Royal Society International Seminar

February 15, 2017

Natal van RielEindhoven University of Technology | University of Amsterdam

Dept of Biomedical Engineering | Academic Medical Center

Systems Biology and Metabolic Diseases

n.a.w.v.riel@tue.nl

@nvanriel

Systems Biology and Metabolic Diseases

Metabolic Syndrome and

comorbidities

• A multifaceted, multi-scale

problem

– macro-models

– micro-models

• Models of metabolism and its

regulatory systems

• Models for science

(understanding)

• Computational diagnostics

2

Rask-Madsen et al. (2012) ArteriosclerThromb Vasc Biol, 32(9):2052-2059

Modelling in Systems Biology and Physiome

• Quantitative and Predictive Modelling

3

TOP-DOWN

BOTTOM-UP

…to whole organisms

and physiology

From molecules and pathways…

Data-driven (statistics)

Hypothesis –based (mechanistic modelling)

Physiology-based models of dynamic biological

systems

• Data-driven mechanistic models

• Physiological endpoints

4

Time-series data

Developing models of dynamic systems

Explaining the data & understanding the system

• Estimating models

• Identifying and implementing a set of constraints (at different levels

and scales – components, system behavior)

• Comparing alternative hypotheses (differences in model structure)

• Given a fixed model structure, find sets of parameter values that

yield a model that accurately describes empirical observations

5

^

arg min Deviation from Observations Penalty on FlexibilityModelClass

Model

Model complexity / granularity

Model parameterization

• Direct measurement of (kinetic) parameters of model components

• Taking numbers from the literature, including stitching together

(sub)components of existing models

• Testing model plausibility

• The ‘Frankenstein model’ as prior knowledge for parameter

identification

• Calibrating the model to in vivo / physiological data

6

Uncertainty

7

• Structural uncertainty resides in simplifications that are inherent

to the process of model building and assumptions that are made in

case the nature and / or kinetic details of certain interactions (e.g.

metabolic pathways, regulatory signals) are unknown or disputed

• Since model parameters are estimated by calibrating the model to

experimental data, uncertainty in the data (noise, errors) will

propagate into the parameter estimates, which subsequently will

limit the accuracy of the model predictions.

• E.g. in case of dietary intervention studies a source of uncertainty

originates from the fact that not all participants will be fully compliant.

Reducing bias while

controlling variance

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Bias - variance

• Networks impose strong constraints on system dynamics

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Rethinking Maximum Likelihood Estimation

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• The bias - variance trade-off is often reached for rather large bias

• Typically, we are far away from the asymptotic situation in which

Maximum Likelihood Estimation (MLE) provides the best possible

estimates

Room for more flexibility

• Instead of increasing structural complexity (increasing model size)

• Introduce more freedom in model parameters to compensate for bias

(‘undermodelling’) in the original model structure

• Increasing model flexibility using time-varying parameters

•ADAPTAnalysis of Dynamic Adaptations in Parameter Trajectories

11

Tiemann et al. (2011) BMC Syst Biol, 5:174Van Riel et al. (2013) Interface Focus 3(2): 20120084,Tiemann et al. (2013) PloS Comput Biol, 9(8):e1003166

Dynamical Systems Theory:

(Extended) Kalman Filter

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Parameter space

State space

.

initial condition

state trajectories

Data space

time-series

Output space

ensemble

parameter trajectories

13 Nyman 2016, Interface Focus 6: 20150075

Disease progression and treatment of T2DM

• 1 year follow-up of treatment-naïve T2DM patients (n=2408)

• 3 treatment arms: monotherapy with different hypoglycemic agents

– Pioglitazone – insulin sensitizer

• enhances peripheral glucose uptake

• reduces hepatic glucose production

– Metformin - insulin sensitizer

• decreases hepatic glucose production

– Gliclazide - insulin secretogogue

• stimulates insulin secretion by the pancreatic beta-cells

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FPG

[m

mo

l/L]

Schernthaner et al, Clin. Endocrinol. Metab. 89:6068–6076 (2004)Charbonnel et al, Diabetic Med. 22:399–405 (2004)

FPG: fasting plasma glucose

Glucose-insulin homeostasis model

• Pharmaco-Dynamic model

• 3 ODE’s, 15 parameters

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hepatic glucose production

glucose utilization

insulin secretion

glucose (FPG)

insulinsensitivity (S)

insulin (FSI)HbA1c

beta-cell function (B)

OHA(insulin sensitizer)

OHA(insulin secretagogue)

1 2

1 2

1 2

1

2

compensation phase: hyperinsulinemia

exhaustion phase: disease onset

treatment effects

De Winter et al. (2006) J PharmacokinetPharmcodyn, 33(3):313-343

FPG: fasting plasma glucoseFSI: fasting serum insulinHbA1c: glycosylated hemoglobin A1c

T2DM disease progression model

• Fixed parameters

• Adaptive changes in -cell function B(t) and insulin sensitivity S(t)

• Parameter trajectories

16Nyman et al, Interface Focus. 2016 Apr 6;6(2): 20150075

Reducing bias while controlling variance

• The common way to handle the flexibility constraint is to restrict /

broaden the model class

• If an explicit penalty is added, this is known as regularization

• In case of parameter estimation:

17

^

arg min Deviation from Observations Penalty on FlexibilityModelClass

Model

2ˆarg min ( ) ( )

r

r r r

Regularization of parameter trajectories

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[ ]

ˆ[ ] arg min Deviation from Data Penalty on Parameters Changes

n

n

r

r

• Shrinkage of changes in parameters values

• Selection of parameters that change

Assessing credibility of computational modeling

and simulation results

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Verification, validation and uncertainty quantification (VVUQ)

Verification Does the computational implementation solve the mathematical model

correctly?

» robust solvers for stiff nonlinear differential equations

Validation Does the mathematical model correctly represent the reality of

interest?

» plausibility, physiological realism (population level) - metabolic

physiology (e.g., post-prandial response dynamics)

» database of individual responses (quantitative resource)

Uncertainty Quantification What is the uncertainty in the inputs (e.g. parameter values, initial

conditions), and what is the resultant uncertainty in the model outputs?

» Maximum Likelihood Estimation, Bayesian inference, Profile

Likelihood Analysis (PLA), Prediction Uncertainty Analysis (PUA),

Global Sensitivity Analysis

Applicability How applicable is the validation evidence to support using the model

in the context of use?

» follow-up data after the intervention serve as validation of predictions

for each individual with his/her personalized model

Credibility Can the computational model make predictions that are reliable in the

context of use?

» platform to generate and test novel hypotheses

» Independent cohorts

» assess the effectiveness of interventions.

Uncertainty Quantification

20NCSB Workshop: Parameter Estimation and Uncertainty Analysis in Systems Biology,EURANDOM workshop “Parameter Estimation for Dynamical Systems“ (PEDS-II), 2012

Conclusions

• The network structure of the biological systems imposes strong

constraints on possible solutions of a model

• The bias - variance trade-off is often reached for rather large bias,

not favoring MLE

• Dynamic models, despite their size and complexity, are not always

flexible enough to correctly describe the data of biological systems

• Computational techniques to introduce more degrees of freedom in

models, but simultaneously enforcing sparsity if extra flexibility is not

required (ADAPT)

• Model estimation tools are complemented with ‘regularization’

methods to reduce the error (bias) in models without escalating

uncertainties (variance)

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• Fianne Sips

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Systems Biology of Disease Progression - ADAPT modelinghttp://www.youtube.com/watch?v=x54ysJDS7i8