Why do we measure physical constants,
and how?
A beginner-friendly introduction to the quantitative language of biology
Life runs on chemistry. Whether a protein folds, a drug reaches its target, or a transcription factor switches on a gene, the outcome is set by a small number of physical constants: how tightly molecules stick to each other, how fast they come together and apart, and how stable their structures are.
A physical constant is a compact summary — usually a single number — that lets you predict a system's behavior across many conditions from one well-designed measurement. A single dissociation constant Kd, for example, determines the fraction of a receptor occupied by its ligand at any concentration. It's the biological analog of a model parameter: measure it once, and it describes an entire response surface.
These pages explain the four families of constants we measure in the Fordyce lab, how they emerge from simple reaction schemes, how we measure them, and the assumptions and pitfalls to watch for.
Four families of measurements
Equilibrium binding
Kd · ΔΔG
How tightly do two molecules stick to each other? The dissociation constant Kd sets the binding fraction at every ligand concentration; ΔΔG compares variants.
2Binding kinetics
kon · koff
How fast do molecules come together and come apart? The two rates determine dwell times, signalling timescales, and whether a system is far from or near equilibrium.
3Folding stability & kinetics
ΔGfold · kfold · kunfold
How stable is a protein's fold, and how often does it visit the unfolded state? These set protein abundance, aggregation risk, and response to mutation.
4Catalytic parameters
kcat · KM · kcat/KM · Ki · EC50 · IC50
How fast do enzymes convert substrate to product, and how do inhibitors or activators modulate that rate? These constants quantify activity, specificity, and drug response.
Why a physicist / AI person might care
These constants are essentially parameters of generative models for how molecules behave. Most of them have a clean statistical-mechanics interpretation:
- ΔG in kcal/mol is just a log-probability ratio: a 1.4 kcal/mol change in ΔG is a 10× change in equilibrium constant at room temperature.
- A Langmuir isotherm is a 2-parameter sigmoid; its slope is the Fisher information about Kd.
- Measuring ΔΔG rather than absolute ΔG is exactly what you do when you care about the learning signal of a mutation, not the uninteresting protein-wide offset.
- ML models trained to predict binding or activity from sequence need physical-constant ground truth to train against; the Fordyce-lab datasets are among the largest sources of such labels.
The following pages lay out the derivations, the experimental logic, and example data, with enough rigor that someone coming from an AI background can reason confidently about what the numbers mean and what they don't.