Maximum Entropy Framework For Inference Of Cell Population Heterogeneity In Signaling Networks

Abstract

Predictive models of signaling networks are essential tools for understanding cell population heterogeneity and designing rational interventions in disease. However, using network models to predict signaling dynamics heterogeneity is often challenging due to the extensive variability of signaling parameters across cell populations. Here, we describe a Maximum Entropy-based fRamework for Inference of heterogeneity in Dynamics of sIgAling Networks (MERIDIAN). MERIDIAN allows us to estimate the joint probability distribution over signaling parameters that is consistent with experimentally observed cell-to-cell variability in abundances of network species. We apply the developed approach to investigate the heterogeneity in the signaling network activated by the epidermal growth factor (EGF) and leading to phosphorylation of protein kinase B (Akt). Using the inferred parameter distribution, we also predict heterogeneity of phosphorylated Akt levels and the distribution of EGF receptor abundance hours after EGF stimulation. We discuss how MERIDIAN can be generalized and applied to problems beyond modeling of heterogeneous signaling dynamics.

A Monte Carlo method to estimate cell population heterogeneity

“…81 Here, we suppose heterogeneity in quantities of interest across cells is 82 generated by idiosyncratic variation in the rates of cellular processes. The 83 modelling approach we follow is similar to that of [12] and is based on an 84 ODE framework. In our model, each cell evolves according to an ODE, with 85 its progression directed by parameters whose value varies between cells.…”

“…These experimental methods are all, however, destructive, 105 meaning individual cells are sacrificed during measurement, and observa-106 tions at each time point hence represent "snapshots" of the underlying 107 population [15]. These snapshots can be described by histograms [12] or 108 density functions [9] fit to measurements of quantities of interest. Since 109 HODEs assume the state of each cell evolves continuously over time, exper-110 imental data tracing individual cell trajectories through time constitutes 111 a richer data resource.…”

“…The 124 count of cells in experiments typically exceeds ∼ 10 4 [15], so approaches 125 where the computational burden scales with this count are usually infeasi-126 ble. To avoid this burden, some approaches fit probability densities to raw 127 snapshot data and use these densities, rather than raw data, for estima-128 tion [12,15,18,19]. We follow this approach here.…”

“…It also does not require the number 154 of cell clusters be chosen beforehand, rather, subpopulations emerge as 155 modes in the posterior parameter distributions. Like [19], CMC can fit 156 multivariate snapshot data and unlike [12], does not use discrete bins to 157 model continuous data. As more experimental techniques elucidating single 158 cell behaviour are developed, interest in models describing measurement 159 snapshots should follow.…”

“…The goal of inference is to characterise the probability distribution p(θ|Y ) 208 representing heterogeneity in cellular processes. The numbers of cells 209 sampled in typical experimental setups is large, and, following previous work, 210 we represent snapshot data Y using probability distributions [12,15,18,19]. 211 In the first step of our workflow (Figure 4(i)), these distributions are 212 approximated by a kernel density model, with support over the space of 213 the QOI vector, q ∈ R m .…”