Conserve total hormone while separating carrier binding and target occupancy

1. Identify the pathway and causal question

Endocrine signals travel through circulation, but target responses depend on receptor expression and downstream machinery. Peptide hormones commonly bind membrane receptors, whereas many lipid-soluble hormones bind intracellular receptors; thyroid hormones are amines with intracellular signaling behavior. Hormone chemical class, transport, receptor location and response time are related but not interchangeable labels.

2. Connect structures, signals and assumptions

Circulating binding proteins can carry hormone without being the target receptor. Total measured hormone combines free and carrier-bound forms; receptor occupancy depends on the relevant free concentration in this simplified equilibrium. A change in binding capacity can therefore alter the relationship between total concentration and target occupancy even when total remains the same. Real feedback can subsequently alter secretion.

The original single-carrier model uses binding capacity B and dissociation constant2, so bound concentration is BF/(2+F) at free concentration F. Conservation requires T=F+BF/(2+F), or F²+(2+B−T)F−2T=0. Choose the nonnegative root. A separate target receptor has dissociation constant1 and occupancy F/(1+F); carrier and receptor constants must not be confused.

Occupancy is not efficacy. Receptor number, amplification, desensitization, intracellular regulation and tissue context determine downstream effects. The invented units do not correspond to a clinical hormone assay, and the model gives no medication, supplement or diagnostic advice. Retain total, free, bound and occupancy as four separate quantities.

3. Reconstruct an original worked comparison

At total 6 and binding capacity 4, the free concentration solves F²−12=0, giving F=2√3≈3.4641. Bound concentration is 6−2√3≈2.5359, and target occupancy is 2√3/(1+2√3)≈0.77599. Neither free nor bound alone equals the total.

4. Predict and investigate

Predict first: Can unchanged total hormone coexist with changed free hormone when carrier capacity changes?

At total 6, compare carrier capacity 0,4 and8. Reconstruct the conservation equation and target occupancy, then state why a receptor-bound fraction does not establish the physiological effect.

5. Discriminate a changed mechanism

Apply the mechanism to a changed boundary

At total 4 and zero carrier capacity, find free, bound and target occupancy.

Retain the first response, units, uncertainty and any prior feedback exposure in the notebook before comparing this public explanation.

Compare a worked response

Free4, bound0 and target occupancy4/5=0.8. The target receptor is still present; zero carrier capacity does not mean zero target binding.

6. Retain a nonclinical evidence defense

Preserve the first prediction, complete signal or quantity ledger, alternative mechanism and missing observation in the Anatomy and Physiology course workspace. Supplied neural and hormonal values are fictional. Do not perform stimulation, reflex testing, hormone manipulation or personal health measurements. Guided feedback is not independently assessed reasoning or actual practical competence.

Supporting anatomical mechanism, checked 30 October 2026. Original models, diagrams, explanations and exercises, not clinical data or a diagnostic decision tool.