Distinct silencer states generate epigenetic states of heterochromatin.

Heterochromatic loci can exhibit different transcriptional states in genetically identical cells. A popular model posits that the inheritance of modified histones is sufficient for inheritance of the silenced state. However, silencing inheritance requires silencers and therefore cannot be driven by the inheritance of modified histones alone. To address these observations, we determined the chromatin architectures produced by strong and weak silencers in Saccharomyces. Strong silencers recruited Sir proteins and silenced the locus in all cells. Strikingly, weakening these silencers reduced Sir protein recruitment and stably silenced the locus in some cells; however, this silenced state could probabilistically convert to an expressed state that lacked Sir protein recruitment. Additionally, changes in the constellation of silencer-bound proteins or the concentration of a structural Sir protein modulated the probability that a locus exhibited the silenced or expressed state. These findings argued that distinct silencer states generate epigenetic states and regulate their dynamics.

Transient Hysteresis in CDK4/6 Activity Underlies Passage of the Restriction Point in G1.

Cells escape the need for mitogens at a restriction point several hours before entering S phase. The restriction point has been proposed to result from CDK4/6 initiating partial Rb phosphorylation to trigger a bistable switch whereby cyclin E-CDK2 and Rb mutually reinforce each other to induce Rb hyperphosphorylation. Here, using single-cell analysis, we unexpectedly found that cyclin E/A-CDK activity can only maintain Rb hyperphosphorylation starting at the onset of S phase and that CDK4/6 activity, but not cyclin E/A-CDK activity, is required to hyperphosphorylate Rb throughout G1 phase. Mitogen removal in G1 results in a gradual loss of CDK4/6 activity with a high likelihood of cells sustaining Rb hyperphosphorylation until S phase, at which point cyclin E/A-CDK activity takes over. Thus, it is short-term memory, or transient hysteresis, in CDK4/6 activity following mitogen removal that sustains Rb hyperphosphorylation, demonstrating a probabilistic rather than an irreversible molecular mechanism underlying the restriction point.

The oscillation of mitotic kinase governs cell cycle latches in mammalian cells.

The mammalian cell cycle alternates between two phases - S-G2-M with high levels of A- and B-type cyclins (CycA and CycB, respectively) bound to cyclin-dependent kinases (CDKs), and G1 with persistent degradation of CycA and CycB by an activated anaphase promoting complex/cyclosome (APC/C) bound to Cdh1 (also known as FZR1 in mammals; denoted APC/C:Cdh1). Because CDKs phosphorylate and inactivate Cdh1, these two phases are mutually exclusive. This 'toggle switch' is flipped from G1 to S by cyclin-E bound to a CDK (CycE:CDK), which is not degraded by APC/C:Cdh1, and from M to G1 by Cdc20-bound APC/C (APC/C:Cdc20), which is not inactivated by CycA:CDK or CycB:CDK. After flipping the switch, cyclin E is degraded and APC/C:Cdc20 is inactivated. Combining mathematical modelling with single-cell timelapse imaging, we show that dysregulation of CycB:CDK disrupts strict alternation of the G1-S and M-G1 switches. Inhibition of CycB:CDK results in Cdc20-independent Cdh1 'endocycles', and sustained activity of CycB:CDK drives Cdh1-independent Cdc20 endocycles. Our model provides a mechanistic explanation for how whole-genome doubling can arise, a common event in tumorigenesis that can drive tumour evolution.

Continuous modeling of creased annuli with tunable bistable and looping behaviors.

Creases are purposely introduced to thin structures for designing deployable origami, artistic geometries, and functional structures with tunable nonlinear mechanics. Modeling the mechanics of creased structures is challenging because creases introduce geometric discontinuity and often have complex mechanical responses due to local material damage. In this work, we propose a continuous description of the sharp geometry of creases and apply it to the study of creased annuli, made by introducing radial creases to annular strips with the creases annealed to behave elastically. We find that creased annuli have generic bistability and can be folded into various compact shapes, depending on the crease pattern and the overcurvature of the flat annulus. We use a regularized Dirac delta function (RDDF) to describe the geometry of a crease, with the finite spike of the RDDF capturing the localized curvature. Together with anisotropic rod theory, we solve the nonlinear mechanics of creased annuli, with its stability determined by the standard conjugate point test. We find excellent agreement between precision tabletop models, numerical predictions from our analytical framework, and modeling results from finite element simulations. We further show that by varying the rest curvature of the thin strip, dynamic switches between different states of creased annuli can be achieved, which could inspire the design of deployable and morphable structures. We believe that our smooth description of discontinuous geometries will benefit the mechanical modeling and design of a wide spectrum of engineering structures that embrace geometric and material discontinuities.

Feedback in the ß-catenin destruction complex imparts bistability and cellular memory.

Wnt ligands are considered classical morphogens, for which the strength of the cellular response is proportional to the concentration of the ligand. Herein, we show an emergent property of bistability arising from feedback among the Wnt destruction complex proteins that target the key transcriptional co-activator ß-catenin for degradation. Using biochemical reconstitution, we identified positive feedback between the scaffold protein Axin and the kinase glycogen synthase kinase 3 (GSK3). Theoretical modeling of this feedback between Axin and GSK3 suggested that the activity of the destruction complex exhibits bistable behavior. We experimentally confirmed these predictions by demonstrating that cellular cytoplasmic ß-catenin concentrations exhibit an "all-or-none" response with sustained memory (hysteresis) of the signaling input. This bistable behavior was transformed into a graded response and memory was lost through inhibition of GSK3. These findings provide a mechanism for establishing decisive, switch-like cellular response and memory upon Wnt pathway stimulation.

Programmable mechanical devices through magnetically tunable bistable elements.

Mechanical instabilities, especially in the form of bistable and multistable mechanisms, have recently garnered a lot of interest as a mode of improving the capabilities and increasing the functionalities of soft robots, structures, and soft mechanical systems in general. Although bistable mechanisms have shown high tunability through the variation of their material and design variables, they lack the option of modifying their attributes dynamically during operation. Here, we propose a facile approach to overcome this limitation by dispersing magnetically active microparticles throughout the structure of bistable elements and using an external magnetic field to tune their responses. We experimentally demonstrate and numerically verify the predictable and deterministic control of the response of different types of bistable elements under varying magnetic fields. Additionally, we show how this approach can be used to induce bistability in intrinsically monostable structures simply by placing them in a controlled magnetic field. Furthermore, we show the application of this strategy in precisely controlling the features (e.g., velocity and direction) of transition waves propagating in a multistable lattice created by cascading a chain of individual bistable elements. Moreover, we can implement active elements like a transistor (gate controlled by magnetic fields) or magnetically reconfigurable functional elements like binary logic gates for processing mechanical signals. This strategy serves to provide programming and tuning capabilities required to allow more extensive utilization of mechanical instabilities in soft systems with potential functions such as soft robotic locomotion, sensing and triggering elements, mechanical computation, and reconfigurable devices.

Network switches and their role in circadian clocks.

Circadian rhythms are generated by complex interactions among genes and proteins. Self-sustained ∼24 h oscillations require negative feedback loops and sufficiently strong nonlinearities that are the product of molecular and network switches. Here, we review common mechanisms to obtain switch-like behavior, including cooperativity, antagonistic enzymes, multisite phosphorylation, positive feedback, and sequestration. We discuss how network switches play a crucial role as essential components in cellular circadian clocks, serving as integral parts of transcription-translation feedback loops that form the basis of circadian rhythm generation. The design principles of network switches and circadian clocks are illustrated by representative mathematical models that include bistable systems and negative feedback loops combined with Hill functions. This work underscores the importance of negative feedback loops and network switches as essential design principles for biological oscillations, emphasizing how an understanding of theoretical concepts can provide insights into the mechanisms generating biological rhythms.

Mechanisms of Persistent Activity in Cortical Circuits: Possible Neural Substrates for Working Memory.

A commonly observed neural correlate of working memory is firing that persists after the triggering stimulus disappears. Substantial effort has been devoted to understanding the many potential mechanisms that may underlie memory-associated persistent activity. These rely either on the intrinsic properties of individual neurons or on the connectivity within neural circuits to maintain the persistent activity. Nevertheless, it remains unclear which mechanisms are at play in the many brain areas involved in working memory. Herein, we first summarize the palette of different mechanisms that can generate persistent activity. We then discuss recent work that asks which mechanisms underlie persistent activity in different brain areas. Finally, we discuss future studies that might tackle this question further. Our goal is to bridge between the communities of researchers who study either single-neuron biophysical, or neural circuit, mechanisms that can generate the persistent activity that underlies working memory.

Noncoding RNAs in Polycomb and Trithorax Regulation: A Quantitative Perspective.

The question of how noncoding RNAs are involved in Polycomb group (PcG) and Trithorax group (TrxG) regulation has been on an extraordinary journey over the last three decades. Favored models have risen and fallen, and healthy debates have swept back and forth. The field has recently reached a critical mass of compelling data that throws light on several previously unresolved issues. The time is ripe for a fruitful combination of these findings with two other long-running avenues of research, namely the biochemical properties of the PcG/TrxG system and the application of theoretical mathematical models toward an understanding of the system's regulatory properties. I propose that integrating our current knowledge of noncoding RNA into a quantitative biochemical and theoretical framework for PcG and TrxG regulation has the potential to reconcile several apparently conflicting models and identifies fascinating questions for future research.

Pervasive transcription enhances the accessibility of H-NS-silenced promoters and generates bistability in Salmonella virulence gene expression.

In Escherichia coli and Salmonella, many genes silenced by the nucleoid structuring protein H-NS are activated upon inhibiting Rho-dependent transcription termination. This response is poorly understood and difficult to reconcile with the view that H-NS acts mainly by blocking transcription initiation. Here we have analyzed the basis for the up-regulation of H-NS-silenced Salmonella pathogenicity island 1 (SPI-1) in cells depleted of Rho-cofactor NusG. Evidence from genetic experiments, semiquantitative 5' rapid amplification of complementary DNA ends sequencing (5' RACE-Seq), and chromatin immunoprecipitation sequencing (ChIP-Seq) shows that transcription originating from spurious antisense promoters, when not stopped by Rho, elongates into a H-NS-bound regulatory region of SPI-1, displacing H-NS and rendering the DNA accessible to the master regulator HilD. In turn, HilD's ability to activate its own transcription triggers a positive feedback loop that results in transcriptional activation of the entire SPI-1. Significantly, single-cell analyses revealed that this mechanism is largely responsible for the coexistence of two subpopulations of cells that either express or do not express SPI-1 genes. We propose that cell-to-cell differences produced by stochastic spurious transcription, combined with feedback loops that perpetuate the activated state, can generate bimodal gene expression patterns in bacterial populations.

Topological transformability and reprogrammability of multistable mechanical metamaterials.

Concepts from quantum topological states of matter have been extensively utilized in the past decade to create mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized elasticity. Maxwell lattices represent a class of topological mechanical metamaterials that exhibit distinct robust mechanical properties at edges/interfaces when they are topologically polarized. Realizing topological phase transitions in these materials would enable on-and-off switching of these edge states, opening opportunities to program mechanical response and wave propagation. However, such transitions are extremely challenging to experimentally control in Maxwell topological metamaterials due to mechanical and geometric constraints. Here we create a Maxwell lattice with bistable units to implement synchronized transitions between topological states and demonstrate dramatically different stiffnesses as the lattice transforms between topological phases both theoretically and experimentally. By combining multistability with topological phase transitions, this metamaterial not only exhibits topologically protected mechanical properties that swiftly and reversibly change, but also offers a rich design space for innovating mechanical computing architectures and reprogrammable neuromorphic metamaterials. Moreover, we design and fabricate a topological Maxwell lattice using multimaterial 3D printing and demonstrate the potential for miniaturization via additive manufacturing. These design principles are applicable to transformable topological metamaterials for a variety of tasks such as switchable energy absorption, impact mitigation, wave tailoring, neuromorphic metamaterials, and controlled morphing systems.

Autoregulation of switching behavior by cellular compartment size.

SignificanceBiochemical reactions often occur in small volumes within a cell, restricting the number of molecules to the hundreds or even tens. At this scale, reactions are discrete and stochastic, making reliable signaling difficult. This paper shows that the transition between discrete, stochastic reactions and macroscopic reactions can be exploited to make a self-regulating switch. This constitutes a previously unidentified kind of reaction network that may be present in small structures, such as synapses.

Critical-like Brain Dynamics in a Continuum from Second- to First-Order Phase Transition.

The classic brain criticality hypothesis postulates that the brain benefits from operating near a continuous second-order phase transition. Slow feedback regulation of neuronal activity could, however, lead to a discontinuous first-order transition and thereby bistable activity. Observations of bistability in awake brain activity have nonetheless remained scarce and its functional significance unclear. Moreover, there is no empirical evidence to support the hypothesis that the human brain could flexibly operate near either a first- or second-order phase transition despite such a continuum being common in models. Here, using computational modeling, we found bistable synchronization dynamics to emerge through elevated positive feedback and occur exclusively in a regimen of critical-like dynamics. We then assessed bistability in vivo with resting-state MEG in healthy adults (7 females, 11 males) and stereo-electroencephalography in epilepsy patients (28 females, 36 males). This analysis revealed that a large fraction of the neocortices exhibited varying degrees of bistability in neuronal oscillations from 3 to 200 Hz. In line with our modeling results, the neuronal bistability was positively correlated with classic assessment of brain criticality across narrow-band frequencies. Excessive bistability was predictive of epileptic pathophysiology in the patients, whereas moderate bistability was positively correlated with task performance in the healthy subjects. These empirical findings thus reveal the human brain as a one-of-a-kind complex system that exhibits critical-like dynamics in a continuum between continuous and discontinuous phase transitions.SIGNIFICANCE STATEMENT In the model, while synchrony per se was controlled by connectivity, increasing positive local feedback led to gradually emerging bistable synchrony with scale-free dynamics, suggesting a continuum between second- and first-order phase transitions in synchrony dynamics inside a critical-like regimen. In resting-state MEG and SEEG, bistability of ongoing neuronal oscillations was pervasive across brain areas and frequency bands and was observed only with concurring critical-like dynamics as the modeling predicted. As evidence for functional relevance, moderate bistability was positively correlated with executive functioning in the healthy subjects, and excessive bistability was associated with epileptic pathophysiology. These findings show that critical-like neuronal dynamics in vivo involves both continuous and discontinuous phase transitions in a frequency-, neuroanatomy-, and state-dependent manner.

A machine-learning tool to identify bistable states from calcium imaging data.

Mapping neuronal activation using calcium imaging in vivo during behavioural tasks has advanced our understanding of nervous system function. In almost all of these studies, calcium imaging is used to infer spike probabilities because action potentials activate voltage-gated calcium channels and increase intracellular calcium levels. However, neurons not only fire action potentials, but also convey information via intrinsic dynamics such as by generating bistable membrane potential states. Although a number of tools for spike inference have been developed and are currently being used, no tool exists for converting calcium imaging signals to maps of cellular state in bistable neurons. Purkinje neurons in the larval zebrafish cerebellum exhibit membrane potential bistability, firing either tonically or in bursts. Several studies have implicated the role of a population code in cerebellar function, with bistability adding an extra layer of complexity to this code. In the present study, we develop a tool, CaMLSort, which uses convolutional recurrent neural networks to classify calcium imaging traces as arising from either tonic or bursting cells. We validate this classifier using a number of different methods and find that it performs well on simulated event rasters as well as real biological data that it had not previously seen. Moreover, we find that CaMLsort generalizes to other bistable neurons, such as dopaminergic neurons in the ventral tegmental area of mice. Thus, this tool offers a new way of analysing calcium imaging data from bistable neurons to understand how they participate in network computation and natural behaviours. KEY POINTS: Calcium imaging, compriising the gold standard of inferring neuronal activity, does not report cellular state in neurons that are bistable, such as Purkinje neurons in the cerebellum of larval zebrafish. We model the relationship between Purkinje neuron electrical activity and its corresponding calcium signal to compile a dataset of state-labelled simulated calcium signals. We apply machine-learning methods to this dataset to develop a tool that can classify the state of a Purkinje neuron using only its calcium signal, which works well on real data even though it was trained only on simulated data. CaMLsort (Calcium imaging and Machine Learning based tool to sort intracellular state) also generalizes well to bistable neurons in a different brain region (ventral tegmental area) in a different model organism (mouse). This tool can facilitate our understanding of how these neurons carry out their functions in a circuit.

A human cortical adaptive mutual inhibition circuit underlying competition for perceptual decision and repetition suppression reversal.

A model based on inhibitory coupling has been proposed to explain perceptual oscillations. This 'adapting reciprocal inhibition' model postulates that it is the strength of inhibitory coupling that determines the fate of competition between percepts. Here, we used an fMRI-based adaptation technique to reveal the influence of neighboring neuronal populations, such as reciprocal inhibition, in motion-selective hMT+/V5. If reciprocal inhibition exists in this region, the following predictions should hold: 1. stimulus-driven response would not simply decrease, as predicted by simple repetition-suppression of neuronal populations, but instead, increase due to the activity from adjacent populations; 2. perceptual decision involving competing representations, should reflect decreased reciprocal inhibition by adaptation; 3. neural activity for the competing percept should also later on increase upon adaptation. Our results confirm these three predictions, showing that a model of perceptual decision based on adapting reciprocal inhibition holds true. Finally, they also show that the net effect of the well-known repetition suppression phenomenon can be reversed by this mechanism.

Effect of size on expression of bistability in mouse spinal motoneurons.

Bistability in spinal motoneurons supports tonic spike activity in the absence of excitatory drive. Earlier work in adult preparations suggested that smaller motoneurons innervating slow antigravity muscle fibers are more likely to generate bistability for postural maintenance. However, whether large motoneurons innervating fast-fatigable muscle fibers display bistability is still controversial. To address this, we examined the relationship between soma size and bistability in lumbar (L4-L5) ventrolateral α-motoneurons of choline acetyltransferase (ChAT)-green fluorescent protein (GFP) and Hb9-GFP mice during the first 4 wk of life. We found that as neuron size increases, the prevalence of bistability rises. Smaller α-motoneurons lack bistability, whereas larger fast α-motoneurons [matrix metalloproteinase-9 (MMP-9)+/Hb9+] with a soma area ≥ 400 µm2 exhibit significantly higher bistability. Ionic currents associated with bistability, including the persistent Nav1.6 current, the thermosensitive Trpm5 Ca2+-activated Na+ current, and the slowly inactivating Kv1.2 current, also scale with cell size. Serotonin evokes full bistability in large motoneurons with partial bistable properties but not in small motoneurons. Our study provides important insights into the neural mechanisms underlying bistability and how motoneuron size correlates with bistability in mice.NEW & NOTEWORTHY Bistability is not a common feature of all mouse spinal motoneurons. It is absent in small, slow motoneurons but present in most large, fast motoneurons. This difference results from differential expression of ionic currents that enable bistability, which are highly expressed in large motoneurons but small or absent in small motoneurons. These results support a possible role for fast motoneurons in maintenance of tonic posture in addition to their known roles in fast movements.

A single-cell resolved cell-cell communication model explains lineage commitment in hematopoiesis.

Cells do not make fate decisions independently. Arguably, every cell-fate decision occurs in response to environmental signals. In many cases, cell-cell communication alters the dynamics of the internal gene regulatory network of a cell to initiate cell-fate transitions, yet models rarely take this into account. Here, we have developed a multiscale perspective to study the granulocyte-monocyte versus megakaryocyte-erythrocyte fate decisions. This transition is dictated by the GATA1-PU.1 network: a classical example of a bistable cell-fate system. We show that, for a wide range of cell communication topologies, even subtle changes in signaling can have pronounced effects on cell-fate decisions. We go on to show how cell-cell coupling through signaling can spontaneously break the symmetry of a homogenous cell population. Noise, both intrinsic and extrinsic, shapes the decision landscape profoundly, and affects the transcriptional dynamics underlying this important hematopoietic cell-fate decision-making system. This article has an associated 'The people behind the papers' interview.

Ultralong Bistable, Electrolytic MnO2-Based, Electrochromic Battery Enabled by Porous, Low-Barrier, Hydroxylated TiO2 Interface.

Electrochromic (EC) battery technology shows great potential in future "zero-energy building" by controlling outdoor solar transmission to tune heat gain as well as storing the consumed energy to reuse across other building systems. However, challenges still exist in exploring an electrochemical system to satisfy requirements on both ultra-long optical memory (also called bistability) without continuous power supply and high energy density. Herein, an EC battery is proposed to demonstrate ultra-long bistability (>760 h) based on the reversible deposition and dissolution of manganese oxide (MnO2) without the addition of any mediators. A porous low-barrier hydroxylated titanium dioxide (TiO2) interface is incorporated to synergistically enrich Mn2+-affinity active sites for deposition and effectively reduce the electron transport barrier of MnO2 for dissolution, thereby significantly improving the reversibility, high optical modulation (60.2% at 400 nm), and energy density (352 mAh m-2). The modification strategy is also verified on the cathode-less button cells with a much higher average coulombic efficiency (99.9%) compared to the batteries without the porous hydroxylated TiO2 interface (74.6%). These achievements lay a foundation for advancements in both electrochromism and Zn-Mn aqueous batteries.

Reassessing the alternative ecosystem states proposition in the African savanna-forest domain.

Ecologists are being challenged to predict how ecosystems will respond to climate changes. According to the Multi-Colored World (MCW) hypothesis, climate impacts may not manifest because consumers such as fire and herbivory can override the influence of climate on ecosystem state. One MCW interpretation is that climate determinism fails because alternative ecosystem states (AES) are possible at some locations in climate space. We evaluated theoretical and empirical evidence for the proposition that forest and savanna are AES in Africa. We found that maps which infer where AES zones are located were contradictory. Moreover, data from longitudinal and experimental studies provide inconclusive evidence for AES. That is, although the forest-savanna AES proposition is theoretically sound, the existing evidence is not yet convincing. We conclude by making the case that the AES proposition has such fundamental consequences for designing management actions to mitigate and adapt to climate change in the savanna-forest domain that it needs a more robust evidence base before it is used to prescribe management actions.

Kinetics of diffusion-influenced multisite phosphorylation with enzyme reactivation.

The simplest way to account for the influence of diffusion on the kinetics of multisite phosphorylation is to modify the rate constants in the conventional rate equations of chemical kinetics. We have previously shown that this is not enough and new transitions between the reactants must also be introduced. Here we extend our results by considering enzymes that are inactive after modifying the substrate and need time to become active again. This generalization leads to a surprising result. The introduction of enzyme reactivation results in a diffusion-modified kinetic scheme with a new transition that has a negative rate constant. The reason for this is that mapping non-Markovian rate equations onto Markovian ones with time-independent rate constants is not a good approximation at short times. We then developed a non-Markovian theory that involves memory kernels instead of rate constants. This theory is now valid at short times, but is more challenging to use. As an example, the diffusion-modified kinetic scheme with new connections was used to calculate kinetics of double phosphorylation and steady-state response in a phosphorylation-dephosphorylation cycle. We have reproduced the loss of bistability in the phosphorylation-dephosphorylation cycle when the enzyme reactivation time decreases, which was obtained by particle-based computer simulations.