Model 1B.Rmd

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```{r}
library(tidyverse)
library(GillespieSSA2)
library(ggplot2)
library(dplyr)

```

```{r echo=TRUE}
rm(list = ls())

simulations <- function() {
# Define initial states
ini_state <- c(
  DD = 10, 
  p53 = 10, 
  p53P = 17,
  MDM2 = 10
)

# Define parameters 
parms <- c(
  CP_DD        = 8.89550362,        
  CD_DD        = 2.82600077, 
  CP_p53       = 5.47504722,
  dephos       = 9.03410545, 
  phos         = 6.88752248, 
  CD_p53       = 9.03410545, 
  CD_p53_MDM2  =  4.61270449,
  CD_p53P      = 3.45737907,
  CD_p53P_MDM2 = 8.55691123,
  CP_MDM2      = 1.26171641,
  CD_MDM2      = 8.94995013,
  CD_MDM2_p53P = 8.97424401
) 
          
# Define reactions
reactions <- list(
  reaction(~CP_DD, c(DD = +1), name = "Prod_DD"),
  reaction(~CD_DD * p53P * DD, c(DD = -1), name = "Decay_DD"),
  reaction(~CP_p53 * DD, c(p53 = +1), name = "Prod_p53"),
  reaction(~CD_p53 * p53, c(p53 = -1), name = "Decay_p53"),
  reaction(~CD_p53_MDM2 * p53 * MDM2, c(p53 = -1), name = "Inhibition_p53_MDM2"),
  reaction(~phos * p53 * DD, c(p53 = -1, p53P = +1), name = "Phos_p53"),
  reaction(~dephos * p53P, c(p53P = -1, p53 = +1), name = "Dephos_p53P"),
  reaction(~CD_p53P * p53P, c(p53P = -1), name = "Decay_p53P"),
  reaction(~CD_p53P_MDM2 * p53P * MDM2, c(p53P = -1), name = "Inhibition_p53P_MDM2"),
  reaction(~CP_MDM2 * p53P, c(MDM2 = +1), name = "Prod_MDM2"),
  reaction(~CD_MDM2 * MDM2, c(MDM2 = -1), name = "Decay_MDM2")
)

# Simulate the model
out <- ssa(
  initial_state = ini_state,
  reactions = reactions,
  params = parms,
  method = ssa_exact(),
  final_time = 24,
  census_interval = 0.01,
  verbose = TRUE,
  sim_name = "p53P_model"
)
data.frame(out$state, time = out$time)
}

# Run the simulation multiple times and store results
num_runs <- 1
results_list <- vector("list", num_runs)

for (i in 1:num_runs) {
  results_list[[i]] <- simulations()
}

# Combine and average results
combined_results <- bind_rows(results_list, .id = "run")

# Reshape data to long format for averaging
long_results <- combined_results %>%
  pivot_longer(cols = -c(run, time), names_to = "variable", values_to = "value")

# Calculate average values for each variable at each time point
avg_results <- long_results %>%
  group_by(time, variable) %>%
  summarise(avg_value = mean(value), .groups = 'drop')

# Plot the averaged results for all variables
ggplot(avg_results, aes(x = time, y = avg_value, color = variable)) +
  geom_smooth() +
  labs(title = "Averaged SSA Simulation Results",
       x = "Time",
       y = "Average Value") 
```

```{r echo=TRUE}
# Plotting a single variable in this case p53P
# Extract only the p53P variable columns
p53P_results <- avg_results %>%
  filter(variable == "p53P")

ggplot(p53P_results, aes(x = time, y = avg_value)) +
 geom_smooth(colour="red") +
  labs(title = "Average phosforylated p53 concentration",
       x = "time",
       y = "Average p53P")
```