Theory-informed experimental design for model identifiability: what needs to be measured?

www.leibniz-hki.de References PAIE PAE PKIE M1,1 N0,1 N1,1 N0,0 N1,0 N2,0 N0,2 M0,2 M0,0 M0,1 M2,0 M1,0 PAE ϕM ϕN ρ ρ κM κN … … … … … … … … Time-course measurement Theory-informed experimental design for model identifiability: what needs to be measured? Anastasia Solomatina1, Paul Rudolph1,2 , Sandra Timme1, Yann Bachelot1,2, Marc Thilo Figge1,3 1 Applied Systems Biology, Leibniz Institute for Natural Product Research and Infection Biology, Hans Knöll Institute (HKI), Jena, Germany 2 Faculty of Biological Sciences, Friedrich Schiller University, Jena, Germany 3 Institute of Microbiology, Faculty of Biological Sciences, Friedrich Schiller University, Jena, Germany [1] Hünniger et al. 2014. PLOS Comput Biol. 10(2) [2] Lehnert et al. 2021. Sci Rep. 11(1) [3] Lehnert et al. 2015. Front Microbiol. 6:608 [email protected] Abstract Conclusions and outlook Human whole-blood infection assay[1] anti-coagulated whole blood pathogen C.albicans Neutrophils Monocytes Phagocytosis Phagocytosis Phagocytosis Intracellular killing Intracellular killing Extracellular killing Immune escape Blood from healthy volunteers Clinical blood samples[2] • monitoring host-pathogen interactions •mimics the in vivo scenario of the innate response against pathogen •many variables are accessible to direct experimental quantification Statebased model Design of experiment Systems biology experiment model prediction •Approximate Bayesian computation (ABC) for parameter inference • Posterior parameter distributions as output M — Monocytes N — Neutrophils P — Pathogens — phagocytosis by Monocytes — killing by Monocytes — phagocytosis by Neutrophils — killing by Neutrophils — immune evasion by Pathogens — activity of antimicrobial peptides — decay of antimicrobial activity ϕM κM ϕN κN ρ κEK γ Conclusions and outlook Parameter estimation •Hyperparameters for ABC parameter inference: •prior •weighted distance function with weights [2]: •tolerance set to the mean variance of experimental data •Jensen-Shannon Divergence ( ) to quantify distributions: ∼U(0,1) ϵc E(p) = ∑ c ϵc 1 n∑ k (xexp k,c−xsim k,c(p))2 ε JSD JSD(P∥Q) = 1 2D(P∥M) + 1 2D(Q∥M), where M=1 2(P+Q), D(P∥Q) = ∑ x∈X P(x) log(P(x) Q(x)) prior distribution posterior distribution parameter values from Lehnert et al. 2015 [3] •Experimental & simulated data for parameter sets sampled from the posterior distributions JSD 0.913 0.884 0.969 0.140 0.147 0.088 0.116 ϕN ϕM ρ γ κN κM κEK •Posterior distributions compared to the prior ( ): 0≤JSD ≤1 • In systems biology, identifying model parameters can prove challenging, often due to high model complexity or insufficient experimental data. • Researchers frequently resort to reducing parameter space using literature-based values or selecting best-fit parameters despite significant variance in obtained distributions. • We present a framework aimed at guiding experimentalists in acquiring data that can reduce parameter uncertainty. • Leveraging Approximate Bayesian Computation, our approach incorporates both experimental and synthetically generated data to assess their impact on parameter distributions and data fitting. • The evaluation criteria encompass Jensen-Shannon Divergence to assess uncertainty in posterior parameter distributions. • We illustrate the power of our framework using whole-blood infection assay data, demonstrating that extremely limited measurements performed at adaptive times are capable to recover parameter distributions. JSD 9 data points (as in the experiment) 0.947 0.948 0.982 0.173 0.235 0.090 0.165 4 data points (equidistant) 0.425 0.567 0.817 0.098 0.100 0.079 0.097 4 data points (adaptive) 0.955 0.944 0.978 0.184 0.493 0.089 0.223 ϕN ϕM ρ γ κN κM κEK Posterior distributions compared to the prior: Equidistant data points Adaptive data points synthetic data Uncertainty: small medium large • Implementation of Approximate Bayesian Computation was used to explore the experimental design of the whole-blood infection assay. • Current experimental design with 9 measurement per variable results in narrow posterior distributions characterized by high Jensen-Shannon divergence for three parameters out of seven. Uncertainty: small large • Using synthetic data, we conducted an analysis of alternative experimental designs, examining the number of measurements per variable at various time intervals, including equidistant and adaptive approaches. •Adaptive time measurements in the whole-blood infection assay lead to a decreased number of measurements per variable while maintaining a consistent level of uncertainty within obtained distributions.