Understand the relationship
The reasoning behind the result
Two factors describe different parameter changes
v = (Vmax/α′)[S] / ((α/α′)Km+[S])
The competitive factor α multiplies the Km term; the uncompetitive factor α′ multiplies the substrate term in the denominator. Dividing numerator and denominator by α′ gives another Michaelis–Menten curve with apparent Vmax=Vmax/α′ and apparent Km=αKm/α′.
The constants Kic and Kiu are positive concentration parameters under the selected model. The inhibitor input [I] is its free concentration, not automatically the amount added to a tightly binding or depleting system.
The special cases must remain distinct
Competitive inhibition sets α′=1. Uncompetitive inhibition sets α=1. Pure noncompetitive inhibition uses equal Kic and Kiu, giving α=α′, an unchanged apparent Km and a lower apparent Vmax. Mixed inhibition allows the two constants to differ.
Increasing substrate can approach the original Vmax in the competitive model. In the other entered cases the limit is the lower apparent Vmax. Similar-looking measured curves alone do not prove these mechanisms.
Reduction needs a nonzero baseline
Rate reduction (%) = 100(1−vinhibited/vuninhibited)
Each scenario is compared with the uninhibited model at the same substrate concentration. This isolates the modeled effect of the entered inhibitor. At zero substrate both rates are zero, so a percentage reduction would divide by zero and is shown as undefined.
These are reversible steady initial-rate scenarios. Irreversible loss, time-dependent inhibition, tight-binding depletion and changing free concentrations require other models; none is approximated by silently substituting total inhibitor here.
Follow the numbers
A mixed-inhibition comparison
- Use Km=2 µM, Vmax=120 µM/min, free inhibitor=2 µM, Kic=1 µM and Kiu=4 µM.
- Then α=3 and α′=1.5, so apparent Vmax=80 µM/min and apparent Km=4 µM.
- At substrate=2 µM, inhibited rate=80×2/(4+2)=26.6667 µM/min. The uninhibited rate is 60 µM/min; reduction is 55.5556%.
Both apparent parameters and the matched-substrate rate comparison are needed to describe this scenario.
Quick guide
How to use this calculator
- Choose a model established independently; a calculated curve cannot identify inhibition mechanism.
- Enter uninhibited parameters and the required positive inhibition constants in the same concentration unit.
- Enter free inhibitor and substrate concentrations for each scenario, including a baseline if useful.
- Compare apparent parameters and paired rates. A reduction percentage is undefined when the uninhibited rate is zero.
Calculation method
Calculation and interpretation
Keep changes in apparent Km, apparent Vmax and rate reduction distinct under an explicitly selected reversible model.
α=1+[I]/Kic; α′=1+[I]/Kiu; v=Vmax[S]/(αKm+α′[S]); Vmax,app=Vmax/α′; Km,app=αKm/α′
Worked example
A mixed-inhibition comparison
Both apparent parameters and the matched-substrate rate comparison are needed to describe this scenario.
α=1+[I]/Kic; α′=1+[I]/Kiu; v=Vmax[S]/(αKm+α′[S]); Vmax,app=Vmax/α′; Km,app=αKm/α′
Supported inputs
Precision and limits
An experimental model, not a biological conclusion
These calculations do not establish enzyme identity, purity, active fraction, assay validity or inhibition mechanism. Temperature, pH, substrate, cofactors and preparation must match the experiment behind the entered values.
Keep measurements and mechanisms separate
A time-window slope is not automatically an initial velocity; Km is not generally an equilibrium dissociation constant. No clinical interpretation, dose or treatment decision follows from these outputs.
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