pkpd.Release (version 0.1.0)

michaelis_menten: Michaelis-Menten Kinetics (Linear Form) with Inhibition Comparison

Description

Performs Michaelis-Menten kinetic analysis using linearized transformations (Lineweaver-Burk by default) to compare multiple datasets and infer inhibition type.

The function fits linear regressions to transformed data and compares slopes and intercepts across conditions.

Interpretation of inhibition patterns (Lineweaver-Burk):

• Competitive inhibition: Same y-intercept (1/Vmax), increased slope -> apparent Km increases

• Noncompetitive inhibition: Same x-intercept (-1/Km), increased y-intercept -> Vmax decreases

• Uncompetitive inhibition: Parallel lines -> both Km and Vmax decrease proportionally

Value

A list containing:

fitted_parameters

A data frame summarizing linear regression results for each group or condition, including the estimated slope, intercept, coefficient of determination (\(R^2\)), and derived Michaelis-Menten parameters (Km and Vmax) computed according to the selected linear transformation.

transformed_data

A data frame containing the processed and linearized concentration and rate data (x and y) used for model fitting and visualization, along with the original group labels.

interpretation

A character string describing the expected inhibition pattern based on the specified inhibition_type and the comparison of slopes and intercepts across groups.

Arguments

data

A data.frame containing concentration and rate data.

conc_col

Column name for substrate or drug concentration.

rate_col

Column name for reaction rate or elimination rate.

group_col

Column indicating different conditions (e.g., inhibitor levels).

transform

Linearization method: "Lineweaver-Burk" (default), "Eadie-Hofstee", or "Hanes-Woolf".

inhibition_type

Expected inhibition type: "competitive", "noncompetitive", "uncompetitive", "multi-inhibition" or "none".

plot

Logical; if TRUE, generates linearized comparison plot.

Author

Paul Angelo C. Manlapaz

References

Michaelis, L. and Menten, M. (1913) Die kinetik der invertinwirkung. Biochemistry Zeitung, 79, 333-369.

Examples

# Example I: Single Michaelis-Menten dataset (no inhibition)
df1 <- data.frame(
  concentration = c(0.5, 1, 2, 4, 6, 8, 10),
  rate = c(0.48, 0.85, 1.45, 2.20, 2.70, 3.05, 3.25),
  group = "No Inhibitor"
)
# Lineweaver-Burk
michaelis_menten(
  data = df1,
  conc_col = "concentration",
  rate_col = "rate",
  group_col = "group",
  transform = "Lineweaver-Burk",
  inhibition_type = "none",
  plot = TRUE
)
# Eadie-Hofstee
michaelis_menten(
  data = df1,
  conc_col = "concentration",
  rate_col = "rate",
  group_col = "group",
  transform = "Eadie-Hofstee",
  inhibition_type = "none",
  plot = TRUE
)
# Hanes-Woolf
michaelis_menten(
  data = df1,
  conc_col = "concentration",
  rate_col = "rate",
  group_col = "group",
  transform = "Hanes-Woolf",
  inhibition_type = "none",
  plot = TRUE
)

# Example II: Two datasets compared (inhibition analysis)
df2 <- data.frame(
  concentration = rep(c(0.5, 1, 2, 4, 6, 8, 10), 2),
  rate = c(
    # Reference (no inhibitor)
    0.50, 0.90, 1.50, 2.30, 2.80, 3.10, 3.30,
    # Condition B (possible inhibitor)
    0.35, 0.65, 1.10, 1.70, 2.10, 2.40, 2.55
  ),
  group = rep(c("No Inhibitor", "Inhibitor"), each = 7)
)
# Lineweaver-Burk
michaelis_menten(
  data = df2,
  conc_col = "concentration",
  rate_col = "rate",
  group_col = "group",
  transform = "Lineweaver-Burk",
  inhibition_type = "uncompetitive",
  plot = TRUE
)
# Eadie-Hofstee
michaelis_menten(
  data = df2,
  conc_col = "concentration",
  rate_col = "rate",
  group_col = "group",
  transform = "Eadie-Hofstee",
  inhibition_type = "competitive",
  plot = TRUE
)
# Hanes-Woolf
michaelis_menten(
  data = df2,
  conc_col = "concentration",
  rate_col = "rate",
  group_col = "group",
  transform = "Hanes-Woolf",
  inhibition_type = "competitive",
  plot = TRUE
)

# Example III: Six datasets compared (one reference, five test conditions)
df3 <- data.frame(
  concentration = rep(c(0.5, 1, 2, 4, 6, 8, 10), 6),
  rate = c(
    # Reference
    0.50, 0.90, 1.50, 2.30, 2.80, 3.10, 3.30,
    # Mixed Noncompetitive inhibitor A
    0.35, 0.65, 1.10, 1.70, 2.10, 2.40, 2.55,
    # Uncompetitive inhibitor
    0.40, 0.70, 1.15, 1.75, 2.15, 2.45, 2.60,
    # Mixed Noncompetitive inhibitor B
    0.30, 0.55, 0.95, 1.45, 1.85, 2.10, 2.20,
    # Mixed Noncompetitive + higher dose
    0.28, 0.50, 0.85, 1.30, 1.65, 1.85, 1.95,
    # Uncompetitive + higher dose
    0.38, 0.65, 1.10, 1.65, 2.05, 2.30, 2.40
  ),
  group = rep(c(
    "Reference",
    "Noncompetitive (Mixed) A",
    "Uncompetitive",
    "Noncompetitive (Mixed) B",
    "Noncompetitive (Mixed) High",
    "Uncompetitive High"
  ), each = 7)
)
# Lineweaver-Burk
michaelis_menten(
  data = df3,
  conc_col = "concentration",
  rate_col = "rate",
  group_col = "group",
  transform = "Lineweaver-Burk",
  inhibition_type = "multi-inhibition",
  plot = TRUE
)
# Eadie-Hofstee
michaelis_menten(
  data = df3,
  conc_col = "concentration",
  rate_col = "rate",
  group_col = "group",
  transform = "Eadie-Hofstee",
  inhibition_type = "multi-inhibition",
  plot = TRUE
)
# Hanes-Woolf
michaelis_menten(
  data = df3,
  conc_col = "concentration",
  rate_col = "rate",
  group_col = "group",
  transform = "Hanes-Woolf",
  inhibition_type = "multi-inhibition",
  plot = TRUE
)