Receptor Competition Model.
Central target engagement of the drug at a specific dose is simulated using quantitative PET imaging displacement studies with specific radiotracers in a QSP model of the dopaminergic synapse [7]. This model reflects the human dynamics of the various neurotransmitters by calibrating the presynaptic autoreceptor coupling physiology using fast cyclic voltammetry data from rodents and primates and constrain it subsequently by human imaging data. In addition, this allows the derivation of free neurotransmitter levels, presynaptic firing frequencies and basal receptor activations associated with conditions in healthy subjects and Parkinson’s patients. For instance, this leads to a substantial difference between rodent and human dopaminergic dynamics [8] .
Subcortical Basal Ganglia Parkinson’s Disease Model
The Parkinson’s Disease QSP model of subcortical motor circuitry has been described in detail [2] and is described in detail in the Supplementary information. Basically, the model consists of the striatum, STN-GP circuitry, and thalamo-cortical circuitry [9] where we have added neuromodulator receptor effects. The STN-GP circuitry consists of two segments of the globus pallidus (GPe and GPi) and the subthalamic nucleus (STN) [10]. The thalamus model is extended from [11] were specific receptor effects of interest were added.
Each cell type is modeled with membrane conductances and each compartment obeys the membrane current balance equation of the Hodgkin-Huxley formalism [12]. The membrane potential, V, is computed by numerically integrating the equation CdV/dt = Σ ga(V-Ea) + Iex, where C is the membrane capacitance, ga is the ionic conductance of an a-type ion channel, and Ea is the reversal potential of an a-type ion channel. The sum is over all types of ion conductances in each model compartment, and Iex represents an externally applied current from synaptic currents.
The striatum model simulates the processing capacity of medium spiny neurons (MSN) in the ventral striatum or nucleus accumbens [10]. The model calculates the excitability of D1 positive MSN cells that project to the direct pathway and D2 positive MSN cells that project to the indirect pathway when driven by afferent cortical projections [13] [9] of STN, GPi, and GPe,.
The spiking properties of Thalamo-Cortical neurons are caused by a fast sodium channel, Na [14], a fast potassium channel, K [14], a low-threshold Ca channel, iTC [15], a hyperpolarization-activated cation channel, Ih [16, 17], a potassium A channel, Ka,[18], and a potassium leak channel [17].
Synaptic currents are used to calculate frequency band activity of local field potentials. We assume that synaptic currents in pyramidal cells are the major contributing dipole that generates field potentials [19], because their large number dominates the synaptic currents in other types of cells. Gamma power () is then calculated as the integral of the gamma band (35–65 Hz), while beta-power is calculated as the integral over the spectrum (20–35 Hz).
Receptor effects, pharmacology and disease state
Membrane conductances and synaptic currents are modulated by actual receptor activation levels as determined using the receptor competition model [8, 10] described above. The percent change in the maximum conductance will determine how the membrane and synaptic currents change as a result of each drug-dose combination and the pathological condition. The modulation of voltage-gated ion channels will lead to a change in spiking activity of the model affecting properties of oscillatory readouts.
Placebo response is robust in most clinical trials in Parkinson’s disease even when the subjects are on stable standard-of-care medications. This is likely due to the pulse of DA release when subjects are expecting a reward, as demonstrated in a healthy volunteer challenge with amphetamine [20]. We have previously calibrated the extent of the dopamine surge associated with the placebo effect as observed in clinical trials.
Adenosine A2A antagonism can intervene at two points in the basal ganglia circuit. D2R activation of the MSN neurons that project into the indirect pathway leads to a decrease in cAMP as a second messenger trough a Gi coupled pathway, while A2A activation leads to an increase in cAMP [4, 5]. Activation of the cAMP pathway leads to enhanced excitatory output of the indirect NoGo pathway. The lower ambient DA as a consequence of Parkinson’s pathology leads to lower reduction and higher level of cAMP formation leading to higher excitatory state of the D2 + MSN neurons, allowing the NoGo pathway to dominate. Blocking the A2A receptor, reduces part of the stimulation on the cAMP and consequently lowers activation of the NoGo pathway. It has to be noted that D2-preferring DA agonists also engage with this same pathway, which has important implications for clinical trial simulation where preladenant is added to standard-of-care.
The second mechanism is based on the colocalization of the A2A-R with the A1R at the level of presynaptic Glu afferents that stimulate the D2 + MSN neurons. Here A2A antagonist are able to reduce the amount of Glu released [6] and therefore mitigate the excess stimulatory drive on the indirect pathway.
Development of the 2-dimensional Look-up table
Because we wanted to simulate the effect of a number of different therapeutic interventions with different PK profiles, we opted for the use of a 2-dimensional look-up table (LUT) of extracellular DA levels and ” target engagement” levels of the intracellular cAMP pathway downstream of the D2R in the indirect pathway, consisting of engagement of the intracellular c-AMP dependent pathway and the presynaptic impact on glutamate release. Maximal reduction of glutamate release is 80% for 100% A2A antagonism, as determined from experimental in vivo microdialysis data [6].
Such a LUT would basically allow to derive the pharmacodynamic effect of STN beta/gamma ratio from the trajectory of the PK profile with the corresponding DA and A2A target engagement along the landscape of this 2-D Look-up table space.
A quadratic function was fitted to the predicted beta/gamma ratio (z) for different levels of D2receptor coupling (x) and dopamine deficit (y) in order to smooth the surface
\(z={b}_{0}+{b}_{1}x+ {b}_{2}y+{b}_{12}xy+{b}_{11} {x}^{2}+{b}_{22} {y}^{2}\) Eq. 1
Coefficients bn were fitted using the weighted least squares method with equal weighting of all data points, performed in R version 3.6.2.
Calculation of the PK profiles
The plasma concentration of various L-dopa formulations and preladenant was modelled using published PK models, when available. Where no published PK model was identified, a PK model was built to describe published plasma concentration profiles. Data was digitised using GetData Graph Digitizer 2.22. Simulations were performed in Phoenix and R version 3.6.2. Detailed calculations are shown in the Supplementary Information.
Model readout for the OFF-time and ON-Time with dyskinesia
OFF-time was estimated for the 16-h period of time awake, starting on the third day (48 h) of simulated dosing of the L-dopa formulation with or without preladenant. For each time point of predicted beta/gamma ratio at 30 minute intervals, the probability of OFF-time was calculated as follows:
\(p\left(t\right)= \left\{\begin{array}{c}1-\frac{threshold-z}{\left(threshold-z\right)+{EC}_{50}} for z<threshold\\ 1 for z=threshold\end{array}\right.\)Eq. 2
And the total OFF-time for 16 h awake estimated the sum of the probability for all time points multiplied by the time interval of 0.5 h, plus the placebo effect:
Off time (h) = placebo+ Σtp(t) * 0.5 Eq. 3
Threshold, EC50 and the placebo effect are free parameters, calibrated with clinical data.
Similarly, for the calculation of the ON-Time with dyskinesia. Threshold and EC50 are calibrated independently for troublesome and non-troublesome dyskinesia.
Equation 4
Pharmacodynamic effect of therapies
A baseline DA deficit (DeficitBaseline) of 95% and 85% were assumed for severe and mild PD, respectively, based on PET-imaging data [21]. Analysis of PET imaging data indicated a transient increase in synaptic dopamine levels following dosing of Sinemet 250/25 (250 mg L-dopa, 25 mg carbidopa) of 500% of baseline concentration in severe PD and 150% of baseline concentration for mild PD, corresponding to a change in DA deficit from 95–70% in severe PD and from 85 to 62.5% in mild PD [22]. The average plasma L-dopa concentration during this time was calculated as 1.98 mg/L from the pharmacokinetic model. The average concentration was used to calculate the relative change in synaptic dopamine per unit plasma concentration (mg/L) (RelChange), hence enabling the dopamine deficit over time following administration of L-dopa formulations to be estimated as follows:
\(Deficit={Deficit}_{baseline}-\left(1-{Deficit}_{baseline}\right)*RelChange*{C}_{P}\)Eq. 4
An underlying assumption is that there is a direct relationship between synaptic dopamine concentration and L-dopa plasma concentration.
The concentration dependent extent of adenosine A2A receptor antagonism by preladenant was estimated from PET imaging data in rhesus monkeys [23]. The reported dose resulting in a half-maximal occupancy (ED50;) in the whole striatum was converted the plasma concentration resulting in half maximal occupancy (EC50 mg/L) using the average plasma concentration of preladenant during the time interval of PET imaging, resulting in a plasma EC50 of 3.2 ng/ml. Adenosine A2A receptor antagonism was assumed equal to the receptor occupancy (RO), defined as:
\(Antagonism= RO=\frac{Bmax*{C}_{p}}{{EC}_{50}+{C}_{p}}\)Eq. 5
Where Bmax is the maximal receptor occupancy, which was assumed to be 100%. It is assumed that there is a direct relationship between plasma concentration and adenosine A2A receptor antagonism.
Dopamine D2 receptor coupling was assumed to be proportional to adenosine A2A receptor antagonism as follows:
\({D}_{2}coupling=a+b*antagonism\)Eq. 6
Where constant a accounts for the contribution of co-administered D2 receptor agonists to D2 receptor coupling and was calibrated to recover the OFF-time for the basal and placebo response data in clinical studies of preladenant in which the majority of all subject (85–96% across all arms) received concomitant dopamine agonists. Constant b is the proportionality constant relating A2A antagonism to D2 receptor coupling, calibrated to recover the OFF-time for the preladenant active arms in clinical studies.