Schedule for: 21w5005 - Connecting Network Structure to its Dynamics: Fantasy or Reality? (Online)

To understand the progression from stem cells to differentiated tissues we are exploiting the simplifying aspects of root development. We have developed new experimental, analytical and imaging methods to identify networks functioning within different cell types and developmental stages of the root. We are particularly interested in a subnetwork that regulates a key asymmetric cell division of a stem cell. To quantify dynamic aspects of these networks, we are employing light-sheet and confocal microscopy to image accumulation of their different components. Analysis of the resulting time series indicated that our previous model was not predictive of actual behavior and a new model was needed. How roots explore their soil environment determines their ability to acquire nutrients and water. We have identified the molecular mechanism underlying the circular movement of the root tip known as circumnutation. In collaboration with Dan Goldman (Physics, Georgia Tech) and Elliot Hawkes (Engineering, UC Santa Barbara) we have shown that circumnutation facilitates the root’s ability to avoid obstacles. We are now using discrete element modeling to develop simulations of circumnutation that predict actual root behavior.

At the crossroad between biology and computational modelling, systems biology has proved to be an important ally to gain a mechanistic understanding of biological systems. But as our knowledge accumulates, the size and complexity of mathematical models increase, calling for the development of efficient dynamical analysis methods. In this respect, we use generic computational techniques to assess the behaviour of complex cellular network models. A first approach, called "model verification", enables the formalisation and the automated verification of validation criteria for whole models or selected subparts, thereby greatly facilitating model development. A second approach, called "value propagation", enables the computation of the impact of specific environmental or genetic conditions on model dynamics. Both methods were applied to the analysis of a comphrehensive Boolean model for T cell activation to compare the impacts of two different checkpoint inhibitors currently used in immunotherapies. These methods and models are available in the CoLoMoTo Docker image, which provides a reproducible modelling environment, and in an interactive companion notebook.

Mammalian cells assume different phenotypes that can have drastically different morphology and gene expression patterns, and can change between distinct phenotypes when subject to specific stimulation and microenvironment. Recent advances in snapshot single cell techniques further catalyze an emerging field of studying cell phenotypic transition (CPT) regulation and dynamics as one of the most exciting frontiers of cell and developmental biology. Mathematically a stable cell phenotype corresponds to a stable attractor in a multi-dimensional state space. How does a cell destabilize its original phenotype and relax to a new attractor? Is it a critical state transition such as pitchfork bifurcation or saddle-node bifurcation? Can we actually follow the transition dynamics experimentally? Here I will share our recent efforts on addressing this fundamental question through live cell imaging/single cell genomics studies and analyzing the data in the context of dynamical systems theory, esp. the transition path theory.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

We seek to model life in the 4th dimension, through time, and most specifically through the course of a circadian day. All circadian clocks are based on negative feedback loops that close within the confines of single cells. Evolution has delivered three distinct regulatory architectures for such clocks, from cyanobacteria, from plants, and from fungi and animals. In the latter of these, heterodimeric transcription factors (WC-1/WC-2 in Neurospora, BMAL1/CLOCK in mammals) drive expression of genes encoding “Negative Arm” proteins which, in complex with other proteins, bring kinases to the heterodimer leading to its inactivation. Gradual phosphorylation of the Negative Arm protein(s) leads to their inactivation; the heterodimer restarts the cycle. Models differ in the role(s) of phosphorylation and protein turnover, and many details are lacking. Core circadian oscillators with nearly identical regulatory architecture operate in most cells of mammals and in Neurospora, but the cell-type-specific biology for which these clocks are used is dictated by the spectrum of outputs. In fungi and animals, the principal initial means of output is through clock control of transcription. In Neurospora the oscillator results in rhythmic WC-1/WC-2 activity that in turn drives rhythms in expression of about 40% of the genome; in broad terms, daytime metabolic potential favors catabolism, energy production, and precursor assembly whereas night activities favor biosynthesis of cellular components and growth. Over 50 transcription factors have been epitope tagged and used for ChIP (chromatin immunoprecipitation) at multiple times after exposure to light or across the circadian day. These data are being used to assemble the hierarchical transcriptional network governing light and clock regulation. WC-1/WC-2 sits on top of the networks governing both light and clock regulation, controlling light- and clock-regulated transcription factors (TFs) that act as second order regulators, transducing regulation from light-responses, or from the core circadian oscillator, to banks of output clock-controlled genes (ccgs) including other TFs. Understanding the basic cell and molecular biology of Neurospora provides the foundational context in which productive modeling of circadian output can take place.

Circadian rhythms are highly conserved, roughly 24-hour, physiological cycles that, through the ideal programming of behavior, are believed to enhance fitness by ensuring organismal functions are optimally synchronized with the appropriate phase of the circadian day. Disruption of proper circadian timing negatively impacts the human long-term medical outlook and organismal fitness. Circadian rhythms are controlled via a highly regulated transcription-translation based negative feedback loop, or clock. The current paradigm for clock regulation over cellular physiology is that transcriptional activity from the positive arm of the transcription– translation negative feedback loop drives the expression of a host of gene promoters that modulate organismal behavior. However, mounting evidence suggests that circadian regulation is imparted on cellular physiology beyond the level of transcription. We have analyzed the clock output on many levels in Neurospora crassa and murine macrophages over circadian time, demonstrating evidence for extensive post-transcriptional regulation of metabolism and the immune response, both in vitro and in vivo. The next goal of this work is to model the measured output to predict functional results in a more directed manner.

We present DSGRN (Dynamics Signatures Generated by Regulatory Networks) which is a mathematically rigorous and computationally efficient method to describe the global dynamics of a regulatory network over all parameter values. In this talk we will describe the details of DSGRN and discuss how it can be used to rank all 3-node networks according to how well they can act as a robust bi-stable switch.

A defining feature of cell growth is that protein and mRNA amounts scale with cell size so that concentrations remain approximately constant, thereby ensuring similar reaction rates and efficient biosynthesis. A key component of this biosynthetic scaling is the scaling of mRNA amounts with cell size, which occurs even among cells with the same DNA template copy number. Here, we identify RNA polymerase II as a major limiting factor increasing transcription with cell size. Other components of the transcriptional machinery are only minimally limiting and the chromatin environment is largely invariant with size. However, RNA polymerase II activity does not increase in direct proportion to cell size, inconsistent with previously proposed DNA-titration models. Instead, our data support a dynamic equilibrium model where the rate of polymerase loading is proportional to the unengaged nuclear polymerase concentration. This sublinear transcriptional increase is then balanced by a compensatory increase in mRNA stability as cells get larger. Taken together, our results show how limiting RNA polymerase II and feedback on mRNA stability work in concert to ensure the precise scaling of mRNA amounts across the physiological cell size range.

In his new book 'What Is Life,' Paul Nurse describes five 'great ideas' in biology; the fifth is 'Life is Information'. In this lecture I will discuss some of the molecular mechanisms that process information in living cells, with focus on regulation of the cell division cycle. I will show how dynamical systems theory, especially bifurcation diagrams, can be used to understand the biochemical networks that control cell growth and division. I will present a 'dynamical paradigm for molecular systems biology' and what it implies for future research and education in the field.

Time series transcriptomics and proteomics data typically record expression levels of thousands of gene products. Discovering the important elements of these data for a specific experimental question is daunting given the combinatorial nature of the problem. Myself and my collaborators take the approach that a sequential set of software tools can reduce hypothesis space tremendously. I will discuss the performance of a set of tools that aims to discover “core oscillators” or clock-like genetic networks that control highly stereotyped cellular phenomena such as the cell cycle and the circadian rhythm. We first reduce the space of potential gene products from thousands to tens, then the space of possible interactions from hundreds to tens, and then we refine this collection of interactions by considering global network dynamics and reducing network space from a factorial down to tens or hundreds again. The first two steps are exhaustive but the last depends on local sampling around an initial guess. We show that this set of software tools is in principle capable of finding core oscillator interactions from high-dimensional data, although sometimes the results are surprising and hard to quantify.

Natural biological networks remain a vastly untapped reservoir of biological control mechanisms and biochemical sensors. Rather than relying on literature surveys to mine new biological function, I introduce a data-driven approach to discovering biological sensors from kinetic transcriptomics data. The approach couples operator-theoretic methods and spectral analysis with classical measures of observability, but requires adaptation when treating experimental biological data. I then show how a broader class of these data-driven mathematical methods can be used to inform design of novel biological networks, to approximate arbitrary user-defined specifications on desired network behavior. I will present both theoretical motivation and experimental validation of most of these ideas.

My group is using network science and discrete dynamic modeling to understand the emergent properties of biological systems at multiple levels of organization. As an example, we think of cell types as attractors of a dynamic system of interacting (macro)molecules, and we aim to find the network patterns that determine these attractors. We use the accumulated knowledge gained from specific models to draw general conclusions that connect a network's structure and dynamics. An example of such a general connection is our identification of stable motifs, which are self-sustaining cyclic structures that determine trap subspaces of the system’s state space. If the system's trajectory enters such a subspace, it cannot exit unless specific control is exerted on the nodes of the respective stable motif. We have shown that control of stable motifs can guide the system into a desired attractor. We implemented the methodologies of stable motif based attractor identification and control in Boolean systems in a new software library called pystablemotifs. We have translated the concept of stable motif to a broad class of continuous (ODE-based) models. I propose that the concept of stable motifs could be used to guide the mapping between network structure and dynamics. Representative references: 1. JC Rozum, R Albert, Identifying (un)controllable dynamical behavior in complex networks, PLOS Computational Biology 14, e1006630 (2018). 2. JC Rozum, JGT Zanudo, X Gan, D Deritei, R Albert, Parity and time reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks, Science Advances 7 (29), eabf8124 (2021).

In this talk, we will see frameworks to study the problem of predicting dynamics from network structure and the problem of inferring network structure from dynamics. To infer dynamical properties of a system from its structure, we use the topological features of the network such as the way subnetworks are connected, and then use a version of the inclusion-exclusion principle on dynamics. To infer the structure of a network from its dynamics, we encode all possible networks that fit the given dynamics as an ideal of polynomials and then use tools from algebraic geometry to find the most likely networks.

My research in Biochemical Systems Theory in collaboration with colleagues has shown that the architecture of mechanistic models can predict numerous properties within and among biochemical phenotypes without knowledge of the underlying biochemical kinetic parameters. In the past decade, this research led to the development of a novel phenotype-centric modeling strategy with several advantages beyond those of the conventional simulation-centric approach. Here I report on work done in collaboration with Miguel Valderrama-Gómez aimed at extending the phenotype-centric approach to address one of the most fundamental problems in population genetics and evolution: predicting the distribution of phenotype diversity generated by mutation and made available for innovation by selection. I show that minimal knowledge of the molecular system allows prediction of phenotype-specific mutation rate constants and equilibrium distributions of phenotype diversity in populations undergoing steady-state exponential growth. As a proof-of-principle, I provide a case study involving a small molecular system, a primordial circadian clock, and suggest experimental approaches for testing the theory.

Modeling cells has many challenges: data is sparse, noisy, and measured over a population instead of over individuals or cell compartments. Moreover, parameters needed to build kinetic and thermodynamic models are extremely labor intensive to obtain. This makes building a physics-based model a very hard problem. We address this challenge by taking advantage of the fact that natural selection selects for the most optimal individuals out of all solutions. We formulate fitness from a thermodynamic perspective to obtain the most likely model parameters, and then use data to constrain the solution space. Rate parameters that are reasonable and statistically the most likely can be inferred in this way. Then we predict regulation of the cellular system using one of two approaches: Assuming that we have an optimal control problem and using control theory to infer regulation, or widely sample the solution space for regulation using reinforcement learning. The result is a model with reasonable parameters and predicts regulation for central metabolism that agrees with the literature.

Dynamic cellular processes such as differentiation are driven by changes in the abundances of transcription factors (TFs). However, despite years of studies, our knowledge about the protein copy number of TFs in the nucleus is limited. We developed a quantitative targeted mass spectrometry approach that allowed us to determine the absolute abundances of 103 TFs and co-factors during the course of human erythropoiesis, providing a dynamic and quantitative scale for TFs in the nucleus. Furthermore, we established the first gene regulatory network of erythropoietic cell fate commitment that integrates temporal protein stoichiometry data with mRNA measurements. The model revealed quantitative imbalances in TFs' cross-antagonistic relationships underlying lineage determination. We also made the surprising discovery that, in the nucleus, co-repressors are dramatically more abundant than co-activators at the protein level, but not at the RNA level, with profound implications for understanding transcriptional regulation.