DuckieDai Michaelis-Menten Enzyme Kinetics Python Program

chemistry · MIT License

Overview

Solve the Michaelis-Menten initial-rate equation for v0, Vmax, Km, substrate concentration, or fraction of Vmax.

Not calculator tested
Downloaded 37 times
Version 1.0.0
1304 bytes
No imports

Download mmEQ.py Read the source How to install

Before you run it

TI-84 Plus CE Python · No calculator OS or Python App version has been verified.
TI Connect CE .py transfer is the intended path; calculator OS, Python App, transfer, and execution have not yet been tested for this release
Initial-rate, steady-state, single-substrate Michaelis-Menten behavior applies.
Substrate is in excess and effects such as inhibition, cooperativity, and product buildup are negligible.
Km and Vmax are positive; substrate is nonnegative; inverse modes require v0 greater than 0 and less than Vmax; target percent is between 0 and 100.

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Follow the same opening, solve menu, prompts, validation, and result flow as the downloadable program.

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Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

Learn the math

How Michaelis-Menten kinetics works

The idea

An enzyme speeds up as you add substrate, but only up to a limit: once every enzyme molecule is busy, adding more substrate changes nothing. The Michaelis-Menten equation describes that curve.

Km is the substrate concentration that gives half the maximum rate. A small Km means the enzyme binds its substrate tightly.

The formula

v0 = Vmax*[S]/(Km + [S])

v0: initial reaction rate
Vmax: maximum rate when the enzyme is saturated
[S]: substrate concentration
Km: Michaelis constant, in the same units as [S]

Using the program

1 finds v0. 2 finds Vmax. 3 finds Km. 4 finds [S].
5 gives the rate as a percent of Vmax. 6 finds the [S] needed to reach a target percent.

Worked example

An enzyme has Vmax = 100 and Km = 5. At [S] = 5, choose 1 and enter 100, 5, and 5.

v0 = 100 x 5/(5 + 5)

The program shows v0 = 50.0, exactly half of Vmax, because [S] equals Km.

Tips and common mistakes

[S] and Km must use the same concentration unit.
The equation describes the initial rate, before much product has formed.
Reaching 90% of Vmax takes a substrate concentration of nine times Km.

Where this comes up

It is the central equation of the enzyme kinetics unit in biochemistry and appears in cell biology and pharmacology whenever a saturable process is described.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

def intro(n):
 print("+----------------------+");print("| "+n+" |");print("|   ___(o )> quack!    |");print("|   by DuckieDai       |");print("+----------------------+");input("ENTER to start: ")
def num(s):
 while 1:
  try:return float(input(s))
  except:print("Enter a number")
def pos(s):
 while 1:
  x=num(s)
  if x>0:return x
  print("Must be positive")
def pick(s,m):
 while 1:
  try:
   x=int(input(s))
   if x>0 and x<=m:return x
  except:pass
  print("Invalid choice")
intro("MICHAELIS-MENTEN")
print("1 v0 2 Vmax 3 Km");print("4 S 5 %Vmax 6 target S")
c=pick("Choose 1-6: ",6)
if c==1:
 m=pos("Vmax: ");s=num("[S]: ");k=pos("Km: ");v=m*s/(k+s)
 print("v0 =",v)
elif c==2:
 v=pos("v0: ");s=pos("[S]: ");k=pos("Km: ");print("Vmax =",v*(k+s)/s)
elif c==3:
 v=pos("v0: ");m=pos("Vmax: ");s=pos("[S]: ")
 if v>=m:print("v0 must be below Vmax")
 else:print("Km =",s*(m-v)/v)
elif c==4:
 v=pos("v0: ");m=pos("Vmax: ");k=pos("Km: ")
 if v>=m:print("v0 must be below Vmax")
 else:print("[S] =",v*k/(m-v))
elif c==5:
 s=num("[S]: ");k=pos("Km: ");print("% Vmax =",100*s/(k+s))
else:
 p=pos("Target %: ")/100;k=pos("Km: ")
 if p>=1:print("Target must be below 100%")
 else:print("[S] =",p*k/(1-p))
input("ENTER for guide: ");print("S=Km gives 50% Vmax");print("DuckieDai: done!");input("ENTER to exit: ")

def intro(n):
print("+----------------------+");print("| "+n+" |");print("| ___(o )> quack! |");print("| by DuckieDai |");print("+----------------------+");input("ENTER to start: ")
def num(s):
while 1:
try:return float(input(s))
except:print("Enter a number")
def pos(s):
while 1:
x=num(s)
if x>0:return x
print("Must be positive")
def pick(s,m):
while 1:
try:
x=int(input(s))
if x>0 and x<=m:return x
except:pass
print("Invalid choice")
intro("MICHAELIS-MENTEN")
print("1 v0 2 Vmax 3 Km");print("4 S 5 %Vmax 6 target S")
c=pick("Choose 1-6: ",6)
if c==1:
m=pos("Vmax: ");s=num("[S]: ");k=pos("Km: ");v=m*s/(k+s)
print("v0 =",v)
elif c==2:
v=pos("v0: ");s=pos("[S]: ");k=pos("Km: ");print("Vmax =",v*(k+s)/s)
elif c==3:
v=pos("v0: ");m=pos("Vmax: ");s=pos("[S]: ")
if v>=m:print("v0 must be below Vmax")
else:print("Km =",s*(m-v)/v)
elif c==4:
v=pos("v0: ");m=pos("Vmax: ");k=pos("Km: ")
if v>=m:print("v0 must be below Vmax")
else:print("[S] =",v*k/(m-v))
elif c==5:
s=num("[S]: ");k=pos("Km: ");print("% Vmax =",100*s/(k+s))
else:
p=pos("Target %: ")/100;k=pos("Km: ")
if p>=1:print("Target must be below 100%")
else:print("[S] =",p*k/(1-p))
input("ENTER for guide: ");print("S=Km gives 50% Vmax");print("DuckieDai: done!");input("ENTER to exit: ")

Filename: mmEQ.py
Size: 1304 bytes
SHA-256: 255b2e7054ff4e3f565c6925219b7db306d26e13354dbdb749392f6c8dcc437e

Usage

Inputs

Initial rate and Vmax in matching rate units
Substrate concentration and Km in matching concentration units
Target percent strictly between 0 and 100

Outputs

Requested kinetic quantity, fractional Vmax, or substrate-to-Km ratio

Units: v0 and Vmax share a rate unit; [S] and Km share a concentration unit.

Assumptions and limitations

Assumptions

Initial-rate, steady-state, single-substrate Michaelis-Menten behavior applies.
Substrate is in excess and effects such as inhibition, cooperativity, and product buildup are negligible.

Constraints

Km and Vmax are positive; substrate is nonnegative; inverse modes require v0 greater than 0 and less than Vmax; target percent is between 0 and 100.

Known failures

At v0 = Vmax, the required substrate tends to infinity.
Cooperative, inhibited, multi-substrate, or transport-limited kinetics require another model.

Compatibility and review

Review status: Not calculator tested
Tested on: The owner reports personally testing the supplied archive programs on a calculator; exact model, OS, and Python App versions were not recorded
What happened: Owner reported interactive testing is disclosed, but the published bytes are not labeled independently calculator tested because the environment is unrecorded and Arrhenius received a narrow intake correction
Dependencies: No imports
Suggested calculator name: MMEQ — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as MMEQ or another name, then open the Python App and try the worked example on this page first. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-09-23. Download this reviewed version

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