Transcriptional rewiring of an evolutionarily conserved circadian clock.

Circadian clocks temporally coordinate daily organismal biology over the 24-h cycle. Their molecular design, preserved between fungi and animals, is based on a core-oscillator composed of a one-step transcriptional-translational-negative-feedback-loop (TTFL). To test whether this evolutionarily conserved TTFL architecture is the only plausible way for achieving a functional circadian clock, we adopted a transcriptional rewiring approach, artificially co-opting regulators of the circadian output pathways into the core-oscillator. Herein we describe one of these semi-synthetic clocks which maintains all basic circadian features but, notably, it also exhibits new attributes such as a "lights-on timer" logic, where clock phase is fixed at the end of the night. Our findings indicate that fundamental circadian properties such as period, phase and temperature compensation are differentially regulated by transcriptional and posttranslational aspects of the clockworks.

Multiflagellarity leads to the size-independent swimming speed of peritrichous bacteria.

To swim through a viscous fluid, a flagellated bacterium must overcome the fluid drag on its body by rotating a flagellum or a bundle of multiple flagella. Because the drag increases with the size of bacteria, it is expected theoretically that the swimming speed of a bacterium inversely correlates with its body length. Nevertheless, despite extensive research, the fundamental size-speed relation of flagellated bacteria remains unclear with different experiments reporting conflicting results. Here, by critically reviewing the existing evidence and synergizing our own experiments of large sample sizes, hydrodynamic modeling, and simulations, we demonstrate that the average swimming speed of Escherichia coli, a premier model of peritrichous bacteria, is independent of their body length. Our quantitative analysis shows that such a counterintuitive relation is the consequence of the collective flagellar dynamics dictated by the linear correlation between the body length and the number of flagella of bacteria. Notably, our study reveals how bacteria utilize the increasing number of flagella to regulate the flagellar motor load. The collective load sharing among multiple flagella results in a lower load on each flagellar motor and therefore faster flagellar rotation, which compensates for the higher fluid drag on the longer bodies of bacteria. Without this balancing mechanism, the swimming speed of monotrichous bacteria generically decreases with increasing body length, a feature limiting the size variation of the bacteria. Altogether, our study resolves a long-standing controversy over the size-speed relation of flagellated bacteria and provides insights into the functional benefit of multiflagellarity in bacteria.

Modeling of lophotrichous bacteria reveals key factors for swimming reorientation.

Lophotrichous bacteria swim through fluid by rotating their flagellar bundle extended collectively from one pole of the cell body. Cells experience modes of motility such as push, pull, and wrapping, accompanied by pauses of motor rotation in between. We present a mathematical model of a lophotrichous bacterium and investigate the hydrodynamic interaction of cells to understand their swimming mechanism. We classify the swimming modes which vary depending on the bending modulus of the hook and the magnitude of applied torques on the motor. Given the hook's bending modulus, we find that there exist corresponding critical thresholds of the magnitude of applied torques that separate wrapping from pull in CW motor rotation, and overwhirling from push in CCW motor rotation, respectively. We also investigate reoriented directions of cells in three-dimensional perspectives as the cell experiences different series of swimming modes. Our simulations show that the transition from a wrapping mode to a push mode and pauses in between are key factors to determine a new path and that the reoriented direction depends upon the start time and duration of the pauses. It is also shown that the wrapping mode may help a cell to escape from the region where the cell is trapped near a wall.

PARG has a robust endo-glycohydrolase activity that releases protein-free poly(ADP-ribose) chains.

Poly(ADP-ribosyl)ation (PARylation) regulates DNA damage response, chromatin structure, and cell-fate. Dynamic regulation of cellular PAR levels is crucial for the maintenance of genomic integrity and excessive cellular PAR activates a PAR-dependent cell death pathway. Thus, PAR serves as a cell-death signal; however, it has been debated how the protein-free PAR is generated. Here, we demonstrate that PAR glycohydrolases (PARGs) from mammals to bacteria have a robust endo-glycohydrolase activity, releasing protein-free PAR chains longer than three ADP-ribose units as early reaction products. Released PAR chains are transient and rapidly degraded to monomeric ADP-ribose, which is consistent with a short half-life of PAR during DNA damage responses. Computational simulations using a tri-ADP-ribose further support that PARG can efficiently bind to internal sites of PAR for the endo-glycosidic cleavage. Our collective results suggest PARG as a key player in producing protein-free PAR during DNA damage signaling and establish bacterial PARG as a useful tool to enrich short PAR chains that emerge as important reagents for biomedical research.

Author Correction: FRQ-CK1 interaction determines the period of circadian rhythms in Neurospora.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

FRQ-CK1 interaction determines the period of circadian rhythms in Neurospora.

Circadian clock mechanisms have been extensively investigated but the main rate-limiting step that determines circadian period remains unclear. Formation of a stable complex between clock proteins and CK1 is a conserved feature in eukaryotic circadian mechanisms. Here we show that the FRQ-CK1 interaction, but not FRQ stability, correlates with circadian period in Neurospora circadian clock mutants. Mutations that specifically affect the FRQ-CK1 interaction lead to severe alterations in circadian period. The FRQ-CK1 interaction has two roles in the circadian negative feedback loop. First, it determines the FRQ phosphorylation profile, which regulates FRQ stability and also feeds back to either promote or reduce the interaction itself. Second, it determines the efficiency of circadian negative feedback process by mediating FRQ-dependent WC phosphorylation. Our conclusions are further supported by mathematical modeling and in silico experiments. Together, these results suggest that the FRQ-CK1 interaction is a major rate-limiting step in circadian period determination.

Circadian clock regulation of the glycogen synthase (gsn) gene by WCC is critical for rhythmic glycogen metabolism in Neurospora crassa.

Circadian clocks generate rhythms in cellular functions, including metabolism, to align biological processes with the 24-hour environment. Disruption of this alignment by shift work alters glucose homeostasis. Glucose homeostasis depends on signaling and allosteric control; however, the molecular mechanisms linking the clock to glucose homeostasis remain largely unknown. We investigated the molecular links between the clock and glycogen metabolism, a conserved glucose homeostatic process, in Neurospora crassa We find that glycogen synthase (gsn) mRNA, glycogen phosphorylase (gpn) mRNA, and glycogen levels, accumulate with a daily rhythm controlled by the circadian clock. Because the synthase and phosphorylase are critical to homeostasis, their roles in generating glycogen rhythms were investigated. We demonstrate that while gsn was necessary for glycogen production, constitutive gsn expression resulted in high and arrhythmic glycogen levels, and deletion of gpn abolished gsn mRNA rhythms and rhythmic glycogen accumulation. Furthermore, we show that gsn promoter activity is rhythmic and is directly controlled by core clock component white collar complex (WCC). We also discovered that WCC-regulated transcription factors, VOS-1 and CSP-1, modulate the phase and amplitude of rhythmic gsn mRNA, and these changes are similarly reflected in glycogen oscillations. Together, these data indicate the importance of clock-regulated gsn transcription over signaling or allosteric control of glycogen rhythms, a mechanism that is potentially conserved in mammals and critical to metabolic homeostasis.

Flagellated bacteria swim in circles near a rigid wall.

The rotation of bacterial flagella driven by rotary motors enables the cell to swim through fluid. Bacteria run and reorient by changing the rotational direction of the motor for survival. Fluid environmental conditions also change the course of swimming; for example, cells near a solid boundary draw circular trajectories rather than straight runs. We present a bacterium model with a single flagellum that is attached to the cell body and investigate the effect of the solid wall on bacterial locomotion. The cell body of the bacterium is considered to be a rigid body and is linked via a rotary motor to the elastic flagellum which is modeled by the Kirchhoff rod theory. The hydrodynamic interaction of the cell near a solid boundary is described using the regularized Stokes formulation combined with the image system. We show that the trajectories of the bacteria near a solid boundary are influenced by the rotation rate of the motor, the shape of the cell body, helical geometry, and elastic properties of the flagellum.

Modeling Reveals a Key Mechanism for Light-Dependent Phase Shifts of Neurospora Circadian Rhythms.

Light shifts and synchronizes the phase of the circadian clock to daily environments, which is critical for maintaining the daily activities of an organism. It has been proposed that such light-dependent phase shifts are triggered by light-induced upregulation of a negative element of the core circadian clock (i.e., frq, Per1/2) in many organisms, including fungi. However, we find, using systematic mathematical modeling of the Neurospora crassa circadian clock, that the upregulation of the frq gene expression alone is unable to reproduce the observed light-dependent phase responses. Indeed, we find that the depression of the transcriptional activator white-collar-1, previously shown to be promoted by FRQ and VVD, is a key molecular mechanism for accurately simulating light-induced phase response curves for wild-type and mutant strains of Neurospora. Our findings elucidate specific molecular pathways that can be utilized to control phase resetting of circadian rhythms.

Synthetic Gene Network with Positive Feedback Loop Amplifies Cellulase Gene Expression in Neurospora crassa.

Second-generation or lignocellulosic biofuels are a tangible source of renewable energy, which is critical to combat climate change by reducing the carbon footprint. Filamentous fungi secrete cellulose-degrading enzymes called cellulases, which are used for production of lignocellulosic biofuels. However, inefficient production of cellulases is a major obstacle for industrial-scale production of second-generation biofuels. We used computational simulations to design and implement synthetic positive feedback loops to increase gene expression of a key transcription factor, CLR-2, that activates a large number of cellulases in a filamentous fungus, Neurospora crassa. Overexpression of CLR-2 reveals previously unappreciated roles of CLR-2 in lignocellulosic gene network, which enabled simultaneous induction of approximately 50% of 78 lignocellulosic degradation-related genes in our engineered Neurospora strains. This engineering results in dramatically increased cellulase activity due to cooperative orchestration of multiple enzymes involved in the cellulose degradation pathway. Our work provides a proof of principle in utilizing mathematical modeling and synthetic biology to improve the efficiency of cellulase synthesis for second-generation biofuel production.

Modeling polymorphic transformation of rotating bacterial flagella in a viscous fluid.

The helical flagella that are attached to the cell body of bacteria such as Escherichia coli and Salmonella typhimurium allow the cell to swim in a fluid environment. These flagella are capable of polymorphic transformation in that they take on various helical shapes that differ in helical pitch, radius, and chirality. We present a mathematical model of a single flagellum described by Kirchhoff rod theory that is immersed in a fluid governed by Stokes equations. We perform numerical simulations to demonstrate two mechanisms by which polymorphic transformation can occur, as observed in experiments. First, we consider a flagellar filament attached to a rotary motor in which transformations are triggered by a reversal of the direction of motor rotation [L. Turner et al., J. Bacteriol. 182, 2793 (2000)10.1128/JB.182.10.2793-2801.2000]. We then consider a filament that is fixed on one end and immersed in an external fluid flow [H. Hotani, J. Mol. Biol. 156, 791 (1982)10.1016/0022-2836(82)90142-5]. The detailed dynamics of the helical flagellum interacting with a viscous fluid is discussed and comparisons with experimental and theoretical results are provided.

Instabilities of a rotating helical rod in a viscous fluid.

Bacteria such as Vibrio alginolyticus swim through a fluid by utilizing the rotational motion of their helical flagellum driven by a rotary motor. The flagellar motor is embedded in the cell body and turns either clockwise (CW) or counterclockwise (CCW), which may lead to straight forward or backward swimming, or reorientation of the cell. In this paper we investigate the dynamics of the helical flagellum by adopting the Kirchhoff rod theory in which the flagellum is described as a space curve associated with orthonormal triads that measure the degree of bending and twisting of the rod. The hydrodynamic interaction with the flagellum is described by the regularized Stokes formulation. We focus on two different types of instabilities: (1) whirling instability of a rotating helical filament in the absence of a hook and (2) buckling instability of a flagellum in the presence of a compliant hook that links the flagellar filament to the rotary motor. Our simulation results show that the helical filament without a hook displays three regimes of dynamical motions: stable twirling, unstable whirling, and stable overwhirling motions depending on the physical parameters, such as rotational frequency and elastic properties of the flagellum. The helical filament with a hook experiences buckling instability when the motor switches the direction of rotation and the elastic properties of the hook change. Variations of physical parameter values of the hook such as the bending modulus and the length make an impact on the buckling angle, which may subsequently affect the reorientation of the cell.

The role of myosin II in glioma invasion: A mathematical model.

Gliomas are malignant tumors that are commonly observed in primary brain cancer. Glioma cells migrate through a dense network of normal cells in microenvironment and spread long distances within brain. In this paper we present a two-dimensional multiscale model in which a glioma cell is surrounded by normal cells and its migration is controlled by cell-mechanical components in the microenvironment via the regulation of myosin II in response to chemoattractants. Our simulation results show that the myosin II plays a key role in the deformation of the cell nucleus as the glioma cell passes through the narrow intercellular space smaller than its nuclear diameter. We also demonstrate that the coordination of biochemical and mechanical components within the cell enables a glioma cell to take the mode of amoeboid migration. This study sheds lights on the understanding of glioma infiltration through the narrow intercellular spaces and may provide a potential approach for the development of anti-invasion strategies via the injection of chemoattractants for localization.

Intercellular Coupling of the Cell Cycle and Circadian Clock in Adult Stem Cell Culture.

Circadian clock-gated cell division cycles are observed from cyanobacteria to mammals via intracellular molecular connections between these two oscillators. Here we demonstrate WNT-mediated intercellular coupling between the cell cycle and circadian clock in 3D murine intestinal organoids (enteroids). The circadian clock gates a population of cells with heterogeneous cell-cycle times that emerge as 12-hr synchronized cell division cycles. Remarkably, we observe reduced-amplitude oscillations of circadian rhythms in intestinal stem cells and progenitor cells, indicating an intercellular signal arising from differentiated cells governing circadian clock-dependent synchronized cell division cycles. Stochastic simulations and experimental validations reveal Paneth cell-secreted WNT as the key intercellular coupling component linking the circadian clock and cell cycle in enteroids.

Finding Clocks in Genes: A Bayesian Approach to Estimate Periodicity.

Identification of rhythmic gene expression from metabolic cycles to circadian rhythms is crucial for understanding the gene regulatory networks and functions of these biological processes. Recently, two algorithms, JTK_CYCLE and ARSER, have been developed to estimate periodicity of rhythmic gene expression. JTK_CYCLE performs well for long or less noisy time series, while ARSER performs well for detecting a single rhythmic category. However, observing gene expression at high temporal resolution is not always feasible, and many scientists are interested in exploring both ultradian and circadian rhythmic categories simultaneously. In this paper, a new algorithm, named autoregressive Bayesian spectral regression (ABSR), is proposed. It estimates the period of time-course experimental data and classifies gene expression profiles into multiple rhythmic categories simultaneously. Through the simulation studies, it is shown that ABSR substantially improves the accuracy of periodicity estimation and clustering of rhythmic categories as compared to JTK_CYCLE and ARSER for the data with low temporal resolution. Moreover, ABSR is insensitive to rhythmic patterns. This new scheme is applied to existing time-course mouse liver data to estimate period of rhythms and classify the genes into ultradian, circadian, and arrhythmic categories. It is observed that 49.2% of the circadian profiles detected by JTK_CYCLE with 1-hour resolution are also detected by ABSR with only 4-hour resolution.

Robustness and period sensitivity analysis of minimal models for biochemical oscillators.

Biological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

Mathematical modeling and validation of glucose compensation of the neurospora circadian clock.

Autonomous circadian oscillations arise from transcriptional-translational feedback loops of core clock components. The period of a circadian oscillator is relatively insensitive to changes in nutrients (e.g., glucose), which is referred to as "nutrient compensation". Recently, a transcription repressor, CSP-1, was identified as a component of the circadian system in Neurospora crassa. The transcription of csp-1 is under the circadian regulation. Intriguingly, CSP-1 represses the circadian transcription factor, WC-1, forming a negative feedback loop that can influence the core oscillator. This feedback mechanism is suggested to maintain the circadian period in a wide range of glucose concentrations. In this report, we constructed a mathematical model of the Neurospora circadian clock incorporating the above WC-1/CSP-1 feedback loop, and investigated molecular mechanisms of glucose compensation. Our model shows that glucose compensation exists within a narrow range of parameter space where the activation rates of csp-1 and wc-1 are balanced with each other, and simulates loss of glucose compensation in csp-1 mutants. More importantly, we experimentally validated rhythmic oscillations of the wc-1 gene expression and loss of glucose compensation in the wc-1(ov) mutant as predicted in the model. Furthermore, our stochastic simulations demonstrate that the CSP-1-dependent negative feedback loop functions in glucose compensation, but does not enhance the overall robustness of oscillations against molecular noise. Our work highlights predictive modeling of circadian clock machinery and experimental validations employing Neurospora and brings a deeper understanding of molecular mechanisms of glucose compensation.

Nonlinear dynamics of a rotating elastic rod in a viscous fluid.

The dynamics of an elastic rod in a viscous fluid at zero Reynolds number is investigated when the bottom end of the rod is tethered at a point in space and rotates at a prescribed angular frequency, while the other part of the rod freely moves through the fluid. A rotating elastic rod, which is intrinsically straight, exhibits three dynamical motions: twirling, overwhirling, and whirling. The first two motions are stable, whereas the last motion is unstable. The stability of dynamical motions is determined by material and geometrical properties of the rod, fluid properties, and the angular frequency of the rod. We employ the regularized Stokes flow to describe the fluid motion and the Kirchhoff rod model to describe the elastic rod. Our simulation results display subcritical Hopf bifurcation diagrams indicating the bistability region. We also investigate the whirling motion generated by the rotation of an intrinsically bent rod. It is observed that the angular frequency determines the handedness of the whirling rod and thus the flow direction and that there is a critical frequency which separates the positive (upward) flow at frequencies above it from the negative (downward) flow at frequencies below it.

Dynamical simulations of DNA supercoiling and compression.

In the present article, we summarize our recent studies of DNA dynamics using the generalized immersed boundary method. Our analysis of the effects of electrostatic repulsion on the dynamics of DNA supercoiling revealed that, after perturbation, a pre-twisted DNA collapses into a compact supercoiled configuration that is sensitive to the initial excess link and ionic strength of the solvent. A stochastic extension of the generalized immersed boundary method shows that DNA in solution subjected to a constant electric field is compressed into a configuration with smaller radius of gyration and smaller ellipticity ratio than those expected for such a molecule in a thermodynamic equilibrium.