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Cell Signaling Explorer

Build and explore signal transduction pathways. Simulate receptor binding, kinase cascade amplification, dose-response pharmacology, and positive/negative feedback loops with interactive visualizations and real-time calculations.

Signal Pathway

ExtracellularLigand (10.0 nM)Receptor (50%)IntracellularG-protein5%10×Adenylyl C39%10×cAMP99%10×PKA100%5×Target Pro100%2×

Controls

Ligand Concentration10.0 nM
Dissociation Constant (Kd)10.0 nM

Results

θ=[L]Kd+[L]=10.010.0+10.0=0.500\theta = \frac{[L]}{K_d + [L]} = \frac{10.0}{10.0 + 10.0} = 0.500
Receptor Occupancy
50.0%
Total Amplification
10,000×
Final Output
5000.0
Cascade Steps
G-protein10× (cumulative: 10×)
Adenylyl Cyclase10× (cumulative: 100×)
cAMP10× (cumulative: 1,000×)
PKA5× (cumulative: 5,000×)
Target Protein2× (cumulative: 10,000×)

Receptor Binding Curve

Reference Guide

Hill Equation and Dose-Response

The Hill equation describes how a biological response varies with the concentration of a signaling molecule (ligand or drug).

E=Emax⁡⋅[C]nEC50n+[C]nE = E_{\max} \cdot \frac{[C]^n}{EC_{50}^n + [C]^n}

The EC50 is the concentration producing 50% of the maximum effect. The Hill coefficient (n) controls the steepness of the sigmoid curve. Higher n values mean a sharper, more switch-like response.

Receptor Occupancy

Receptor binding follows a saturation curve. The fraction of receptors bound depends on the ligand concentration and the dissociation constant (Kd).

θ=[L]Kd+[L]\theta = \frac{[L]}{K_d + [L]}

When [L] = Kd, exactly 50% of receptors are occupied. Lower Kd means higher affinity and the receptor binds the ligand more tightly.

Signal Amplification

Signal transduction cascades amplify weak extracellular signals through sequential enzyme activation. Each step can activate multiple copies of the next enzyme.

Total Amplification=∏i=1nfi\text{Total Amplification} = \prod_{i=1}^{n} f_i

With 5 cascade steps each providing 10-fold amplification, a single receptor activation can trigger 100,000 downstream events. This is why cells can respond to very low hormone concentrations.

Feedback Loops

Negative feedback dampens the signal, maintaining homeostasis. The downstream product inhibits an upstream step, keeping the output within a stable range.

Outputneg=G⋅S1+β⋅G⋅S\text{Output}_{neg} = \frac{G \cdot S}{1 + \beta \cdot G \cdot S}

Positive feedback creates bistable switches, where the system can exist in either a low or high state. This is used in cell fate decisions and all-or-nothing responses like blood clotting.