Methods and tools for multiscale modelling in Systems ... · approach for calculating the unknown...
1
i i i art i i P V Q C F dt dQ B E CYP B liver B C C i in liver Complex k B E CYP V k B B F B dt dB outliver art 1 2 2 1 1 2 2 2 1 1 50 ) ( 50 ) ( 1 1 ) ( IC t I IC t I t E 0 * v S dt dx Steady-state of metabolite concentration BACKGROUND. Systems Pharmacology aims to quantitatively study the dynamic interactions between drugs and biological systems by integrating models and data at different scales, to understand how the behaviour of individual constituents (modelled, e.g., via biological networks) and the behaviour of the whole system (modelled, e.g., via PBPK models) mutually interact. The objective of this work is to present and discuss: how models at different scales can be coupled; the types of data that can be used; the tools supporting the implementation; the practical research and drug development studies the models were built for. Methods and tools for multiscale modelling in Systems Pharmacology: a review E. Borella, L. Carrara, S.M. Lavezzi, I. Massaiu, E. Sauta, E.M. Tosca, F. Vitali, S. Zucca, L. Pasotti, G. De Nicolao, P. Magni BMS Lab, Department of Electrical, Computer and Biomedical Engineering, University of Pavia (Italy) METHODOLOGY AND TOOLS. From literature three main methods for coupling PBPK models and biological networks were identified: Integration of genic information as covariate in PBPK models parameters Genic information is included as a covariate for tissue-specific transporter-activity. Here an example relative to SNP in OATP1B1 transporter is presented [J. Lippert, 2010]. Example of application: A PBPK model representing ADME genes involved in simvastatin and pravastatin metabolism to predict the risk of myopathy in individuals with specific genotype was developed [J. Lippert, 2010]. • PBPK models for simvastatin and pravastatin were built for the reference homozygous TT genotype using plasma data. • PBPK models for the CC genotype were built based on the TT models by adjusting OATP1B1 transporter activity. PBPK model for the CT genotype uses the average of the transporter activities. CC TT Other organs GI tract Kidney Muscle Blood Liver cells Bile TT CC cat V V r E K V max max 0 max / Tools: OATP1B1 Combination of PBPK and networks ODEs As an illustrative example, a simple generic PBPK rat model considering absorption, transport and excretion of benzene is shown [S. Cheng,2011]. Here, only inhalation is modelled. The metabolism of the substance is described by the network below. Example of application: A joint PBPK model, including paracetamol PK combined with a network of GSH homeostasis, was developed to study candidate biomarkers of liver toxicity [S. Geenen, 2010]. PBPK and network models are both represented by ODEs and the connection is provided by network exchange rates affecting the PBPK concentrations [F.Y. Bois, 2009]. The mass-balance equations of the network are coupled with the PBPK model: • Ophthalmic acid and 5-oxoproline were evaluated as biomarkers to monitor GSH depletion toxicity. • Some parameters are derived from literature, while others are estimated. The PBPK model well describes paracetamol concentration in plasma. Tools: Example of application: A multiscale PK/PD model is developed to study the therapeutic effect of allopurinol in the treatment of hyperuricemia [M. Krauss, 2012]. • PBPK models for allopurinol, oxypurinol and uric acid were built using physiological information and plasma concentration data. • Feedback coupling was used to study the effect of drug on xanthine oxidase in the hepatic metabolic network. Maximization of uric acid production was considered as objective function. • Model evaluation: comparison between simulation of uric acid and venous plasma concentration after a single dose of allopurinol. = xanthine oxidase Allopurinol PB-PK Oxypurinol PB-PK Xanthine Uric Acid Hypoxanthine Uric acid PB-PK Liver cell Tools: Coupling with dynamic Flux Balance Analysis Metabolites, reactions and fluxes in a metabolic network are represented by a stoichiometric matrix and a vector of fluxes [D. Orth, 2010]. Flux Balance Analysis (FBA) is a mathematical approach for calculating the unknown fluxes given a set of constraints and an objective function. The PBPK model, represented by ODEs, can be coupled to the network via dynamic FBA by feed- forward (steps 1-3) or feed-back (steps 1-5) approach [M. Krauss, 2012]. (1) Update PBPK metabolization rate from tissue concentrations (5) Simulate whole-body concentrations for next time step (3) Calculate flux distribution at cellular scale (2) Use PBPK metabolization rate as upper bound for FBA (4) Use FBA uptake as upstream PBPK metabolization rate FBA PBPK Benzene Benzene Oxide Benzene CYP2E1 CYP2E1 Complex k 1B k 2B k 3B Liver cell C inhaled C exhaled Poorly perfused Well perfused Fat Liver Lungs • Safety risk was evaluated to forecast the incidence rate in the CC subgroup population given the incidence rate of TT and TC subpopulations. ODEs FBA Covariate ✔ • Mechanistic approach • Traditional solving methods • Mechanistic approach • Enables genome-scale models • Easy estimation of network parameters • Easy implementation • Inclusion of genetic information ✖ • Need for parameter values and rescaling • Large-scale networks implementation • Jointly solving of ODEs and FBA • Non-mechanistic at cellular level CONCLUSIONS. • The PBPK-network combination with ODEs is the most widely used approach. • Computational tools have been proposed to facilitate model coupling for the ODE and covariate approaches; databases, e.g., BioModels Database (EBI), JWS and SABIO-RK, are available to retrieve networks and their parameters. • Multiscale modelling is a major challenge in Systems Pharmacology, for which guidelines are still missing. Efficient integration of heterogeneous data, including genetic information, will greatly improve our knowledge of the mechanisms underlying complex diseases and drive new approaches for drug discovery.
Transcript of Methods and tools for multiscale modelling in Systems ... · approach for calculating the unknown...
ii
iarti
i
PV
QCF
dt
dQ
BECYPBliverB
CCiinliver
ComplexkBECYPVk
BBFBdt
dBoutliverart
1221 12
2
2
1
1
50
)(
50
)(1
1)(
IC
tI
IC
tItE
0* vSdt
dx
Steady-state ofmetabolite concentration
BACKGROUND. Systems Pharmacology aims to quantitatively study the dynamic interactions between drugs and biological systems by integrating modelsand data at different scales, to understand how the behaviour of individual constituents (modelled, e.g., via biological networks) and the behaviour of thewhole system (modelled, e.g., via PBPK models) mutually interact. The objective of this work is to present and discuss: how models at different scales canbe coupled; the types of data that can be used; the tools supporting the implementation; the practical research and drug development studies themodels were built for.
Methods and tools for multiscale modelling inSystems Pharmacology: a review
E. Borella, L. Carrara, S.M. Lavezzi, I. Massaiu, E. Sauta, E.M. Tosca, F. Vitali, S. Zucca,
L. Pasotti, G. De Nicolao, P. MagniBMS Lab, Department of Electrical, Computer and Biomedical Engineering, University of Pavia (Italy)
METHODOLOGY AND TOOLS. From literature three main methods for coupling PBPK models and biological networks were identified:Integration of genic information
as covariate in PBPK models parameters
Genic information is included as a covariate for tissue-specific transporter-activity. Here an example relative to SNP in OATP1B1 transporter is presented [J. Lippert, 2010].
Example of application:A PBPK model representing ADME genesinvolved in simvastatin and pravastatinmetabolism to predict the risk of myopathy inindividuals with specific genotype wasdeveloped [J. Lippert, 2010].
• PBPK models for simvastatin and pravastatinwere built for the reference homozygous TTgenotype using plasma data.
• PBPK models for the CC genotype were builtbased on the TT models by adjustingOATP1B1 transporter activity. PBPK modelfor the CT genotype uses the average of thetransporter activities.
CC TT
Other organs
GI tract
Kidney
Muscle
Blood
Liver cells
Bile
TTCC
cat
VVr
EKV
maxmax
0max
/
Tools:
OA
TP1
B1
Combination of PBPK and networks ODEs
As an illustrative example, asimple generic PBPK rat modelconsidering absorption,transport and excretion ofbenzene is shown [S.Cheng,2011]. Here, onlyinhalation is modelled.
The metabolism of the substance is described by thenetwork below.
Example of application:A joint PBPK model, including paracetamol PK combinedwith a network of GSH homeostasis, was developed tostudy candidate biomarkers of liver toxicity [S. Geenen,2010].
PBPK and network models are both represented by ODEs and the connection is provided by network exchange rates affecting the PBPK concentrations [F.Y. Bois, 2009].
The mass-balance equations of the network are coupledwith the PBPK model:
• Ophthalmic acid and 5-oxoproline were evaluated asbiomarkers to monitor GSH depletion toxicity.
• Some parameters are derived from literature, whileothers are estimated. The PBPK model well describesparacetamol concentration in plasma.
Tools:
Example of application:A multiscale PK/PD model is developed to study thetherapeutic effect of allopurinol in the treatment ofhyperuricemia [M. Krauss, 2012].
• PBPK models for allopurinol, oxypurinol and uricacid were built using physiological informationand plasma concentration data.
• Feedback coupling was used to study the effect ofdrug on xanthine oxidase in the hepatic metabolicnetwork. Maximization of uric acid productionwas considered as objective function.
• Model evaluation: comparison betweensimulation of uric acid and venous plasmaconcentration after a single dose of allopurinol.
= xanthine oxidase
AllopurinolPB-PK
OxypurinolPB-PK
Xanthine Uric AcidHypoxanthine
Uric acidPB-PK
Liver cell
Tools:
Coupling with dynamic Flux Balance Analysis
Metabolites, reactions and fluxes in a metabolicnetwork are represented by a stoichiometric matrixand a vector of fluxes [D. Orth, 2010].
Flux Balance Analysis (FBA) is a mathematicalapproach for calculating the unknown fluxes givena set of constraints and an objective function.
The PBPK model, represented by ODEs, can becoupled to the network via dynamic FBA by feed-forward (steps 1-3) or feed-back (steps 1-5)approach [M. Krauss, 2012].
(1) Update PBPK metabolization rate
from tissueconcentrations
(5) Simulate whole-body
concentrationsfor next time step
(3) Calculate flux distributionat cellular scale
(2) Use PBPK metabolizationrate as upper bound for FBA
(4) Use FBA uptakeas upstream PBPK
metabolization rate
FBA
PBPK
Benzene BenzeneOxide
Benzene
CYP2E1
CYP2E1
Complex
k1B
k2B
k3B
Liver cell
C inhaled C exhaled
Poorly perfused
Well perfused
Fat
Liver
Lungs
• Safety risk was evaluated to forecast the incidence rate in the CC subgroup population given the incidence rate of TT and TC subpopulations.
ODEs FBA Covariate
✔ • Mechanistic approach • Traditional solving methods
• Mechanistic approach• Enables genome-scale models• Easy estimation of network
parameters
• Easy implementation• Inclusion of genetic information
✖• Need for parameter values
and rescaling• Large-scale networks
implementation
• Jointly solving of ODEs and FBA • Non-mechanistic at cellular
level
CONCLUSIONS.• The PBPK-network combination with ODEs is
the most widely used approach.
• Computational tools have been proposed tofacilitate model coupling for the ODE andcovariate approaches; databases, e.g.,BioModels Database (EBI), JWS andSABIO-RK, are available to retrieve networksand their parameters.
• Multiscale modelling is a major challengein Systems Pharmacology, for whichguidelines are still missing. Efficientintegration of heterogeneous data, includinggenetic information, will greatly improve ourknowledge of the mechanisms underlyingcomplex diseases and drive new approachesfor drug discovery.
