Target-Mediated Drug Disposition (TMDD)¶

Advanced PK model for drugs that bind to their pharmacological target, forming drug-target complexes that affect both PK and PD behavior.

Usage¶

using NeoPKPD

# Create TMDD model specification
model = target_mediated_drug_disposition()
params = CustomODEParams(
    kel = 0.1,    # Drug elimination rate (1/h)
    kon = 0.01,   # Association rate
    koff = 0.001, # Dissociation rate
    ksyn = 1.0,   # Receptor synthesis
    kdeg = 0.1,   # Receptor degradation
    kint = 0.05,  # Complex internalization
    V = 50.0      # Volume (L)
)

doses = [DoseEvent(0.0, 500.0)]
spec = ModelSpec(model, "tmdd_sim", params, doses)
grid = SimGrid(0.0, 72.0, 0:1:72)
solver = SolverSpec(:Tsit5, 1e-10, 1e-12, 10^7)

result = simulate(spec, grid, solver)

Parameters¶

Parameter	Type	Description
`kel`	Float64	Drug elimination rate constant (1/h)
`kon`	Float64	Association rate constant (1/(conc*h))
`koff`	Float64	Dissociation rate constant (1/h)
`ksyn`	Float64	Receptor synthesis rate (conc/h)
`kdeg`	Float64	Receptor degradation rate constant (1/h)
`kint`	Float64	Complex internalization rate constant (1/h)
`V`	Float64	Volume of distribution (L)

Derived Parameters¶

KD (dissociation constant): \(K_D = k_{off} / k_{on}\)
Receptor baseline: \(R_0 = k_{syn} / k_{deg}\)

Model Equations¶

Three-state ODE system:

\[\frac{dL}{dt} = -k_{el} \cdot L - k_{on} \cdot L \cdot R + k_{off} \cdot RL\]

\[\frac{dR}{dt} = k_{syn} - k_{deg} \cdot R - k_{on} \cdot L \cdot R + k_{off} \cdot RL\]

\[\frac{dRL}{dt} = k_{on} \cdot L \cdot R - k_{off} \cdot RL - k_{int} \cdot RL\]

Where: - L = Free drug (ligand) concentration - R = Free receptor concentration - RL = Drug-receptor complex concentration

Basic Example¶

using NeoPKPD

model = target_mediated_drug_disposition()
params = CustomODEParams(
    kel = 0.1,
    kon = 0.01,
    koff = 0.001,
    ksyn = 1.0,
    kdeg = 0.1,
    kint = 0.05,
    V = 50.0
)

doses = [DoseEvent(0.0, 500.0)]
spec = ModelSpec(model, "tmdd", params, doses)
grid = SimGrid(0.0, 72.0, 0:0.5:72)
solver = SolverSpec(:Tsit5, 1e-10, 1e-12, 10^7)

result = simulate(spec, grid, solver)

# Access states
conc = result.observations[:conc]
println("Initial free drug: $(conc[1]) mg/L")
println("Free drug at 24h: $(conc[49]) mg/L")

Non-Linear PK Behavior¶

using NeoPKPD

model = target_mediated_drug_disposition()

doses_list = [50.0, 100.0, 200.0, 500.0, 1000.0]

println("Dose (mg) | Cmax (mg/L) | Apparent t1/2")
println("-" ^ 45)

for dose in doses_list
    params = CustomODEParams(
        kel = 0.1, kon = 0.01, koff = 0.001,
        ksyn = 1.0, kdeg = 0.1, kint = 0.05, V = 50.0
    )

    doses = [DoseEvent(0.0, dose)]
    spec = ModelSpec(model, "tmdd", params, doses)
    grid = SimGrid(0.0, 96.0, 0:0.5:96)
    solver = SolverSpec(:Tsit5, 1e-10, 1e-12, 10^7)

    result = simulate(spec, grid, solver)
    conc = result.observations[:conc]

    cmax = maximum(conc)
    println("$dose | $cmax | ...")
end

Clinical Applications¶

TMDD is relevant for:

Monoclonal antibodies binding to soluble targets
Therapeutic proteins with receptor-mediated clearance
Small molecules with high-affinity target binding
Biologics with target-mediated disposition

Equations Summary¶

Quantity	Formula
KD	\(k_{off} / k_{on}\)
Receptor baseline	\(R_0 = k_{syn} / k_{deg}\)
Free drug rate	\(-k_{el}L - k_{on}LR + k_{off}RL\)
Complex rate	\(k_{on}LR - k_{off}RL - k_{int}RL\)
Total drug	\(L + RL\)