Elements of biological oscillations in time and space

Arp2/3-dependent endocytosis ensures Cdc42 oscillations by removing Pak1-mediated negative feedback

The GTPase Cdc42 regulates polarized growth in most eukaryotes. In the bipolar yeast Schizosaccharomyces pombe, Cdc42 activation cycles periodically at sites of polarized growth. These periodic cycles are caused by alternating positive feedback and time-delayed negative feedback loops. At each polarized end, negative feedback is established when active Cdc42 recruits the Pak1 kinase to prevent further Cdc42 activation. It is unclear how Cdc42 activation returns to each end after Pak1-dependent negative feedback. We find that disrupting branched actin-mediated endocytosis disables Cdc42 reactivation at the cell ends. Using experimental and mathematical approaches, we show that endocytosis-dependent Pak1 removal from the cell ends allows the Cdc42 activator Scd1 to return to that end to enable reactivation of Cdc42. Moreover, we show that Pak1 elicits its own removal via activation of endocytosis. These findings provide a deeper insight into the self-organization of Cdc42 regulation and reveal previously unknown feedback with endocytosis in the establishment of cell polarity.

Biomolecular condensates can function as inherent catalysts

We report the discovery that chemical reactions such as ATP hydrolysis can be catalyzed by condensates formed by intrinsically disordered proteins (IDPs), which themselves lack any intrinsic ability to function as enzymes. This inherent catalytic feature of condensates derives from the electrochemical environments and the electric fields at interfaces that are direct consequences of phase separation. The condensates we studied were capable of catalyzing diverse hydrolysis reactions, including hydrolysis and radical-dependent breakdown of ATP whereby ATP fully decomposes to adenine and multiple carbohydrates. This distinguishes condensates from naturally occurring ATPases, which can only catalyze the dephosphorylation of ATP. Interphase and interfacial properties of condensates can be tuned via sequence design, thus enabling control over catalysis through sequence-dependent electrochemical features of condensates. Incorporation of hydrolase-like synthetic condensates into live cells enables activation of transcriptional circuits that depend on products of hydrolysis reactions. Inherent catalytic functions of condensates, which are emergent consequences of phase separation, are likely to affect metabolic regulation in cells.

An oscillating reaction network with an exact closed form solution in the time domain

BACKGROUND

Oscillatory behavior is critical to many life sustaining processes such as cell cycles, circadian rhythms, and notch signaling. Important biological functions depend on the characteristics of these oscillations (hereafter, oscillation characteristics or OCs): frequency (e.g., event timings), amplitude (e.g., signal strength), and phase (e.g., event sequencing). Numerous oscillating reaction networks have been documented or proposed. Some investigators claim that oscillations in reaction networks require nonlinear dynamics in that at least one rate law is a nonlinear function of species concentrations. No one has shown that oscillations can be produced for a reaction network with linear dynamics. Further, no one has obtained closed form solutions for the frequency, amplitude and phase of any oscillating reaction network. Finally, no one has published an algorithm for constructing oscillating reaction networks with desired OCs.

RESULTS

This is a theoretical study that analyzes reaction networks in terms of their representation as systems of ordinary differential equations. Our contributions are: (a) construction of an oscillating, two species reaction network [two species harmonic oscillator (2SHO)] that has no nonlinearity; (b) obtaining closed form formulas that calculate frequency, amplitude, and phase in terms of the parameters of the 2SHO reaction network, something that has not been done for any published oscillating reaction network; and (c) development of an algorithm that parameterizes the 2SHO to achieve desired oscillation, a capability that has not been produced for any published oscillating reaction network.

CONCLUSIONS

Our 2SHO demonstrates the feasibility of creating an oscillating reaction network whose dynamics are described by a system of linear differential equations. Because it is a linear system, we can derive closed form expressions for the frequency, amplitude, and phase of oscillations, something that has not been done for other published reaction networks. With these formulas, we can design 2SHO reaction networks to have desired oscillation characteristics. Finally, our sensitivity analysis suggests an approach to constructing a 2SHO for a biochemical system.

The Arp2/3 complex promotes periodic removal of Pak1-mediated negative feedback to facilitate anticorrelated Cdc42 oscillations

The conserved GTPase Cdc42 is a major regulator of polarized growth in most eukaryotes. Cdc42 periodically cycles between active and inactive states at sites of polarized growth. These periodic cycles are caused by positive feedback and time-delayed negative feedback loops. In the bipolar yeast S. pombe, both growing ends must regulate Cdc42 activity. At each cell end, Cdc42 activity recruits the Pak1 kinase which prevents further Cdc42 activation thus establishing negative feedback. It is unclear how Cdc42 activation returns to the end after Pak1-dependent negative feedback. Using genetic and chemical perturbations, we find that disrupting branched actin-mediated endocytosis disables Cdc42 reactivation at the cell ends. With our experimental data and mathematical models, we show that endocytosis-dependent Pak1 removal from the cell ends allows the Cdc42 activator Scd1 to return to that end to enable reactivation of Cdc42. Moreover, we show that Pak1 elicits its own removal via activation of endocytosis. In agreement with these observations, our model and experimental data show that in each oscillatory cycle, Cdc42 activation increases followed by an increase in Pak1 recruitment at that end. These findings provide a deeper insight into the self-organization of Cdc42 regulation and reveal previously unknown feedback with endocytosis in the establishment of cell polarity.

An improved rhythmicity analysis method using Gaussian Processes detects cell-density dependent circadian oscillations in stem cells

MOTIVATION

Detecting oscillations in time series remains a challenging problem even after decades of research. In chronobiology, rhythms (for instance in gene expression, eclosion, egg-laying, and feeding) tend to be low amplitude, display large variations amongst replicates, and often exhibit varying peak-to-peak distances (non-stationarity). Most currently available rhythm detection methods are not specifically designed to handle such datasets, and are also limited by their use of P-values in detecting oscillations.

RESULTS

We introduce a new method, ODeGP (Oscillation Detection using Gaussian Processes), which combines Gaussian Process regression and Bayesian inference to incorporate measurement errors, non-uniformly sampled data, and a recently developed non-stationary kernel to improve detection of oscillations. By using Bayes factors, ODeGP models both the null (non-rhythmic) and the alternative (rhythmic) hypotheses, thus providing an advantage over P-values. Using synthetic datasets, we first demonstrate that ODeGP almost always outperforms eight commonly used methods in detecting stationary as well as non-stationary symmetric oscillations. Next, by analyzing existing qPCR datasets, we demonstrate that our method is more sensitive compared to the existing methods at detecting weak and noisy oscillations. Finally, we generate new qPCR data on mouse embryonic stem cells. Surprisingly, we discover using ODeGP that increasing cell-density results in rapid generation of oscillations in the Bmal1 gene, thus highlighting our method's ability to discover unexpected and new patterns. In its current implementation, ODeGP is meant only for analyzing single or a few time-trajectories, not genome-wide datasets.

AVAILABILITY AND IMPLEMENTATION

ODeGP is available at https://github.com/Shaonlab/ODeGP.

Dynamic behavior of P53-Mdm2-Wip1 gene regulatory network under the influence of time delay and noise

The tumor suppressor protein P53 can regulate the cell cycle, thereby preventing cell abnormalities. In this paper, we study the dynamic characteristics of the P53 network under the influence of time delay and noise, including stability and bifurcation. In order to study the influence of several factors on the concentration of P53, bifurcation analysis on several important parameters is conducted; the results show that the important parameters could induce P53 oscillations within an appropriate range. Then we study the stability of the system and the existing conditions of Hopf bifurcation by using Hopf bifurcation theory with time delays as the bifurcation parameter. It is found that time delay plays a key role in inducing Hopf bifurcation and regulating the period and amplitude of system oscillation. Meanwhile, the combination of time delays can not only promote the oscillation of the system but it also provides good robustness. Changing the parameter values appropriately can change the bifurcation critical point and even the stable state of the system. In addition, due to the low copy number of the molecules and the environmental fluctuations, the influence of noise on the system is also considered. Through numerical simulation, it is found that noise not only promotes system oscillation but it also induces system state switching. The above results may help us to further understand the regulation mechanism of the P53-Mdm2-Wip1 network in the cell cycle.

Light-Programmed Bistate Colloidal Actuation Based on Photothermal Active Plasmonic Substrate

Active particles have been regarded as the key models to mimic and understand the complex systems of nature. Although chemical and field-powered active particles have received wide attentions, light-programmed actuation with long-range interaction and high throughput remains elusive. Here, we utilize photothermal active plasmonic substrate made of porous anodic aluminum oxide filled with Au nanoparticles and poly( N -isopropylacrylamide) (PNIPAM) to optically oscillate silica beads with robust reversibility. The thermal gradient generated by the laser beam incurs the phase change of PNIPAM, producing gradient of surface forces and large volume changes within the complex system. The dynamic evolution of phase change and water diffusion in PNIPAM films result in bistate locomotion of silica beads, which can be programmed by modulating the laser beam. This light-programmed bistate colloidal actuation provides promising opportunity to control and mimic the natural complex systems.

An autonomously oscillating supramolecular self-replicator

A key goal of chemistry is to develop synthetic systems that mimic biology, such as self-assembling, self-replicating models of minimal life forms. Oscillations are often observed in complex biological networks, but oscillating, self-replicating species are unknown, and how to control autonomous supramolecular-level oscillating systems is also not yet established. Here we show how a population of self-assembling self-replicators can autonomously oscillate, so that simple micellar species repeatedly appear and disappear in time. The interplay of molecular and supramolecular events is key to observing oscillations: the repeated formation and disappearance of compartments is connected to a reaction network where molecular-level species are formed and broken down. The dynamic behaviour of our system across different length scales offers the opportunities for mass transport, as we demonstrate via reversible dye uptake. We believe these findings will inspire new biomimetic systems and may unlock nanotechnology systems such as (supra)molecular pumps, where compartment formation is controlled in time and space.

Neural Synchrony and Network Dynamics in Social Interaction: A Hyper-Brain Cell Assembly Hypothesis

Mounting neurophysiological evidence suggests that interpersonal interaction relies on continual communication between cell assemblies within interacting brains and continual adjustments of these neuronal dynamic states between the brains. In this Hypothesis and Theory article, a Hyper-Brain Cell Assembly Hypothesis is suggested on the basis of a conceptual review of neural synchrony and network dynamics and their roles in emerging cell assemblies within the interacting brains. The proposed hypothesis states that such cell assemblies can emerge not only within, but also between the interacting brains. More precisely, the hyper-brain cell assembly encompasses and integrates oscillatory activity within and between brains, and represents a common hyper-brain unit, which has a certain relation to social behavior and interaction. Hyper-brain modules or communities, comprising nodes across two or several brains, are considered as one of the possible representations of the hypothesized hyper-brain cell assemblies, which can also have a multidimensional or multilayer structure. It is concluded that the neuronal dynamics during interpersonal interaction is brain-wide, i.e., it is based on common neuronal activity of several brains or, more generally, of the coupled physiological systems including brains.

Temporal control of the integrated stress response by a stochastic molecular switch

Stress granules (SGs) are formed in the cytosol as an acute response to environmental cues and activation of the integrated stress response (ISR), a central signaling pathway controlling protein synthesis. Using chronic virus infection as stress model, we previously uncovered a unique temporal control of the ISR resulting in recurrent phases of SG assembly and disassembly. Here, we elucidate the molecular network generating this fluctuating stress response by integrating quantitative experiments with mathematical modeling and find that the ISR operates as a stochastic switch. Key elements controlling this switch are the cooperative activation of the stress-sensing kinase PKR, the ultrasensitive response of SG formation to the phosphorylation of the translation initiation factor eIF2α, and negative feedback via GADD34, a stress-induced subunit of protein phosphatase 1. We identify GADD34 messenger RNA levels as the molecular memory of the ISR that plays a central role in cell adaptation to acute and chronic stress.

A variable refractory period increases collective performance in noisy environments

In biological and artificial systems, synchronization is an important means of achieving coordination. During hunting, social spiders alternate their moving and stopping phases in unison as they move toward their prey. We combined fieldwork and modeling to investigate the behavioral rules that lead to the emergence of synchronized oscillations in hunting groups. We showed that an individual's decision to move depends on the relative intensity of vibrations emitted by the prey and the moving spiders. This rule allows the group to adapt quickly to any change in prey size or the number of spiders involved in the hunt. Such synchronization ensures that the spiders can locate their prey without being disturbed by signals from conspecifics and thus improves hunting performance.

Synchronized oscillations are found in all living systems, from cells to ecosystems and on varying time scales. A generic principle behind the production of oscillations involves a delay in the response of one entity to stimulations from the others in the system. Communication among entities is required for the emergence of synchronization, but its efficacy can be impaired by surrounding noise. In the social spider Anelosimus eximius, individuals coordinate their activity to catch large prey that are otherwise inaccessible to solitary hunters. When hunting in groups, dozens of spiders move rhythmically toward their prey by synchronizing moving and stopping phases. We proposed a mechanistic model implementing individual behavioral rules, all derived from field experiments, to elucidate the underlying principles of synchronization. We showed that the emergence of oscillations in spiders involves a refractory state, the duration of which depends on the relative intensity of prey versus conspecific signals. This flexible behavior allows individuals to rapidly adapt to variations in their vibrational landscapes. Exploring the model reveals that the benefits of synchronization resulting from improved accuracy in prey detection and reduced latency to capture prey more than offset the cost of the delay associated with immobility phases. Overall, our study shows that a refractory period whose duration is variable and dependent on information accessible to all entities in the system contributes to the emergence of self-organized oscillations in noisy environments. Our findings may inspire the design of artificial systems requiring fast and flexible synchronization between their components.

Origins of human disease: the chrono-epigenetic perspective

Epigenetics has enriched human disease studies by adding new interpretations to disease features that cannot be explained by genetic and environmental factors. However, identifying causal mechanisms of epigenetic origin has been challenging. New opportunities have risen from recent findings in intra-individual and cyclical epigenetic variation, which includes circadian epigenetic oscillations. Cytosine modifications display deterministic temporal rhythms, which may drive ageing and complex disease. Temporality in the epigenome, or the 'chrono' dimension, may help the integration of epigenetic, environmental and genetic disease studies, and reconcile several disparities stemming from the arbitrarily delimited research fields. The ultimate goal of chrono-epigenetics is to predict disease risk, age of onset and disease dynamics from within individual-specific temporal dynamics of epigenomes.

CRISPR-based gene expression control for synthetic gene circuits

Synthetic gene circuits allow us to govern cell behavior in a programmable manner, which is central to almost any application aiming to harness engineered living cells for user-defined tasks. Transcription factors (TFs) constitute the 'classic' tool for synthetic circuit construction but some of their inherent constraints, such as insufficient modularity, orthogonality and programmability, limit progress in such forward-engineering endeavors. Here we review how CRISPR (clustered regularly interspaced short palindromic repeats) technology offers new and powerful possibilities for synthetic circuit design. CRISPR systems offer superior characteristics over TFs in many aspects relevant to a modular, predictable and standardized circuit design. Thus, the choice of CRISPR technology as a framework for synthetic circuit design constitutes a valid alternative to complement or replace TFs in synthetic circuits and promises the realization of more ambitious designs.

Misuse of the Michaelis-Menten rate law for protein interaction networks and its remedy

For over a century, the Michaelis-Menten (MM) rate law has been used to describe the rates of enzyme-catalyzed reactions and gene expression. Despite the ubiquity of the MM rate law, it accurately captures the dynamics of underlying biochemical reactions only so long as it is applied under the right condition, namely, that the substrate is in large excess over the enzyme-substrate complex. Unfortunately, in circumstances where its validity condition is not satisfied, especially so in protein interaction networks, the MM rate law has frequently been misused. In this review, we illustrate how inappropriate use of the MM rate law distorts the dynamics of the system, provides mistaken estimates of parameter values, and makes false predictions of dynamical features such as ultrasensitivity, bistability, and oscillations. We describe how these problems can be resolved with a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA). Furthermore, we show that the tQSSA can be used for accurate stochastic simulations at a lower computational cost than using the full set of mass-action rate laws. This review describes how to use quasi-steady state approximations in the right context, to prevent drawing erroneous conclusions from in silico simulations.

Filtering and inference for stochastic oscillators with distributed delays

Motivation

The time evolution of molecular species involved in biochemical reaction networks often arises from complex stochastic processes involving many species and reaction events. Inference for such systems is profoundly challenged by the relative sparseness of experimental data, as measurements are often limited to a small subset of the participating species measured at discrete time points. The need for model reduction can be realistically achieved for oscillatory dynamics resulting from negative translational and transcriptional feedback loops by the introduction of probabilistic time-delays. Although this approach yields a simplified model, inference is challenging and subject to ongoing research. The linear noise approximation (LNA) has recently been proposed to address such systems in stochastic form and will be exploited here.

Results

We develop a novel filtering approach for the LNA in stochastic systems with distributed delays, which allows the parameter values and unobserved states of a stochastic negative feedback model to be inferred from univariate time-series data. The performance of the methods is tested for simulated data. Results are obtained for real data when the model is fitted to imaging data on Cry1, a key gene involved in the mammalian central circadian clock, observed via a luciferase reporter construct in a mouse suprachiasmatic nucleus.

Availability and implementation

Programmes are written in MATLAB and Statistics Toolbox Release 2016 b, The MathWorks, Inc., Natick, Massachusetts, USA. Sample code and Cry1 data are available on GitHub https://github.com/scalderazzo/FLNADD.

Supplementary information

Supplementary data are available at Bioinformatics online.

Long-range temporal coordination of gene expression in synthetic microbial consortia

Synthetic microbial consortia have an advantage over isogenic synthetic microbes because they can apportion biochemical and regulatory tasks among the strains. However, it is difficult to coordinate gene expression in spatially extended consortia because the range of signaling molecules is limited by diffusion. Here, we show that spatio-temporal coordination of gene expression can be achieved even when the spatial extent of the consortium is much greater than the diffusion distance of the signaling molecules. To do this, we examined the dynamics of a two-strain synthetic microbial consortium that generates coherent oscillations in small colonies. In large colonies, we find that temporally coordinated oscillations across the population depend on the presence of an intrinsic positive feedback loop that amplifies and propagates intercellular signals. These results demonstrate that synthetic multicellular systems can be engineered to exhibit coordinated gene expression using only transient, short-range coupling among constituent cells.

A chemically fueled non-enzymatic bistable network

One of the grand challenges in contemporary systems chemistry research is to mimic life-like functions using simple synthetic molecular networks. This is particularly true for systems that are out of chemical equilibrium and show complex dynamic behaviour, such as multi-stability, oscillations and chaos. We report here on thiodepsipeptide-based non-enzymatic networks propelled by reversible replication processes out of equilibrium, displaying bistability. Accordingly, we present quantitative analyses of the bistable behaviour, featuring a phase transition from the simple equilibration processes taking place in reversible dynamic chemistry into the bistable region. This behaviour is observed only when the system is continuously fueled by a reducing agent that keeps it far from equilibrium, and only when operating within a specifically defined parameter space. We propose that the development of biomimetic bistable systems will pave the way towards the study of more elaborate functions, such as information transfer and signalling.

Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity

Lineage switches are genetic regulatory motifs that govern and maintain the commitment of a developing cell to a particular cell fate. A canonical example of a lineage switch is the pair of transcription factors PU.1 and GATA-1, of which the former is affiliated with the myeloid and the latter with the erythroid lineage within the haematopoietic system. On a molecular level, PU.1 and GATA-1 positively regulate themselves and antagonize each other via direct protein-protein interactions. Here we use mathematical modelling to identify a novel type of dynamic behaviour that can be supported by such a regulatory architecture. Guided by the specifics of the PU.1-GATA-1 interaction, we formulate, using the law of mass action, a system of differential equations for the key molecular concentrations. After a series of systematic approximations, the system is reduced to a simpler one, which is tractable to phase-plane and linearization methods. The reduced system formally resembles, and generalizes, a well-known model for competitive species from mathematical ecology. However, in addition to the qualitative regimes exhibited by a pair of competitive species (exclusivity, bistable exclusivity, stable-node coexpression) it also allows for oscillatory limit-cycle coexpression. A key outcome of the model is that, in the context of cell-fate choice, such oscillations could be harnessed by a differentiating cell to prime alternately for opposite outcomes; a bifurcation-theory approach is adopted to characterize this possibility.

Bi-functional biochemical networks

Understanding the relationship between the topology of a network and its function remains an important question in biological physics. However, this is not a one-to-one mapping. Often the behavior of a signaling system varies with the input signal it receives. For example, some biological systems show adaptation when they receive a low input signal while they show oscillation with a high input signal. We therefore set out to find all possible two-node and three-node networks that can perform both adaptation and oscillation with transcriptional regulation and enzymatic reactions. For two-node networks, we identified all bi-functional topologies by analyzing the Jacobean matrix. For three-node networks, they were identified by enumeration. We further investigated how the system can be transformed between these two functions. We found that the switching of functions can be achieved through changing anyone of the several key parameters, including the input signal level.

Secretory pathway calcium ATPase 1 (SPCA1) controls mouse neural tube closure by regulating cytoskeletal dynamics

Neural tube closure relies on the apical constriction of neuroepithelial cells. Research in frog and fly embryos has found links between the levels of intracellular calcium, actomyosin dynamics and apical constriction. However, genetic evidence for a role of calcium in apical constriction during mammalian neurulation is still lacking. Secretory pathway calcium ATPase (SPCA1) regulates calcium homeostasis by pumping cytosolic calcium into the Golgi apparatus. Loss of function in Spca1 causes cranial exencephaly and spinal cord defects in mice, phenotypes previously ascribed to apoptosis. However, our characterization of a novel allele of Spca1 revealed that neurulation defects in Spca1 mutants are not due to cell death, but rather to a failure of neuroepithelial cells to apically constrict. We show that SPCA1 influences cell contractility by regulating myosin II localization. Furthermore, we found that loss of Spca1 disrupts actin dynamics and the localization of the actin remodeling protein cofilin 1. Taken together, our results provide evidence that SPCA1 promotes neurulation by regulating the cytoskeletal dynamics that promote apical constriction and identify cofilin 1 as a downstream effector of SPCA1 function.

Parallel signaling pathways regulate excitable dynamics differently for pseudopod formation in eukaryotic chemotaxis

In eukaryotic chemotaxis, parallel signaling pathways regulate the spatiotemporal pseudopod dynamics at the leading edge of a motile cell through characteristic dynamics of an excitable system; however, differences in the excitability and the physiological roles of individual pathways remain to be elucidated. Here we found that two different pathways, soluble guanylyl cyclase (sGC) and phosphatidylinositol 3-kinase (PI3K), exhibited similar all-or-none responses but different refractory periods by simultaneous observations of their excitable properties. Due to the shorter refractory period, sGC signaling responded more frequently to chemoattractants, leading to pseudopod formation with higher frequency. sGC excitability was regulated negatively by its product, cGMP, and cGMP-binding protein C (GbpC) through the suppression of F-actin polymerization, providing the underlying delayed negative feedback mechanism for the cyclical pseudopod formation. These results suggest that parallel pathways respond on different time-scales to environmental cues for chemotactic motility based on their intrinsic excitability. Key words: cGMP signaling, chemotaxis, excitability, pseudopod formation

Sterol transfer, PI4P consumption, and control of membrane lipid order by endogenous OSBP

The network of proteins that orchestrate the distribution of cholesterol among cellular organelles is not fully characterized. We previously proposed that oxysterol-binding protein (OSBP) drives cholesterol/PI4P exchange at contact sites between the endoplasmic reticulum (ER) and the trans-Golgi network (TGN). Using the inhibitor OSW-1, we report here that the sole activity of endogenous OSBP makes a major contribution to cholesterol distribution, lipid order, and PI4P turnover in living cells. Blocking OSBP causes accumulation of sterols at ER/lipid droplets at the expense of TGN, thereby reducing the gradient of lipid order along the secretory pathway. OSBP consumes about half of the total cellular pool of PI4P, a consumption that depends on the amount of cholesterol to be transported. Inhibiting the spatially restricted PI4-kinase PI4KIIIβ triggers large periodic traveling waves of PI4P across the TGN These waves are cadenced by long-range PI4P production by PI4KIIα and PI4P consumption by OSBP Collectively, these data indicate a massive spatiotemporal coupling between cholesterol transport and PI4P turnover via OSBP and PI4-kinases to control the lipid composition of subcellular membranes.