DDMoRe Model Repository

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Model Definition
Estimation Steps

Short description:

This is a semi-mechanistic PK model for immunotherapy by a cytokine-based drug, interleukin (IL)-21, administered for solid tumors (i.e. metastatic melanoma, renal cell carcinoma). IL-21 affects the dynamics of various cellular entities toward creating a favored adaptive immune response, i.e. drives the proliferation of CTLs while lowering the survival of NK cells. At the same time, IL-21 boosts the killing capabilities of each of these effector cells, by increasing the levels of the intracellular cytotoxic proteins that mediate tumor cell lysis. The system comprises seven equations descibing drug pharmacokinetics for three different modes of administration. The model was originally trained and validated on data from several independent in vivo experiments in mice treated with IL-21 by various administration strategies (i.e. genetically-modified IL-21-secreting tumor cells termed cytokine gene therapy, IL-21-encoding plasmids termed hydrodynamics-based gene therapy, and recombinant murine IL-21 given systemically as in the clinic). The present version of the model was slightly modified for the DDMoRe platform, and the parameters were estimated in Monolix 3.2. The analysis of the model in the original study showed that IL-21 dose reduction and regimen fractionation are beneficial for obtaining substantial reductions in the tumor mass. The IL-21 mechanism of action in the studied murine setting seems to be very similar to that observed in clinical trials in solid cancer patients treated by IL-21. Thus, following a relatively straightforward up-scaling process to the human system, the model can be helpful for optimizing IL-21 systemic therapy in the clinic.

Format:	PharmML (0.6.1)
Related Publication:	An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers. Elishmereni M, Kheifetz Y, Søndergaard H, Overgaard RV, Agur Z PLoS computational biology, 9/2011, Volume 7, Issue 9, pages: e1002206 Affiliation: Institute for Medical Biomathematics, Bene-Ataroth, Israel. Abstract: Interleukin (IL)-21 is an attractive antitumor agent with potent immunomodulatory functions. Yet thus far, the cytokine has yielded only partial responses in solid cancer patients, and conditions for beneficial IL-21 immunotherapy remain elusive. The current work aims to identify clinically-relevant IL-21 regimens with enhanced efficacy, based on mathematical modeling of long-term antitumor responses. For this purpose, pharmacokinetic (PK) and pharmacodynamic (PD) data were acquired from a preclinical study applying systemic IL-21 therapy in murine solid cancers. We developed an integrated disease/PK/PD model for the IL-21 anticancer response, and calibrated it using selected "training" data. The accuracy of the model was verified retrospectively under diverse IL-21 treatment settings, by comparing its predictions to independent "validation" data in melanoma and renal cell carcinoma-challenged mice (R(2)>0.90). Simulations of the verified model surfaced important therapeutic insights: (1) Fractionating the standard daily regimen (50 µg/dose) into a twice daily schedule (25 µg/dose) is advantageous, yielding a significantly lower tumor mass (45% decrease); (2) A low-dose (12 µg/day) regimen exerts a response similar to that obtained under the 50 µg/day treatment, suggestive of an equally efficacious dose with potentially reduced toxicity. Subsequent experiments in melanoma-bearing mice corroborated both of these predictions with high precision (R(2)>0.89), thus validating the model also prospectively in vivo. Thus, the confirmed PK/PD model rationalizes IL-21 therapy, and pinpoints improved clinically-feasible treatment schedules. Our analysis demonstrates the value of employing mathematical modeling and in silico-guided design of solid tumor immunotherapy in the clinic.
Contributors:	Moran Optimata

Context of model development:	Dose & Schedule Selection and Label Recommendation; Mechanistic Understanding;
Discrepancy between implemented model and original publication:	The model was simplified by removing one of the compartments and the parameters were estimated using Monolix;
Model compliance with original publication:	No;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	This is PK model of IL-21 in mice, encompassing three different, modes of drug administration.;
Modelling task in scope:	simulation; estimation;
Nature of research:	In vivo; Fundamental/Basic research; Discovery stage;
Therapeutic/disease area:	Oncology;

Validation Status:	Annotations are correct.
Certification Comment:	This model is not certified.

Mandatory file
- IL_21_PK_mode.xml

Additional Files

Model owner: Moran Optimata
Submitted: Nov 1, 2016 11:02:14 AM
Last Modified: Nov 1, 2016 11:02:14 AM

Revisions

Version: 4
- Submitted on: Nov 1, 2016 11:02:14 AM
- Submitted by: Moran Optimata
- With comment: Model revised without commit message

Independent variable T

Function Definitions

proportionalError (proportional, f) = (proportional \times f)

Structural Model sm

Variable definitions

kk = \frac{cl}{v2}

k12 = q12

k32 = q23

k24 = q24

k42 = \frac{(q24 \times v2)}{v4}

k25 = q25

k52 = \frac{(q25 \times v2)}{v5}

\frac{dA1}{dT} = (\frac{(- k12 \times A1)}{(1 + (A1 \times sa1))} - (k10 \times A1))

\frac{dA2}{dT} = ((((((\frac{(k12 \times A6)}{(1 + (A6 \times sa1))} - \frac{(kk \times A2)}{(1 + (A2 \times sa0))}) + \frac{(k32 \times A7)}{(1 + (A7 \times sa2))}) - (k24 \times A2)) + (k42 \times A4)) - (k25 \times A2)) + (k52 \times A5))

\frac{dA3}{dT} = (\frac{(- k32 \times A3)}{(1 + (A3 \times sa2))} - (k30 \times A3))

\frac{dA4}{dT} = ((k24 \times A2) - (k42 \times A4))

\frac{dA5}{dT} = ((k25 \times A2) - (k52 \times A5))

\frac{dA6}{dT} = ((\frac{(k12 \times A1)}{(1 + (A1 \times sa1))} - \frac{(k12 \times A6)}{(1 + (A6 \times sa1))}) - (k10 \times A6))

\frac{dA7}{dT} = ((\frac{(k32 \times A3)}{(1 + (A3 \times sa2))} - \frac{(k32 \times A7)}{(1 + (A7 \times sa2))}) - (k30 \times A7))

output1 = \frac{A2}{v2}

Initial conditions

A1 = 0

A2 = 0

A3 = 0

A4 = 0

A5 = 0

A6 = 0

A7 = 0

Variability Model

Level	Type
DV	residualError
ID	parameterVariability

Parameter Model

Parameters

POP_cl

;

POP_v1

;

POP_v2

;

POP_k10

;

POP_k30

;

POP_q12

;

POP_q23

;

POP_v3

;

POP_v4

;

POP_q24

;

POP_v5

;

POP_q25

;

POP_sa1

;

POP_sa2

;

POP_sa0

;

b

;

omega_cl

;

omega_v1

;

omega_v2

;

omega_k10

;

omega_k30

;

omega_q12

;

omega_q23

;

omega_v3

;

omega_v4

;

omega_q24

;

omega_v5

;

omega_q25

;

omega_sa1

;

omega_sa2

;

omega_sa0

;

ETA_cl \sim N (0.0, omega_cl)

— ID

ETA_v1 \sim N (0.0, omega_v1)

— ID

ETA_v2 \sim N (0.0, omega_v2)

— ID

ETA_k10 \sim N (0.0, omega_k10)

— ID

ETA_k30 \sim N (0.0, omega_k10)

— ID

ETA_q12 \sim N (0.0, omega_q12)

— ID

ETA_q23 \sim N (0.0, omega_q23)

— ID

ETA_v3 \sim N (0.0, omega_v3)

— ID

ETA_v4 \sim N (0.0, omega_v4)

— ID

ETA_q24 \sim N (0.0, omega_q24)

— ID

ETA_v5 \sim N (0.0, omega_v5)

— ID

ETA_q25 \sim N (0.0, omega_q25)

— ID

ETA_sa1 \sim N (0.0, omega_sa1)

— ID

ETA_sa2 \sim N (0.0, omega_sa2)

— ID

ETA_sa0 \sim N (0.0, omega_sa0)

— ID

EPS_Y \sim N (0.0, 1.0)

— DV

log (cl) = (log (POP_cl) + ETA_cl)

log (v1) = (log (POP_v1) + ETA_v1)

log (v2) = (log (POP_v2) + ETA_v2)

log (k10) = (log (POP_k10) + ETA_k10)

log (k30) = (log (POP_k30) + ETA_k10)

log (q12) = (log (POP_q12) + ETA_q12)

log (q23) = (log (POP_q23) + ETA_q23)

log (v3) = (log (POP_v3) + ETA_v3)

log (v4) = (log (POP_v4) + ETA_v4)

log (q24) = (log (POP_q24) + ETA_cl)

log (v5) = (log (POP_v5) + ETA_v5)

log (q25) = (log (POP_q25) + ETA_q25)

log (sa1) = (log (POP_sa1) + ETA_sa1)

log (sa2) = (log (POP_sa2) + ETA_sa2)

log (sa0) = (log (POP_sa0) + ETA_sa0)

Correlation matrix for level ID and random effects: ETA_v2, ETA_cl

(\begin{matrix} 1 & - 0.27 \\ - 0.27 & 1 \end{matrix})

Observation Model

Observation Y
Continuous / Residual Data

Parameters

Y = (output1 + (proportionalError (b, output1) \times EPS_Y))

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Initial estimates for non-fixed parameters

$POP_cl = 0.0229$
$POP_v1 = 0.001$
$POP_v2 = 0.00551$
$POP_k10 = 0.4$
$POP_k30 = 0$
$POP_q12 = 0.693$
$POP_q23 = 0.727$
$POP_v3 = 0.001$
$POP_v4 = 9.0E-4$
$POP_q24 = 0.48$
$POP_v5 = 24.4$
$POP_q25 = 6.38$
$POP_sa1 = 0$
$POP_sa2 = 0$
$POP_sa0 = 0$
$b = 0.00975$
$omega_cl = 0.407$
$omega_v1 = 0$
$omega_v2 = 0.74$
$omega_k10 = 0$
$omega_k30 = 0$
$omega_q12 = 0.235$
$omega_q23 = 0.304$
$omega_v3 = 0$
$omega_v4 = 0$
$omega_q24 = 0$
$omega_v5 = 0$
$omega_q25 = 0$
$omega_sa1 = 0$
$omega_sa2 = 0$
$omega_sa0 = 0$

Estimation operations

1) Estimate the population parameters

Algorithm SAEM

Step Dependencies

estimStep_1

DDMODEL00000230: A pharmacokinetic model for interleukin-21 therapy validated prospectively in murine experiments in melanoma

Revisions

Function Definitions

Structural Model sm

Variability Model

Parameter Model

Observation Model

Observation YContinuous / Residual Data

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Estimation operations

Step Dependencies

Observation Y
Continuous / Residual Data