Single-Molecule Approaches to Study DNA Condensation.

Proteins drive genome compartmentalization across different length scales. While the identities of these proteins have been well-studied, the physical mechanisms that drive genome organization have remained largely elusive. Studying these mechanisms is challenging owing to a lack of methodologies to parametrize physical models in cellular contexts. Furthermore, because of the complex, entangled, and dense nature of chromatin, conventional live imaging approaches often lack the spatial resolution to dissect these principles. In this chapter, we will describe how to image the interactions of λ-DNA with proteins under purified and cytoplasmic conditions. First, we will outline how to prepare biotinylated DNA, functionalize coverslips with biotin-conjugated poly-ethylene glycol (PEG), and assemble DNA microchannels compatible for the imaging of protein-DNA interactions using total internal fluorescence microscopy. Then we will describe experimental methods to image protein-DNA interactions in vitro and DNA loop extrusion using Xenopus laevis egg extracts.

PARP1-DNA co-condensation drives DNA repair site assembly to prevent disjunction of broken DNA ends.

DNA double-strand breaks (DSBs) are repaired at DSB sites. How DSB sites assemble and how broken DNA is prevented from separating is not understood. Here we uncover that the synapsis of broken DNA is mediated by the DSB sensor protein poly(ADP-ribose) (PAR) polymerase 1 (PARP1). Using bottom-up biochemistry, we reconstitute functional DSB sites and show that DSB sites form through co-condensation of PARP1 multimers with DNA. The co-condensates exert mechanical forces to keep DNA ends together and become enzymatically active for PAR synthesis. PARylation promotes release of PARP1 from DNA ends and the recruitment of effectors, such as Fused in Sarcoma, which stabilizes broken DNA ends against separation, revealing a finely orchestrated order of events that primes broken DNA for repair. We provide a comprehensive model for the hierarchical assembly of DSB condensates to explain DNA end synapsis and the recruitment of effector proteins for DNA damage repair.

Cohesin and condensin extrude DNA loops in a cell cycle-dependent manner.

Loop extrusion by structural maintenance of chromosomes (SMC) complexes has been proposed as a mechanism to organize chromatin in interphase and metaphase. However, the requirements for chromatin organization in these cell cycle phases are different, and it is unknown whether loop extrusion dynamics and the complexes that extrude DNA also differ. Here, we used Xenopus egg extracts to reconstitute and image loop extrusion of single DNA molecules during the cell cycle. We show that loops form in both metaphase and interphase, but with distinct dynamic properties. Condensin extrudes DNA loops non-symmetrically in metaphase, whereas cohesin extrudes loops symmetrically in interphase. Our data show that loop extrusion is a general mechanism underlying DNA organization, with dynamic and structural properties that are biochemically regulated during the cell cycle.

Predicting the onset of period-doubling bifurcations in noisy cardiac systems.

Biological, physical, and social systems often display qualitative changes in dynamics. Developing early warning signals to predict the onset of these transitions is an important goal. The current work is motivated by transitions of cardiac rhythms, where the appearance of alternating features in the timing of cardiac events is often a precursor to the initiation of serious cardiac arrhythmias. We treat embryonic chick cardiac cells with a potassium channel blocker, which leads to the initiation of alternating rhythms. We associate this transition with a mathematical instability, called a period-doubling bifurcation, in a model of the cardiac cells. Period-doubling bifurcations have been linked to the onset of abnormal alternating cardiac rhythms, which have been implicated in cardiac arrhythmias such as T-wave alternans and various tachycardias. Theory predicts that in the neighborhood of the transition, the system's dynamics slow down, leading to noise amplification and the manifestation of oscillations in the autocorrelation function. Examining the aggregates' interbeat intervals, we observe the oscillations in the autocorrelation function and noise amplification preceding the bifurcation. We analyze plots--termed return maps--that relate the current interbeat interval with the following interbeat interval. Based on these plots, we develop a quantitative measure using the slope of the return map to assess how close the system is to the bifurcation. Furthermore, the slope of the return map and the lag-1 autocorrelation coefficient are equal. Our results suggest that the slope and the lag-1 autocorrelation coefficient represent quantitative measures to predict the onset of abnormal alternating cardiac rhythms.

Computational study of synchrony in fields and microclusters of ephaptically coupled neurons.

Neuronal hypersynchrony is implicated in epilepsy and other diseases. The low-frequency, spatially averaged electric fields from many thousands of neurons have been shown to promote synchrony. It remains unclear whether highly transient, spatially localized electric fields from single action potentials (ephaptic coupling) significantly affect spike timing of neighboring cells and in consequence, population synchrony. In this study, we simulated the extracellular potentials and the resulting coupling between neurons in the NEURON environment and generalized their connection rules to create an oscillator network model of a sheet of ephaptically coupled neurons. With the use of both models, we explained several aspects of epileptiform behavior not previously modeled by synaptically coupled networks. Importantly, reduction of neuron spacing induced synchronization via single-spike ephaptic coupling, agreeing with seizure suppression seen clinically and in vitro via extracellular volume adjustment. Further reduction of neuron spacing yielded locally synchronized clusters, providing a mechanism for recent in vitro observations of localized neuronal synchrony in the absence of synaptic and gap-junction coupling.

Spatial symmetry breaking determines spiral wave chirality.

Chirality represents a fundamental property of spiral waves. Introducing obstacles into cardiac monolayers leads to the initiation of clockwise-rotating, counterclockwise-rotating, and pairs of spiral waves. Simulations show that the precise location of the obstacle and the pacing frequency determine spiral wave chirality. Instabilities predicted by curves relating the action potential duration and the pacing frequency at different spatial locations predict sites of wave break initiation and, hence, spiral wave chirality.

Vitamin D receptor as a master regulator of the c-MYC/MXD1 network.

Vitamin D signaling regulates cell proliferation and differentiation, and epidemiological data suggest that it functions as a cancer chemopreventive agent, although the underlying mechanisms are poorly understood. Vitamin D signaling can suppress expression of genes regulated by c-MYC, a transcription factor that controls epidermal differentiation and cell proliferation and whose activity is frequently elevated in cancer. We show through cell- and animal-based studies and mathematical modeling that hormonal 1,25-dihydroxyvitamin D (1,25D) and the vitamin D receptor (VDR) profoundly alter, through multiple mechanisms, the balance in function of c-MYC and its antagonist the transcriptional repressor MAD1/MXD1. 1,25D inhibited transcription of c-MYC-regulated genes in vitro, and topical 1,25D suppressed expression of c-MYC and its target setd8 in mouse skin, whereas MXD1 levels increased. 1,25D inhibited MYC gene expression and accelerated its protein turnover. In contrast, it enhanced MXD1 expression and stability, dramatically altering ratios of DNA-bound c-MYC and MXD1. Remarkably, F-box protein FBW7, an E3-ubiquitin ligase, controlled stability of both arms of the c-MYC/MXD1 push-pull network, and FBW7 ablation attenuated 1,25D regulation of c-MYC and MXD1 turnover. Additionally, c-MYC expression increased upon VDR knockdown, an effect abrogated by ablation of MYC regulator ß-catenin. c-MYC levels were widely elevated in vdr(-/-) mice, including in intestinal epithelium, where hyperproliferation has been reported, and in skin epithelia, where phenotypes of VDR-deficient mice and those overexpressing epidermal c-MYC are similar. Thus, 1,25D and the VDR regulate the c-MYC/MXD1 network to suppress c-MYC function, providing a molecular basis for cancer preventive actions of vitamin D.

Chaotic dynamics in cardiac aggregates induced by potassium channel block.

Chaotic rhythms in deterministic models can arise as a consequence of changes in model parameters. We carried out experimental studies in which we induced a variety of complex rhythms in aggregates of embryonic chick cardiac cells using E-4031 (1.0-2.5 µM), a drug that blocks the hERG potassium channel. Following the addition of the drug, the regular rhythm evolved to display a spectrum of complex dynamics: irregular rhythms, bursting oscillations, doublets, and accelerated rhythms. The interbeat intervals of the irregular rhythms can be described by one-dimensional return maps consistent with chaotic dynamics. A Hodgkin-Huxley-style cardiac ionic model captured the different types of complex dynamics following blockage of the hERG mediated potassium current.

Tunable oscillations and chaotic dynamics in systems with localized synthesis.

Biological systems contain biochemical control networks that reside within a remarkable spatial structure. We present a theoretical study of a biological system in which two chemically coupled species, an activating species and an inhibiting species forming a negative feedback, are synthesized at unique sites and interact with each other through diffusion. The dynamical behaviors in these systems depend on the spatial locations of these synthetic sites. In a negative feedback system with two sites, we find two dynamical modes: fixed point and stable oscillations whose frequency can be tuned by varying the distance between the sites. When there are multiple synthetic sites, we find more diverse dynamics, including chaos, quasiperiodicity, and bistability. Based on this theoretical analysis, it should be possible to create in the laboratory synthetic circuits displaying these dynamics. This study illustrates the concept of "spatial switching," in which bifurcations in the dynamics occur as a function of the geometry of the system.