Data-Guided Controllability: Learning from the Human Genome

We develop a framework for the control of dynamical systems that we know very little about. From limited, high-dimensional data observations, we approximate the natural dynamics of the system and investigate the controllability of the identified equations. The linear discrete-time-invariant model identification is done using dynamic mode decomposition (DMD), which is motivated by Koopman operator theory and can capture, from data, underlying nonlinear coherent structures. Viewing the identified linear model as a network, we propose three “control evaluations” to recommend intelligent control placements for steering the system to a specific target. The motivating application for this work is the control of genetic networks, in the context of cell reprogramming. We show that our targeted control evaluations identify known cell reprogramming strategies better than existing, general control metrics. Our framework is a first step toward using mathematics, guided by data, to control the genome. When the governing equations of a dynamical system are known or can be well approximated, there are effective methods to study the controllability of that system. However, data limitations in complex dynamical systems that are difficult or resource-intensive to observe make it challenging to generate adequate governing equations. Biological systems in particular have limited data, thus it has been difficult to acquire insight into controllability. The motivating application and focus for this work is the control of genetic networks, specifically in the context of cell reprogramming. While it is generally accepted that the human genome is a dynamical system [1, 2], the dynamic properties of the genome are little understood, despite increasingly advanced technologies and assays (e.g. RNA-seq, ChIP-seq, Hi-C). Nevertheless, Weintraub et al. demonstrated control over that system with the reprogramming of fibroblasts (FIB) into muscle cells via the introduction of a single transcription factor, MyoD [3]. In addition, Yamanaka et al. (2007) successfully reprogrammed a human FIB into an induced pluripotent stem cell (iPSC). With information regarding merely the initial state (FIB) and the desired final state (embryonic stem cell, ESC), Yamanaka and colleagues predicted and determined experimentally that the system can be driven from one cell type to another using just the four transcription factors OCT4, SOX2, KLF4, and MYC (all four abbreviated OSKM). In the same spirit, our aim is to formalize and validate mathematically the findings of Yamanaka. Using function (RNA-seq) and form (Hi-C) data, as well as binding location data for 222 transcription factors (TFs), our goal is to recommend mathematically which TFs are the best candidates to reprogram FIB into another cell type. More generally, we present methodology for making inferences about the controllability of a dynamical system with respect to a specific target, and when the precise dynamic equations are unknown and only minimal data is available. We present the proposed framework in a general context, followed by the application to controlling genetic networks. We show that ...