SigCoop | Cooperativity and Control of Signaling

Teaching scenarios

Start from the regimes you said you want students to compare.

Primary knobs

All values are relative units intended for interactive intuition. Ligand is treated as limiting, with a fixed 1 minute pulse starting at time zero.

Receptor abundance Dimerization Kd2 Ligand pulse amplitude

Cooperativity regime

Kd1 is treated as a fixed ligand-capture term, conceptually around 200 nM. This toggle shifts the second-step dimerization term Kd2 relative to that fixed capture step, so negative cooperativity means weaker Kd2 and positive cooperativity means stronger Kd2. Each button loads a representative regime preset.

Trafficking

Strong activation drives receptor loss from the surface, which shortens the pulse.

Internalization rate Recycling rate

Model structure

This app uses a reduced phenomenological RTK model rather than a full mechanistic reaction network. Time is simulated from 0 to 60 minutes in 0.25 minute steps, with a fixed 1 minute ligand pulse starting at time zero.

Ligand and effective dimerization drive. The pulse is represented as L(t) = L0 / (1 + exp((t - 1) / 0.12)), receptor occupancy as theta(t) = L(t) / (L(t) + 0.7), and peak dimerization drive as D = R * theta_peak / Kd2eff, with Kd2eff = Kd2 * c_coop. In this teaching app, Kd1 is held fixed as a ligand-capture term (conceptually about 200 nM), while the user changes Kd2 and the cooperativity factor shifts it relative to that fixed first step.
Two-component signaling response. The signal is written as the sum of a fast transient branch and a weak sustained branch. The transient term uses a gamma-like peak, g(t) = (t / t_peak) * exp(1 - t / t_peak), multiplied by an early shutoff gate. The sustained term is the product of a rise logistic and a fall logistic. Their amplitudes are heuristic functions of D, receptor abundance, and a near-threshold weak-Kd window, which allows weak dimerization to remain low and prolonged at low receptor abundance but switch to a high transient when receptor abundance is increased.
Trafficking and signal collapse. Internalized receptor fraction follows I(t + dt) = clamp(I + [kint * (T + 0.22S) * (1 - I) - krec * I]dt). Surface receptors are Rs = R * (1 - I), and displayed signaling is scaled by surface availability, signal = (T + S) * (0.58 + 0.42 * Rs / R). This produces rapid decay after a strong burst when internalization outpaces recycling.
Summary metrics and labels. Peak signal, peak time, area-under-the-curve-derived effective duration, and final surface receptor loss are calculated from the simulated trace. The transient versus sustained label comes from a score that increases with peak amplitude and receptor loss and decreases with effective duration, so it should be interpreted as a compact teaching summary of the waveform rather than a direct fate prediction.

Limitations

Parameters are in relative units and are tuned for qualitative behavior, not globally fit to a single experimental dataset.
The simulator does not explicitly solve monomer-dimer mass-action equations with ligand depletion, adaptor competition, phosphatases, endosomal signaling, or downstream ERK/AKT feedback loops.
Cooperativity is represented by an effective shift in Kd2 relative to a fixed Kd1 capture term, not by a full microscopic thermodynamic fit of all ligand binding and dimerization states.
The phase map is drawn as a fixed canonical background in Kd2 versus receptor abundance space, so the x-position follows the displayed Kd2 slider directly while the background itself stays fixed.
The growth-like and differentiation-like labels summarize curve shape in this reduced model and should not be treated as universal predictions across all ligands, cell types, or RTKs.

Peak signal

Peak time

Plateau width

Surface receptor loss

Time course

Signal versus receptor availability

Current trace

Signal Surface receptor Ligand pulse

Phase map

Dimerization Kd2 versus receptor abundance

Current setting

Growth-like Differentiation-like

State snapshot

Where the receptors are at peak and late phase

Active receptors shrink when internalization strips the cell surface.

At signal peak

Late phase

Silent surface Active dimers Internalized