The power of weak, transient interactions across biology: A paradigm of emergent behavior.

A growing list of diverse biological systems and their equally diverse functionalities provides realizations of a paradigm of emergent behavior. In each of these biological systems, pervasive ensembles of weak, short-lived, spatially local interactions act autonomously to convey functionalities at larger spatial and temporal scales. In this article, a range of diverse systems and functionalities are presented in a cursory manner with literature citations for further details. Then two systems and their properties are discussed in more detail: yeast chromosome biology and human respiratory mucus.

Dynamic balance of pro- and anti-inflammatory signals controls disease and limits pathology.

Immune responses to pathogens are complex and not well understood in many diseases, and this is especially true for infections by persistent pathogens. One mechanism that allows for long-term control of infection while also preventing an over-zealous inflammatory response from causing extensive tissue damage is for the immune system to balance pro- and anti-inflammatory cells and signals. This balance is dynamic and the immune system responds to cues from both host and pathogen, maintaining a steady state across multiple scales through continuous feedback. Identifying the signals, cells, cytokines, and other immune response factors that mediate this balance over time has been difficult using traditional research strategies. Computational modeling studies based on data from traditional systems can identify how this balance contributes to immunity. Here we provide evidence from both experimental and mathematical/computational studies to support the concept of a dynamic balance operating during persistent and other infection scenarios. We focus mainly on tuberculosis, currently the leading cause of death due to infectious disease in the world, and also provide evidence for other infections. A better understanding of the dynamically balanced immune response can help shape treatment strategies that utilize both drugs and host-directed therapies.

Transient crosslinking kinetics optimize gene cluster interactions.

Our understanding of how chromosomes structurally organize and dynamically interact has been revolutionized through the lens of long-chain polymer physics. Major protein contributors to chromosome structure and dynamics are condensin and cohesin that stochastically generate loops within and between chains, and entrap proximal strands of sister chromatids. In this paper, we explore the ability of transient, protein-mediated, gene-gene crosslinks to induce clusters of genes, thereby dynamic architecture, within the highly repeated ribosomal DNA that comprises the nucleolus of budding yeast. We implement three approaches: live cell microscopy; computational modeling of the full genome during G1 in budding yeast, exploring four decades of timescales for transient crosslinks between 5kbp domains (genes) in the nucleolus on Chromosome XII; and, temporal network models with automated community (cluster) detection algorithms applied to the full range of 4D modeling datasets. The data analysis tools detect and track gene clusters, their size, number, persistence time, and their plasticity (deformation). Of biological significance, our analysis reveals an optimal mean crosslink lifetime that promotes pairwise and cluster gene interactions through "flexible" clustering. In this state, large gene clusters self-assemble yet frequently interact (merge and separate), marked by gene exchanges between clusters, which in turn maximizes global gene interactions in the nucleolus. This regime stands between two limiting cases each with far less global gene interactions: with shorter crosslink lifetimes, "rigid" clustering emerges with clusters that interact infrequently; with longer crosslink lifetimes, there is a dissolution of clusters. These observations are compared with imaging experiments on a normal yeast strain and two condensin-modified mutant cell strains. We apply the same image analysis pipeline to the experimental and simulated datasets, providing support for the modeling predictions.

Enrichment of dynamic chromosomal crosslinks drive phase separation of the nucleolus.

Regions of highly repetitive DNA, such as those found in the nucleolus, show a self-organization that is marked by spatial segregation and frequent self-interaction. The mechanisms that underlie the sequestration of these sub-domains are largely unknown. Using a stochastic, bead-spring representation of chromatin in budding yeast, we find enrichment of protein-mediated, dynamic chromosomal cross-links recapitulates the segregation, morphology and self-interaction of the nucleolus. Rates and enrichment of dynamic crosslinking have profound consequences on domain morphology. Our model demonstrates the nucleolus is phase separated from other chromatin in the nucleus and predicts that multiple rDNA loci will form a single nucleolus independent of their location within the genome. Fluorescent labeling of budding yeast nucleoli with CDC14-GFP revealed that a split rDNA locus indeed forms a single nucleolus. We propose that nuclear sub-domains, such as the nucleolus, result from phase separations within the nucleus, which are driven by the enrichment of protein-mediated, dynamic chromosomal crosslinks.

Entropy gives rise to topologically associating domains.

We investigate chromosome organization within the nucleus using polymer models whose formulation is closely guided by experiments in live yeast cells. We employ bead-spring chromosome models together with loop formation within the chains and the presence of nuclear bodies to quantify the extent to which these mechanisms shape the topological landscape in the interphase nucleus. By investigating the genome as a dynamical system, we show that domains of high chromosomal interactions can arise solely from the polymeric nature of the chromosome arms due to entropic interactions and nuclear confinement. In this view, the role of bio-chemical related processes is to modulate and extend the duration of the interacting domains.

Polymer Modeling Reveals Interplay between Physical Properties of Chromosomal DNA and the Size and Distribution of Condensin-Based Chromatin Loops.

Transient DNA loops occur throughout the genome due to thermal fluctuations of DNA and the function of SMC complex proteins such as condensin and cohesin. Transient crosslinking within and between chromosomes and loop extrusion by SMCs have profound effects on high-order chromatin organization and exhibit specificity in cell type, cell cycle stage, and cellular environment. SMC complexes anchor one end to DNA with the other extending some distance and retracting to form a loop. How cells regulate loop sizes and how loops distribute along chromatin are emerging questions. To understand loop size regulation, we employed bead-spring polymer chain models of chromatin and the activity of an SMC complex on chromatin. Our study shows that (1) the stiffness of the chromatin polymer chain, (2) the tensile stiffness of chromatin crosslinking complexes such as condensin, and (3) the strength of the internal or external tethering of chromatin chains cooperatively dictate the loop size distribution and compaction volume of induced chromatin domains. When strong DNA tethers are invoked, loop size distributions are tuned by condensin stiffness. When DNA tethers are released, loop size distributions are tuned by chromatin stiffness. In this three-way interaction, the presence and strength of tethering unexpectedly dictates chromatin conformation within a topological domain.

Neutrophil Dynamics Affect Mycobacterium tuberculosis Granuloma Outcomes and Dissemination.

Neutrophil infiltration into tuberculous granulomas is often associated with higher bacteria loads and severe disease but the basis for this relationship is not well understood. To better elucidate the connection between neutrophils and pathology in primate systems, we paired data from experimental studies with our next generation computational model GranSim to identify neutrophil-related factors, including neutrophil recruitment, lifespan, and intracellular bacteria numbers, that drive granuloma-level outcomes. We predict mechanisms underlying spatial organization of neutrophils within granulomas and identify how neutrophils contribute to granuloma dissemination. We also performed virtual deletion and depletion of neutrophils within granulomas and found that neutrophils play a nuanced role in determining granuloma outcome, promoting uncontrolled bacterial growth in some and working to contain bacterial growth in others. Here, we present three key results: We show that neutrophils can facilitate local dissemination of granulomas and thereby enable the spread of infection. We suggest that neutrophils influence CFU burden during both innate and adaptive immune responses, implying that they may be targets for therapeutic interventions during later stages of infection. Further, through the use of uncertainty and sensitivity analyses, we predict which neutrophil processes drive granuloma severity and structure.

Global sensitivity analysis of biological multi-scale models.

Mathematical models of biological systems need to both reflect and manage the inherent complexities of biological phenomena. Through their versatility and ability to capture behavior at multiple scales, multi-scale models offer a valuable approach. Due to the typically nonlinear and stochastic nature of multi-scale models as well as unknown parameter values, various types of uncertainty are present; thus, effective assessment and quantification of such uncertainty through sensitivity analysis is important. In this review, we discuss global sensitivity analysis in the context of multi-scale and multi-compartment models and highlight its value in model development and analysis. We present an overview of sensitivity analysis methods, approaches for extending such methods to a multi-scale setting, and examples of how sensitivity analysis can inform model reduction. Through schematics and references to past work, we aim to emphasize the advantages and usefulness of such techniques.

The Role of Dimensionality in Understanding Granuloma Formation.

Within the first 2-3 months of a Mycobacterium tuberculosis (Mtb) infection, 2-4 mm spherical structures called granulomas develop in the lungs of the infected hosts. These are the hallmark of tuberculosis (TB) infection in humans and non-human primates. A cascade of immunological events occurs in the first 3 months of granuloma formation that likely shapes the outcome of the infection. Understanding the main mechanisms driving granuloma development and function is key to generating treatments and vaccines. In vitro, in vivo, and in silico studies have been performed in the past decades to address the complexity of granuloma dynamics. This study builds on our previous 2D spatio-temporal hybrid computational model of granuloma formation in TB (GranSim) and presents for the first time a more realistic 3D implementation. We use uncertainty and sensitivity analysis techniques to calibrate the new 3D resolution to non-human primate (NHP) experimental data on bacterial levels per granuloma during the first 100 days post infection. Due to the large computational cost associated with running a 3D agent-based model, our major goal is to assess to what extent 2D and 3D simulations differ in predictions for TB granulomas and what can be learned in the context of 3D that is missed in 2D. Our findings suggest that in terms of major mechanisms driving bacterial burden, 2D and 3D models return very similar results. For example, Mtb growth rates and molecular regulation mechanisms are very important both in 2D and 3D, as are cellular movement and modulation of cell recruitment. The main difference we found was that the 3D model is less affected by crowding when cellular recruitment and movement of cells are increased. Overall, we conclude that the use of a 2D resolution in GranSim is warranted when large scale pilot runs are to be performed and if the goal is to determine major mechanisms driving infection outcome (e.g., bacterial load). To comprehensively compare the roles of model dimensionality, further tests and experimental data will be needed to expand our conclusions to molecular scale dynamics and multi-scale resolutions.