如何用R tidyverse计算酶动力学各处理重复的Vmax与Km值

完全可以通过tidyverse系列函数实现需求，核心用到dplyr分组嵌套+purrr批量拟合+broom提取模型参数的逻辑，完整实现流程如下：

第一步：加载依赖包 #

library(tidyverse)
library(broom)

第二步：预处理原始数据 #

你提供的示例数据中，每个处理下每个浓度对应5个独立重复，首先需要给每个重复标注唯一ID，方便后续按重复分组拟合：

# 你提供的原始数据
df <- data.frame(
  Treatment = c("A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A","A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A","B", "B", "B", "B", "B","B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B","B", "B"),
  Concentration = c(0,0,0,0,0,10,10,10,10,10,50,50,50,50,50,100,100,100,100,100,200,200,200,200,200,0,0,0,0,0,10,10,10,10,10,50,50,50,50,50,100,100,100,100,100,200,200,200,200,200), 
  v = c(0,0,0,0,0,13,14,15,12,14,59,53,57,54,56,110,115,108,101,110,221,228,229,221,221,0,0,0,0,0,20,21,21,24,26,90,96,98,93,91, 179,175,176,179,170, 290,298,291,290,298)
)

# 给每个处理下的重复加编号，每个重复对应5个浓度梯度
df <- df %>%
  group_by(Treatment, Concentration) %>%
  mutate(Replicate = row_number()) %>%
  ungroup()

第三步：分组拟合nls模型并提取参数 #

按Treatment和Replicate分组后嵌套数据，批量拟合米氏方程，提取Vmax和Km输出为数据框：

mm_result <- df %>%
  # 按处理+重复分组
  group_by(Treatment, Replicate) %>%
  # 每组数据嵌套为子数据框
  nest() %>%
  mutate(
    # 对每个子数据拟合米氏方程，起始值根据你的数据范围调整避免报错
    fit = map(data, ~nls(v ~ Vmax * Concentration / (Km + Concentration),
                         data = .x,
                         start = list(Vmax = 300, Km = 20))),
    # 提取模型参数
    param = map(fit, tidy)
  ) %>%
  # 展开参数结果
  unnest(param) %>%
  # 整理为宽表，每行对应一个重复的Vmax和Km结果
  select(Treatment, Replicate, term, estimate) %>%
  pivot_wider(names_from = term, values_from = estimate) %>%
  ungroup()

输出结果说明 #

运行后mm_result就是你需要的结果数据框，格式如下：

原有绘图代码修正 #

你之前的绘图代码报错是因为列名不匹配（数据中酶活列是v不是Activity，数据集名是df不是data），修正后代码如下：

ggplot(df, aes(x=Concentration, y = v, color=Treatment)) +
  geom_point() +
  theme_bw() +
  xlab("Substrate (mM)") +
  ylab("Velocity (nmol/s)")+
  geom_smooth(method = "nls", 
              formula = y ~ Vmax * x / (Km + x), 
              start = list(Vmax = 300, Km = 20),
              se = F, size = 1)

不需要分别子集化处理，ggplot会自动按color分组拟合。

内容的提问来源于stack exchange，提问作者Amit