne-related inflammation. Like IL1B, NOS2 was selected from the initial pool of 13,000+ genes based on variance, and its elevated expression in our analysis validates it as a target for acne treatment.
The presence of IL1B and NOS2 among the 500 selected features strongly validates our biosensor's targets for acne therapy. These genes have been proven to be specific predictors of acne-related inflammation and confirm that NO and H2O2 pathways are altered in inflammatory acne conditions. This validates our therapeutic strategy of using IAA, as it can help reduce NF-κB activation and consequently decrease the expression of inflammatory mediators like IL1B and NOS2 in acne lesions.
Conclusion
This model helps to link transcriptoic signatures of inflammation to pathways that are biologically relevant. We were able to identify genes that predict inflammatory states.
By combining a feature selection based on variance with a ranking of importance through SHAP, both univariate and multivariate evidence for gene relevance was found. This ensured the robust identification of inflammation-associated genes.
Beyond prediction, our model helps to demonstrate the link between computational analysis and biological mechanisms and proves how machine learning can be used to validate experimental designs.
References
“GEO Accession Viewer.” Nih.gov, 2024, www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE54456.