Inferring a network from dynamical signals at its nodes

The maximum entropy principle for compositional data

BACKGROUND

Compositional systems, represented as parts of some whole, are ubiquitous. They encompass the abundances of proteins in a cell, the distribution of organisms in nature, and the stoichiometry of the most basic chemical reactions. Thus, a central goal is to understand how such processes emerge from the behaviors of their components and their pairwise interactions. Such a study, however, is challenging for two key reasons. Firstly, such systems are complex and depend, often stochastically, on their constituent parts. Secondly, the data lie on a simplex which influences their correlations.

RESULTS

To resolve both of these issues, we provide a general and data-driven modeling tool for compositional systems called Compositional Maximum Entropy (CME). By integrating the prior geometric structure of compositions with sample-specific information, CME infers the underlying multivariate relationships between the constituent components. We provide two proofs of principle. First, we measure the relative abundances of different bacteria and infer how they interact. Second, we show that our method outperforms a common alternative for the extraction of gene-gene interactions in triple-negative breast cancer.

CONCLUSIONS

CME provides novel and biologically-intuitive insights and is promising as a comprehensive quantitative framework for compositional data.

Quantifying biochemical reaction rates from static population variability within incompletely observed complex networks

Quantifying biochemical reaction rates within complex cellular processes remains a key challenge of systems biology even as high-throughput single-cell data have become available to characterize snapshots of population variability. That is because complex systems with stochastic and non-linear interactions are difficult to analyze when not all components can be observed simultaneously and systems cannot be followed over time. Instead of using descriptive statistical models, we show that incompletely specified mechanistic models can be used to translate qualitative knowledge of interactions into reaction rate functions from covariability data between pairs of components. This promises to turn a globally intractable problem into a sequence of solvable inference problems to quantify complex interaction networks from incomplete snapshots of their stochastic fluctuations.

SiGMoiD: A super-statistical generative model for binary data

In modern computational biology, there is great interest in building probabilistic models to describe collections of a large number of co-varying binary variables. However, current approaches to build generative models rely on modelers’ identification of constraints and are computationally expensive to infer when the number of variables is large (N~100). Here, we address both these issues with Super-statistical Generative Model for binary Data (SiGMoiD). SiGMoiD is a maximum entropy-based framework where we imagine the data as arising from super-statistical system; individual binary variables in a given sample are coupled to the same ‘bath’ whose intensive variables vary from sample to sample. Importantly, unlike standard maximum entropy approaches where modeler specifies the constraints, the SiGMoiD algorithm infers them directly from the data. Due to this optimal choice of constraints, SiGMoiD allows us to model collections of a very large number (N>1000) of binary variables. Finally, SiGMoiD offers a reduced dimensional description of the data, allowing us to identify clusters of similar data points as well as binary variables. We illustrate the versatility of SiGMoiD using multiple datasets spanning several time- and length-scales.

Collectively varying binary variables are ubiquitous in modern biology. Given that the number of possible configurations of these systems typically far exceeds the number of available samples, generative models have become an essential tool in quantitative descriptions of binary data. The state-of-the-art approaches to build generative models have several conceptual limitations. Specifically, they rely on the modeler choosing system-appropriate constraints, which can be challenging in systems with many complex interactions. Moreover, they are computationally expensive to infer when the number of variables is large (N~100). To address this issue, we propose a theoretical generalization of the maximum entropy approach that allows us to model very high dimensional data; at least an order of magnitude higher than what is currently possible. This framework will be a significant advancement in the computational analysis of covarying binary variables.