Jane Kondev

The logic of RNA-based silencing involves nascent RNA molecules that serve as scaffolds to recruit proteins that repress transcription. Despite transcription and silencing being antagonistic, RNA-based recruitment mechanisms have been widely adopted in organisms ranging from yeast to humans. In fission yeast ( Schizosaccharomyces pombe ), the nuclear RNAi pathway that establishes heterochromatin at pericentromeric repeats to silence transcription exemplifies this paradox. Current models propose that cells reconcile these opposing activities by confining pericentromeric transcription to S phase while maintaining silencing during the rest of the cell cycle. Here, using strand-specific single-molecule RNA FISH (smFISH), we detect forward and reverse pericentromeric transcripts with high sensitivity and single-cell resolution. We find that repeat-associated transcription is rare, heterogeneous and happens independently of cell-cycle control. Instead, transcript production is governed solely by feedback involving small RNA biogenesis and H3K9 methylation. By combining mathematical modeling with experiments, we show that low levels of H3K9me or siRNAs prevent heterochromatin establishment, whereas high levels of H3K9me cause stochastic switching. Our work reveals that the same RNA-based feedback architecture can sample distinct transcriptional regimes, with feedback strength determining how often cells produce transcripts without any external regulatory inputs.

Biochemical and genetic networks in cells evolve to produce new functions. Evolution is guided by the genotype to phenotype map which describes how mutations at the molecular scale lead to changes in network function at the cellular scale. The number of genotypes is astronomically large which makes these maps very high dimensional. In this context, the simple question: How many mutations does it take to evolve a new function?, is usually hard to answer. Here we consider this question in the context of a simple Boolean-network model of a genotype-phenotype map. The nodes and edges of the Boolean network represent the genotype while the Boolean function the network computes is the phenotype. The network evolves by rewiring of its edges, while keeping the number of nodes fixed. We compute the number of mutations needed to achieve a new Boolean function as a function of the number of nodes in the network. We show that the number of mutations scales with the number of nodes of the network as a power-law with an exponent determined by local geometrical features of the genotype-phenotype map. Our theoretical study emphasizes the role of the genotype-phenotype map in determining the time to evolve a new function.

Biological processes, from molecules diffusing to their regulatory destinations to whales pursuing food or mates, are widely exploratory. Such behaviors are effective when some verifiable functional state or outcome can be reached regardless of initial conditions. In these cases, systems repeatedly undergo distinct and abortive trajectories; the process only ends when the system finds “right” outcomes. This dominance of the terminal condition (and indifference to the initial state) provokes a very different perspective than the conventional “dynamical systems” framework that has been a centerpiece of the quantitative sciences for centuries. We hypothesize that many of these problems defy the initial-condition driven or gradients on landscapes so useful in problems ranging from mechanics to electrodynamics to chemical kinetics to mass and heat transport. We examine several mathematical frameworks that capture and unify key aspects of exploratory dynamics. One powerful way of thinking of such processes is the geometric distribution, where repeated failures are punctuated by a successful trajectory. We develop intuitions for how random walks with resets accelerate search processes. We highlight fresh and surprising behaviors of search under drift, cues, and checkpoints. Last, appreciating the probability of trajectories conditioned on satisfying macroscopic final outcomes reveals a language for the potency of variation sculpted by selection in their broadest forms. This can give the fictitious appearance of the future making itself known in the present, but we view this as conceptually similar to the way “fictitious forces” arise in non-inertial reference frames. These approaches stress unity, open questions, and applications across a range of biological phenomena.

Bacterial RNA polymerases (RNAPs) have two flexibly tethered α subunit C-terminal domains (α-CTDs) that bind DNA. Interaction between α-CTDs and some promoter DNA motifs is known to accelerate transcription initiation, but the physical mechanism by which it does so is unclear. We used single-molecule multiwavelength fluorescence microscopy to test how the diffusion-limited binding kinetics of core RNAP to non-promoter DNA differ from those of mutant RNAPs that lack one or both α-CTDs. We find that even though α-CTDs and their tethers are small compared to the complete RNAP molecule, the presence of two α-CTDs accelerates DNA binding by ∼10-fold and ∼55-fold respectively relative to RNAP constructs in which one or both α-CTDs are deleted. In contrast, the presence of α-CTDs did not have a detectable effect on RNAP-DNA complex lifetimes in the absence of RNA synthesis. We explain how α-CTDs achieve the dramatic acceleration of RNAP binding to DNA using a quantitative three-state kinetic model that includes a transient binding intermediate where only the α-CTD(s) are bound to DNA, tethering the rest of the RNAP in the vicinity of DNA. The model and assumed parameters are validated using Brownian dynamics simulations of the DNA association reactions for two-, one-, or zero-CTD RNAP constructs. The combination of single-molecule experiments, mathematical theory, and simulations suggests that adding a flexible DNA-binding tether is a general physical mechanism which can accelerate the diffusion-limited binding of a large protein like RNAP to DNA and quantitatively defines the conditions under which this acceleration can occur. Significance Statement: Large enzymes that must associate with DNA to perform their biological functions are expected to bind DNA only slowly because of slow enzyme diffusion. However, some DNA-binding enzymes have one or more additional small DNA-binding domains that can diffuse rapidly but are attached to the enzyme through an unstructured flexible tether. Combining single-molecule experiments, theory, and computation, we present evidence for a general mechanism by which such tethered domains can accelerate enzyme binding to DNA by orders of magnitude, while not significantly changing the duration of the DNA-bound state. We demonstrate this effect for the flexibly-tethered α-subunit C-terminal domain of bacterial RNA polymerase. The mechanism may allow the polymerase to rapidly bind DNA while minimizing non-functional sequestration on the genome.

Actin is a key cytoskeletal protein that forms filaments that bundle into linear structures in vivo, which are involved in motility, signaling, and cell division. Despite the rapid turnover of individual actin monomers, these structures are often maintained at a specific length, which is important for their function. Length control is commonly attributed to length-dependent assembly or disassembly of the structure, whereby a stable length is achieved when the two opposing processes are balanced. Here we show that regardless of the nature of the length-dependent feedback, such “balance point” models predict a Gaussian distribution of lengths with a variance that is proportional to the steady state length. Contrary to this prediction, a reexamination of experimental measurements on the lengths of stereocilia, microvilli, actin cables, and filopodia reveals that the variance scales with the square of the steady state length. We propose a model in which the individual filaments in bundles undergo independent assembly dynamics, and the length of the bundle is set by the length of the longest filament. This model predicts a non-Gaussian distribution of bundle lengths with a variance that scales with the square of the steady state length. Our theory underscores the importance of crosslinking filaments into networks for size control of cytoskeleton structures.

Many biological processes can be thought of as the result of an underlying dynamics in which the system repeatedly undergoes distinct and abortive trajectories with the dynamical process only ending when some specific process, purpose, structure or function is achieved. A classic example is the way in which microtubules attach to kinetochores as a prerequisite for chromosome segregation and cell division. In this example, the dynamics is characterized by apparently futile time histories in which microtubules repeatedly grow and shrink without chromosomal attachment. We hypothesize that for biological processes for which it is not the initial conditions that matter, but rather the final state, this kind of exploratory dynamics is biology's unique and necessary solution to achieving these functions with high fidelity. This kind of cause and effect relationship can be contrasted to examples from physics and chemistry where the initial conditions determine the outcome. In this paper, we examine the similarities of many biological processes that depend upon random trajectories starting from the initial state and the selection of subsets of these trajectories to achieve some desired functional final state. We begin by reviewing the long history of the principles of dynamics, first in the context of physics, and then in the context of the study of life. These ideas are then stacked against the broad categories of biological phenomenology that exhibit exploratory dynamics. We then build on earlier work by making a quantitative examination of a succession of increasingly sophisticated models for exploratory dynamics, all of which share the common feature of being a series of repeated trials that ultimately end in a "winning" trajectory. We also explore the ways in which microscopic parameters can be tuned to alter exploratory dynamics as well as the energetic burden of performing such processes.

The nucleolus is a multicomponent structure made of RNA and proteins that serves as the site of ribosome biogenesis within the nucleus. It has been extensively studied as a prototype of a biomolecular condensate whose assembly is driven by phase separation. While the steady-state size of the nucleolus is quantitatively accounted for by the thermodynamics of phase separation, we show that experimental measurements of the assembly dynamics are inconsistent with a simple model of a phase-separating system relaxing to its equilibrium state. Instead, we show that the dynamics are well described by a model in which the transcription of ribosomal RNA actively drives nucleolar assembly. We find that our model of active transcription-templated assembly quantitatively accounts for the rapid kinetics observed in early embryos at different developmental stages, and for different RNA interference (RNAi) perturbations of embryo size. Our model predicts a scaling of the time to assembly with the volume of the nucleus to the one-third power, which is confirmed by experimental data. Our study highlights the role of active processes such as transcription in controlling the placement and timing of assembly of membraneless organelles.

Summary: Transcription activators trigger transcript production by RNA Polymerase II (RNApII) via the Mediator coactivator complex. Here the dynamics of activator, Mediator, and RNApII binding at promoter DNA were analyzed using multi-wavelength single-molecule microscopy of fluorescently labeled proteins in budding yeast nuclear extract. Binding of Mediator and RNApII to the template required activator and an upstream activator sequence (UAS), but not a core promoter. While Mediator and RNApII sometimes bind as a pre-formed complex, more commonly Mediator binds first and subsequently recruits RNApII to form a preinitiation complex precursor (pre-PIC) tethered to activators on the UAS. Interestingly, Mediator occupancy has a highly non-linear response to activator concentration, and fluorescence intensity measurements show Mediator preferentially associates with templates having at least two activators bound. Statistical mechanical modeling suggests this “synergy” is not due to cooperative binding between activators, but instead occurs when multiple DNA-bound activator molecules simultaneously interact with a single Mediator.

Many cytoskeletal networks consist of individual filaments that are organized into elaborate higher order structures. While it is appreciated that the size and architecture of these networks are critical for their biological functions, much of the work investigating control over their assembly has focused on mechanisms that regulate the turnover of individual filaments through size-dependent feedback. Here, we propose a very different, feedback-independent mechanism to explain how yeast cells control the length of their actin cables. Our findings, supported by quantitative cell imaging and mathematical modeling, indicate that actin cable length control is an emergent property that arises from the cross-linked and bundled organization of the filaments within the cable. Using this model, we further dissect the mechanisms that allow cables to grow longer in larger cells, and propose that cell length-dependent tuning of formin activity allows cells to scale cable length with cell length. This mechanism is a significant departure from prior models of cytoskeletal filament length control and presents a new paradigm to consider how cells control the size, shape, and dynamics of higher order cytoskeletal structures. Significance Statement Cells control the sizes of their cytoskeletal networks to ensure that these structures can efficiently perform their cellular functions. Until now, this ability has been attributed to molecular feedback mechanisms that control the rates at which individual filaments are assembled and disassembled. We find that size control of cytoskeletal networks does not require this type of feedback and can instead be encoded through the physical arrangement of the filaments within that network. These findings have important implications for understanding how the underlying geometry of higher order cytoskeletal networks contributes to cellular control over these structures.