The Dynamic Spatial Structure of Flocks.

Studies of collective motion have heretofore been dominated by a thermodynamic perspective in which the emergent "flocked" phases are analyzed in terms of their time-averaged orientational and spatial properties. Studies that attempt to scrutinize the dynamical processes that spontaneously drive the formation of these flocks from initially random configurations are far more rare, perhaps owing to the fact that said processes occur far from the eventual long-time steady state of the system and thus lie outside the scope of traditional statistical mechanics. For systems whose dynamics are simulated numerically, the nonstationary distribution of system configurations can be sampled at different time points, and the time evolution of the average structural properties of the system can be quantified. In this paper, we employ this strategy to characterize the spatial dynamics of the standard Vicsek flocking model using two correlation functions common to condensed matter physics. We demonstrate, for modest system sizes with 800 to 2000 agents, that the self-assembly dynamics can be characterized by three distinct and disparate time scales that we associate with the corresponding physical processes of clustering (compaction), relaxing (expansion), and mixing (rearrangement). We further show that the behavior of these correlation functions can be used to reliably distinguish between phenomenologically similar models with different underlying interactions and, in some cases, even provide a direct measurement of key model parameters.

Magnetic induction inspires a schematic theory for crosstalk-driven relaxation dynamics in cells.

Establishing formal mathematical analogies between disparate physical systems can be a powerful tool, allowing for the well studied behavior of one system to be directly translated into predictions about the behavior of another that may be harder to probe. In this paper we lay the foundation for such an analogy between the macroscale electrodynamics of simple magnetic circuits and the microscale chemical kinetics of transcriptional regulation in cells. By artificially allowing the inductor coils of the former to elastically expand under the action of their Lorentz pressure, we introduce nonlinearities into the system that we interpret through the lens of our analogy as a schematic model for the impact of crosstalk on the rates of gene expression near steady state. Synthetic plasmids introduced into a cell must compete for a finite pool of metabolic and enzymatic resources against a maelstrom of crisscrossing biological processes, and our theory makes sensible predictions about how this noisy background might impact the expression profiles of synthetic constructs without explicitly modeling the kinetics of numerous interconnected regulatory interactions. We conclude the paper with a discussion of how our theory might be expanded to a broader class of plasmid circuits and how our predictions might be tested experimentally.

Devil in the details: Mechanistic variations impact information transfer across models of transcriptional cascades.

The transcriptional network determines a cell's internal state by regulating protein expression in response to changes in the local environment. Due to the interconnected nature of this network, information encoded in the abundance of various proteins will often propagate across chains of noisy intermediate signaling events. The data-processing inequality (DPI) leads us to expect that this intracellular game of "telephone" should degrade this type of signal, with longer chains losing successively more information to noise. However, a previous modeling effort predicted that because the steps of these signaling cascades do not truly represent independent stages of data processing, the limits of the DPI could seemingly be surpassed, and the amount of transmitted information could actually increase with chain length. What that work did not examine was whether this regime of growing information transmission was attainable by a signaling system constrained by the mechanistic details of more complex protein-binding kinetics. Here we address this knowledge gap through the lens of information theory by examining a model that explicitly accounts for the binding of each transcription factor to DNA. We analyze this model by comparing stochastic simulations of the fully nonlinear kinetics to simulations constrained by the linear response approximations that displayed a regime of growing information. Our simulations show that even when molecular binding is considered, there remains a regime wherein the transmitted information can grow with cascade length, but ends after a critical number of links determined by the kinetic parameter values. This inflection point marks where correlations decay in response to an oversaturation of binding sites, screening informative transcription factor fluctuations from further propagation down the chain where they eventually become indistinguishable from the surrounding levels of noise.

Modeling the impacts of a simple meiotic gene drive on small, homeostatic populations.

Gene drives offer unprecedented control over the fate of natural ecosystems by leveraging non-Mendelian inheritance mechanisms to proliferate synthetic genes across wild populations. However, these benefits are offset by a need to avoid the potentially disastrous consequences of unintended ecological interactions. The efficacy of many gene-editing drives has been brought into question due to predictions that they will inevitably be thwarted by the emergence of drive-resistant mutations, but these predictions derive largely from models of large or infinite populations that cannot be driven to extinction faster than mutations can fixate. To address this issue, we characterize the impact of a simple, meiotic gene drive on a small, homeostatic population whose genotypic composition may vary due to the stochasticity inherent in natural mating events (e.g., partner choice, number of offspring) or the genetic inheritance process (e.g., mutation rate, gene drive fitness). To determine whether the ultimate genotypic fate of such a population is sensitive to such stochastic fluctuations, we compare the results of two dynamical models: a deterministic model that attempts to predict how the genetics of an average population evolve over successive generations, and an agent-based model that examines how stable these predictions are to fluctuations. We find that, even on average, our stochastic model makes qualitatively distinct predictions from those of the deterministic model, and we identify the source of these discrepancies as a dynamic instability that arises at short times, when genetic diversity is maximized as a consequence of the gene drive's rapid proliferation. While we ultimately conclude that extinction can only beat out the fixation of drive-resistant mutations over a limited region of parameter space, the reason for this is more complex than previously understood, which could open new avenues for engineered gene drives to circumvent this weakness.

Fluctuation sensitivity of a transcriptional signaling cascade.

The internal biochemical state of a cell is regulated by a vast transcriptional network that kinetically correlates the concentrations of numerous proteins. Fluctuations in protein concentration that encode crucial information about this changing state must compete with fluctuations caused by the noisy cellular environment in order to successfully transmit information across the network. Oftentimes, one protein must regulate another through a sequence of intermediaries, and conventional wisdom, derived from the data processing inequality of information theory, leads us to expect that longer sequences should lose more information to noise. Using the metric of mutual information to characterize the fluctuation sensitivity of transcriptional signaling cascades, we find, counter to this expectation, that longer chains of regulatory interactions can instead lead to enhanced informational efficiency. We derive an analytic expression for the mutual information from a generalized chemical kinetics model that we reduce to simple, mass-action kinetics by linearizing for small fluctuations about the basal biological steady state, and we find that at long times this expression depends only on a simple ratio of protein production to destruction rates and the length of the cascade. We place bounds on the values of these parameters by requiring that the mutual information be at least one bit-otherwise, any received signal would be indistinguishable from noise-and we find not only that nature has devised a way to circumvent the data processing inequality, but that it must be circumvented to attain this one-bit threshold. We demonstrate how this result places informational and biochemical efficiency at odds with one another by correlating high transcription factor binding affinities with low informational output, and we conclude with an analysis of the validity of our assumptions and propose how they might be tested experimentally.

DNA motion capture reveals the mechanical properties of DNA at the mesoscale.

Single-molecule studies probing the end-to-end extension of long DNAs have established that the mechanical properties of DNA are well described by a wormlike chain force law, a polymer model where persistence length is the only adjustable parameter. We present a DNA motion-capture technique in which DNA molecules are labeled with fluorescent quantum dots at specific sites along the DNA contour and their positions are imaged. Tracking these positions in time allows us to characterize how segments within a long DNA are extended by flow and how fluctuations within the molecule are correlated. Utilizing a linear response theory of small fluctuations, we extract elastic forces for the different, ∼2-µm-long segments along the DNA backbone. We find that the average force-extension behavior of the segments can be well described by a wormlike chain force law with an anomalously small persistence length.

Reentrance in an active glass mixture.

Active matter, whose motion is driven, and glasses, whose dynamics are arrested, seem to lie at opposite ends of the spectrum in nonequilibrium systems. In spite of this, both classes of systems exhibit a multitude of stable states that are dynamically isolated from one another. While this defining characteristic is held in common, its origin is different in each case: for active systems, the irreversible driving forces can produce dynamically frozen states, while glassy systems vitrify when they get kinetically trapped on a rugged free energy landscape. In a mixture of active and glassy particles, the interplay between these two tendencies leads to novel phenomenology. We demonstrate this with a spin glass model that we generalize to include an active component. In the absence of a ferromagnetic bias, we find that the spin glass transition temperature depresses with the active fraction, consistent with what has been observed for fully active glassy systems. When a bias does exist, however, a new type of transition becomes possible: the system can be cooled out of the glassy phase. This unusual phenomenon, known as reentrance, has been observed before in a limited number of colloidal and micellar systems, but it has not yet been observed in active glass mixtures. Using low order perturbation theory, we study the origin of this reentrance and, based on the physical picture that results, suggest how our predictions might be measured experimentally.

Flocking with minimal cooperativity: the panic model.

We present a two-dimensional lattice model of self-propelled spins that can change direction only upon collision with another spin. We show that even with ballistic motion and minimal cooperativity, these spins display robust flocking behavior at nearly all densities, forming long bands of stripes. The structural transition in this system is not a thermodynamic phase transition, but it can still be characterized by an order parameter, and we demonstrate that if this parameter is studied as a dynamical variable rather than a steady-state observable, we can extract a detailed picture of how the flocking mechanism varies with density.