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[S] 10.0 mM substrate now
v 71.4 µmol/min speed now
Vmax 100 µmol/min top speed
Km 4.0 mM substrate for half speed
turnover 1.4 s⁻¹ reactions finished / second
speed v = Vmax ·[S]/(Km +[S]) = 100 × 10.0 / (4.0 + 10.0 ) = 71.4 µmol/min
· at [S] = Km ⇒ v = Vmax /2 = 50 µmol/min (half speed)
What you'll learn
An enzyme is a biological catalyst — a reusable tool that speeds up one chemical
reaction without being used up. This story shows, in order, how it works and then how fast
it works, so a beginner can follow it step by step.
The idea, in plain words
The enzyme has a pocket called the active site — a slot whose shape is the exact
complement of one substrate, like a jigsaw socket for one puzzle piece
(lock-and-key ; the slot also flexes to grip it — induced fit ). Only the matching shape
fits: a differently-shaped molecule bumps the pocket and is turned away. When the right
substrate (the molecule to be changed) clicks in, it is converted to product , which
leaves; the enzyme is unchanged and immediately grabs another. One enzyme repeats this thousands of
times — that repeating loop is turnover .
How the animation shows it
Beat 2 proves specificity: a wrong-shaped molecule is rejected, then the matching substrate nests
flush into the socket. Beat 3 shows it convert to product and be released. Beat 4 reveals the
Michaelis–Menten rate curve and links it to the cycle: more substrate makes the cycle run faster
and the dot climb the curve — until every enzyme is always busy, when the speed levels off at
Vmax . Beat 5 lets you change the substrate amount and add a competitive blocker.
Quantities shown
[S] — substrate concentration (mM), the amount you set.
v — reaction speed (µmol/min), computed from the formula below.
Vmax (top speed) = 100 µmol/min — the fastest possible, when every enzyme is busy.
Km (substrate for half speed) = 4.0 mM — the [S] that gets you to half of top
speed. With a competitive blocker the apparent Km = Km (1+[I]/Ki ) = 12 mM
(needs more substrate for the same speed); Vmax is unchanged.
turnover — reactions finished per second in the scene; it rises and falls with v (enzyme reuse).
Real enzymes span a huge range: the turnover number kcat runs from about 1 s⁻¹ up to
1000000 s⁻¹ (carbonic anhydrase); one enzyme keeps working, so a single cycle here takes on the order
of 1 s at these teaching values.
Formula: v = Vmax ·[S]/(Km +[S]). At [S] = Km , v = Vmax /2.
Sources
Berg, Tymoczko & Stryer, Biochemistry ; Nelson & Cox, Lehninger Principles of
Biochemistry (enzyme-kinetics chapter); Fischer 1894 (lock-and-key); Koshland 1958 (induced fit).
Km = 4 mM and Vmax = 100 µmol/min are a mid-range teaching model, not one datasheet enzyme.
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