Supplementary Materials for Elucidating cellular population dynamics by molecular density function perturbations 1 2,3, Thanneer Malai Perumal and Rudiyanto Gunawan * 1 Sage Bionetworks, Seattle, Washington, USA;
[email protected] 2 Institute for Chemical and Bioengineering, ETH Zurich, Zurich, Switzerland;
[email protected] 3 Swiss Institute of Bioinformatics, Lausanne, Switzerland * Correspondence:
[email protected]; Tel.: +41-44-633-2134 Supplementary Material S1. Probability Distance Metrics Signed Engineering Metric: ∞ 2 ∆ (f A (t, x )||f B (t, x )) = sign(∆μ ) ∫ (x f A (t, x ) − x f B (t, x )) dx (S. 1) E Xi i Xi i Xi i Xi i i Xi i i −∞ Signed Jeffrey Divergence: ∞ f A (t,x ) A B A B Xi i ∆ (f (t, x )||f (t, x )) = sgn(∆μ ) ∫ (f (t, x ) − f (t, x ))ln ( B ) )dx (S. 2) JD Xi i Xi i Xi Xi i Xi i f (t,x ) i −∞ Xi i Signed Kullback-Leibler Distance: ∞ f B (t,x ) A B B Xi i ∆ (f (t, x )||f (t, x )) = sgn(∆μ ) ∫ f (t, x )ln ( A ) dx (S. 3) KLD Xi i Xi i Xi Xi i f (t,x ) i −∞ Xi i Signed Jensen-Shannon Divergence: f + (t,x )+f − (t,x ) Xi i Xi i ∆ f (t, x ) = sgn(∆μ ) (S. 4) JSD Xi i Xi 2 Signed Kolmogorov-Smirnov Metric: ∆ (f A (t, x )||f B (t, x )) = sgn(∆μ )sup|F A (t, x ) − F B (t, x )| (S. 5) KS Xi i Xi i Xi Xi i Xi i Supplementary Material S2.