Morrison Tight-Binding Inhibitor Ki and Enzyme Titration
Examine how inhibitor depletion distorts inhibition data when active enzyme concentration is comparable to the inhibition constant. This page opens with the inhibition analysis already fitted with the competitive model on its synthetic rate example; the tight-binding (Morrison) model is one you can choose, which needs the active enzyme concentration you enter, and the article explains when that choice is justified.
Duplicate initial rates at four inhibitor concentrations, generated from a competitive model with Vmax 10 µM/min, Km 2 µM and Ki 5 µM and fixed noise. It is not a tight-binding dataset: its Ki is far above any plausible enzyme concentration, so it shows where the Morrison model is offered rather than a case that needs it.
Recognise when free inhibitor conservation breaks down
Standard logistic curve fitting and the classical Cheng–Prusoff equation assume that the fraction of inhibitor bound to the target is negligible compared with the total concentration added to the well. As structure-activity optimisation drives affinity into the low-nanomolar or picomolar regime, that assumption fails unless the enzyme concentration can be lowered proportionally without losing measurable signal.
When total enzyme concentration approaches or exceeds the apparent inhibition constant, adding inhibitor titrates active sites almost stoichiometrically through the central transition. On a semilogarithmic plot, this mutual depletion compresses the transition into a narrower concentration span and inflates the empirical Hill magnitude. A two-fold inhibitor spacing near the transition captures that compression, whereas a coarse ten-fold series can miss it entirely.
Design experiments that separate affinity from stoichiometry
When a compound approaches the tight-binding limit of an assay, the most informative diagnostic experiment is to repeat the titration at two or three different enzyme concentrations while holding substrate and readout linearity constant. A true tight-binding inhibitor displays a linear increase in apparent IC50 with increasing enzyme concentration, with a slope of one half and an intercept equal to the apparent inhibition constant.
Always document the nominal enzyme concentration, the method used to quantify protein mass or active sites, and the reaction progress window. If an empirical 4PL curve is fitted to such data instead, treat the resulting C50 as an upper bound constrained by the assay stoichiometry rather than an unconstrained equilibrium constant.
Equations and variables
Morrison fractional velocity equation
vi / v0 = 1 − (([E]t + [I]t + Ki,app) − √(([E]t + [I]t + Ki,app)² − 4[E]t[I]t)) / (2[E]t)
- vi / v0
- Fractional initial velocity in the presence of inhibitor relative to uninhibited control
- [E]t
- Total active enzyme concentration in the reaction vessel (mol/L)
- [I]t
- Total added inhibitor concentration (mol/L)
- Ki,app
- Apparent dissociation constant before substrate-competition correction (mol/L)
Apparent midpoint under tight binding
IC50 = Ki,app + [E]t / 2
- IC50
- Total inhibitor concentration giving fifty percent velocity reduction (mol/L)
- Ki,app
- Apparent inhibition constant at the assay substrate level (mol/L)
- [E]t
- Total concentration of catalytically active enzyme sites (mol/L)
Scope and limitations
- The inhibition analysis fits the Morrison quadratic only when you choose it, using the total active-site concentration [E]T you enter; it does not estimate [E]T from the rates.
- A steep Hill slope in a four-parameter fit can arise from inhibitor depletion, micellar aggregation, cooperative binding or signal saturation; curve shape alone cannot separate these causes.
- Nominal protein concentration from a mass assay often overstates active catalytic sites when a preparation is partially folded or incompletely modified.
Sources and provenance
- Published numerical verification inputs and independent referencesOriginal synthetic inputs; see individual fixture notices
The generated inputs are demonstrations, not experimental measurements. Existing versioned fixtures are retained unchanged.
- Morrison: kinetics of the reversible inhibition of enzyme-catalysed reactions by tight-binding inhibitorsCited method; no reproduced article data
- Copeland: evaluation of enzyme inhibitors in drug discoveryCited reference methodology; no reproduced tables
Technical questions
Why does tight binding create a floor on the measurable IC50?
Even if an inhibitor has picomolar affinity, inhibiting half of a ten-nanomolar enzyme solution requires binding five nanomolar of active sites. The total inhibitor midpoint can therefore never fall below half the active enzyme concentration, creating an assay wall when potency exceeds enzyme dilution limits.
Can I distinguish tight binding from compound aggregation using the Hill slope?
Both phenomena can produce Hill slopes steeper than unity, but they occur in different concentration regimes. Tight binding occurs near the nanomolar enzyme concentration and shifts linearly when enzyme concentration is doubled, whereas colloidal aggregation typically appears at micromolar compound levels and is sensitive to non-ionic detergent.
How is apparent Ki converted to true Ki for a competitive tight-binding inhibitor?
Once the apparent inhibition constant Ki,app is separated from the active enzyme term, the competitive substrate factor is applied in the same manner as the Cheng–Prusoff relation by dividing Ki,app by one plus the ratio of substrate concentration to Km.
Connected workflows
- 4PL IC50 curve fitting
Compare standard 4PL plateau and slope diagnostics on an ordinary curve.
- Protein A280 concentration calculation
Check how nominal protein concentration is estimated before setting enzyme assay levels.
- Chemical structure and canonical SMILES
Record the inhibitor chemical graph alongside its stoichiometric assay notes.