Oscillatory genetic circuits: new designs and mathematical models

Introduction and motivation: A wide variety of organisms have developed in-ternal biomolecular clocks in order to adapt to cyclic changes of the environment. Clock operation involves genetic networks. These genetic networks have to be mod¬eled in order to understand the underlying mechanism of oscillations and to design new synthetic cellular clocks. This doctoral thesis has resulted in two contributions to the fields of genetic clocks and systems and synthetic biology, generally. The first contribution is a new genetic circuit model that exhibits an oscillatory behav¬ior through catalytic RNA molecules. The second and major contribution is a new genetic circuit model demonstrating that a repressor molecule acting on the positive feedback of a self-activating gene produces reliable oscillations. First contribution: A new model of a synthetic genetic oscillator based on a typical two-gene motif with one positive and one negative feedback loop is pre¬sented. The originality is that the repressor is a catalytic RNA molecule rather than a protein or a non-catalytic RNA molecule. This catalytic RNA is a ribozyme that acts post-transcriptionally by binding to and cleaving target mRNA molecules. This genetic clock involves just two genes, a mRNA and an activator protein, apart from the ribozyme. Parameter values that produce a circadian period in both determin¬istic and stochastic simulations have been chosen as an example of clock operation. The effects of the stochastic fluctuations are quantified by a period histogram and autocorrelation function. The conclusion is that catalytic RNA molecules can act as repressor proteins and simplify the design of genetic oscillators. Second and major contribution: It is demonstrated that a self-activating gene in conjunction with a simple negative interaction can easily produce robust matically validated. This model is comprised of two clearly distinct parts. The first is a positive feedback created by a protein that binds to the promoter of its own gene and activates the transcription. The second is a negative interaction in which a repressor molecule prevents this protein from binding to its promoter. A stochastic study shows that the system is robust to noise. A deterministic study identifies that the oscillator dynamics are mainly driven by two types of biomolecules: the protein, and the complex formed by the repressor and this protein. The main conclusion of this study is that a simple and usual negative interaction, such as degradation, se¬questration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations. One gene is enough and the positive transcriptional feedback signal does not need to activate a second repressor gene. At the genetic level, this means that an explicit negative feedback loop is not necessary. Unlike many genetic oscillators, this model needs neither cooperative binding reactions nor the formation of protein multimers. Applications and future research directions: Recently, RNA molecules have been found to play many new catalytic roles. The first oscillatory genetic model proposed in this thesis uses ribozymes as repressor molecules. This could provide new synthetic biology design principles and a better understanding of cel¬lular clocks regulated by RNA molecules. The second genetic model proposed here involves only a repression acting on a self-activating gene and produces robust oscil¬lations. Unlike current two-gene oscillators, this model surprisingly does not require a second repressor gene. This result could help to clarify the design principles of cellular clocks and constitute a new efficient tool for engineering synthetic genetic oscillators. Possible follow-on research directions are: validate models in vivo and in vitro, research the potential of second model as a genetic memory, investigate new genetic oscillators regulated by non-coding RNAs and design a biosensor of positive feedbacks in genetic networks based on the operation of the second model Resumen Introduccion y motivacion: Una amplia variedad de organismos han desarro-llado relojes biomoleculares internos con el fin de adaptarse a los cambios ciclicos del entorno. El funcionamiento de estos relojes involucra redes geneticas. El mo delado de estas redes geneticas es esencial tanto para entender los mecanismos que producen las oscilaciones como para diseiiar nuevos circuitos sinteticos en celulas. Esta tesis doctoral ha dado lugar a dos contribuciones dentro de los campos de los circuitos geneticos en particular, y biologia de sistemas y sintetica en general. La primera contribucion es un nuevo modelo de circuito genetico que muestra un comportamiento oscilatorio usando moleculas de ARN cataliticas. La segunda y principal contribucion es un nuevo modelo de circuito genetico que demuestra que una molecula represora actuando sobre el lazo de un gen auto-activado produce oscilaciones robustas. Primera contribucion: Es un nuevo modelo de oscilador genetico sintetico basado en una tipica red genetica compuesta por dos genes con dos lazos de retroa-limentacion, uno positivo y otro negativo. La novedad de este modelo es que el represor es una molecula de ARN catalftica, en lugar de una protefna o una molecula de ARN no-catalitica. Este ARN catalitico es una ribozima que actua despues de la transcription genetica uniendose y cortando moleculas de ARN mensajero (ARNm). Este reloj genetico involucra solo dos genes, un ARNm y una proteina activadora, aparte de la ribozima. Como ejemplo de funcionamiento, se han escogido valores de los parametros que producen oscilaciones con periodo circadiano (24 horas) tanto en simulaciones deterministas como estocasticas. El efecto de las fluctuaciones es-tocasticas ha sido cuantificado mediante un histograma del periodo y la función de auto-correlacion. La conclusion es que las moleculas de ARN con propiedades cataliticas pueden jugar el misnio papel que las protemas represoras, y por lo tanto, simplificar el diseno de los osciladores geneticos. Segunda y principal contribucion: Es un nuevo modelo de oscilador genetico que demuestra que un gen auto-activado junto con una simple interaction negativa puede producir oscilaciones robustas. Este modelo ha sido estudiado y validado matematicamente. El modelo esta compuesto de dos partes bien diferenciadas. La primera parte es un lazo de retroalimentacion positiva creado por una proteina que se une al promotor de su propio gen activando la transcription. La segunda parte es una interaction negativa en la que una molecula represora evita la union de la proteina con el promotor. Un estudio estocastico muestra que el sistema es robusto al ruido. Un estudio determinista muestra que la dinamica del sistema es debida principalmente a dos tipos de biomoleculas: la proteina, y el complejo formado por el represor y esta proteina. La conclusion principal de este estudio es que una simple y usual interaction negativa, tal como una degradation, un secuestro o una inhibition, actuando sobre el lazo de retroalimentacion positiva de un solo gen es una condition suficiente para producir oscilaciones robustas. Un gen es suficiente y el lazo de retroalimentacion positiva no necesita activar a un segundo gen represor, tal y como ocurre en los relojes actuales con dos genes. Esto significa que a nivel genetico un lazo de retroalimentacion negativa no es necesario de forma explicita. Ademas, este modelo no necesita reacciones cooperativas ni la formation de multimeros proteicos, al contrario que en muchos osciladores geneticos. Aplicaciones y futuras lineas de investigacion: En los liltimos anos, se han descubierto muchas moleculas de ARN con capacidad catalitica. El primer modelo de oscilador genetico propuesto en esta tesis usa ribozimas como moleculas repre¬soras. Esto podria proporcionar nuevos principios de diseno en biologia sintetica y una mejor comprension de los relojes celulares regulados por moleculas de ARN. El segundo modelo de oscilador genetico propuesto aqui involucra solo una represion actuando sobre un gen auto-activado y produce oscilaciones robustas. Sorprendente-mente, un segundo gen represor no es necesario al contrario que en los bien conocidos osciladores con dos genes. Este resultado podria ayudar a clarificar los principios de diseno de los relojes celulares naturales y constituir una nueva y eficiente he-rramienta para crear osciladores geneticos sinteticos. Algunas de las futuras lineas de investigation abiertas tras esta tesis son: (1) la validation in vivo e in vitro de ambos modelos, (2) el estudio del potential del segundo modelo como circuito base para la construction de una memoria genetica, (3) el estudio de nuevos osciladores geneticos regulados por ARN no codificante y, por ultimo, (4) el rediseno del se¬gundo modelo de oscilador genetico para su uso como biosensor capaz de detectar genes auto-activados en redes geneticas.

A contribution to the deterministic modelling of circadian rhythms in cell proliferation activity

This paper presents a deterministic continuous model of proliferative cell activity. The classical series of connected compartments is revisited along with a simple mathematical treatment of two hypotheses: constant transit times and harmonic Ts. Several examples are presented to support these ideas, both taken from previous literature and recent experiences with the fish Carassius auratus, developed at the Junta de Energía Nuclear, Madrid, Spain.

High-peak-power pulse generation from a monolithic master oscillator power amplifier at 1.5 μm

We present an experimental study on the generation of high-peak-power short optical pulses from a fully integrated master-oscillator power-amplifier emitting at 1.5 μm. High-peak-power (2.7 W) optical pulses with short duration (100 ps) have been generated by gain switching the master oscillator under optimized driving conditions. The static and dynamic characteristics of the device have been studied as a function of the driving conditions. The ripples appearing in the power-current characteristics under cw conditions have been attributed to mode hopping between the master oscillator resonant mode and the Fabry-Perot modes of the entire device cavity. Although compound cavity effects have been evidenced to affect the static and dynamic performance of the device, we have demonstrated that trains of single-mode short optical pulses at gigahertz frequencies can be conveniently generated in these devices.

Provisos for classic linear oscillator design methods. New linear oscillator design based on the NDF/RRT

In this paper, the classic oscillator design methods are reviewed, and their strengths and weaknesses are shown. Provisos for avoiding the misuse of classic methods are also proposed. If the required provisos are satisfied, the solutions provided by the classic methods (oscillator start-up linear approximation) will be correct. The provisos verification needs to use the NDF (Network Determinant Function). The use of the NDF or the most suitable RRT (Return Relation Transponse), which is directly related to the NDF, as a tool to analyze oscillators leads to a new oscillator design method. The RRT is the "true" loop-gain of oscillators. The use of the new method is demonstrated with examples. Finally, a comparison of NDF/RRT results with the HB (Harmonic Balance) simulation and practical implementation measurements prove the universal use of the new methods.

Comments and remarks over classic linear loop-gain method for oscillator design and analysis. New proposed method based on NDF/RRT

Abstract. This paper describes a new and original method for designing oscillators based on the Normalized Determinant Function (NDF) and Return Relations (RRT)- Firstly, a review of the loop-gain method will be performed. The loop-gain method pros, cons and some examples for exploring wrong solutions provided by this method will be shown. This method produces in some cases wrong solutions because some necessary conditions have not been fulfilled. The required necessary conditions to assure a right solution will be described. The necessity of using the NDF or the Transpose Return Relations (RRT), which are related with the True Loop-Gain, to test the additional conditions will be demonstrated. To conclude this paper, the steps for oscillator design and analysis, using the proposed NDF/RRj method, will be presented. The loop-gain wrong solutions will be compared with the NDF/RRj and the accuracy of this method to estimate the oscillation frequency and QL will be demonstrated. Some additional examples of plane reference oscillators (Z/Y/T), will be added and they will be analyzed with the new NDF/RRj proposed method, even these oscillators cannot be analyzed using the classic loop gain method.

Dynamic response of a monolithic master-oscillator power-amplifier at 1.5 µm

We study experimentally the dynamic properties of a fully integrated high power master-oscillator power-amplifier emitting at 1.5 μm under continuous wave and gain-switching conditions. High peak power (2.7 W) optical pulses with short duration (~ 110 ps) have been generated by gain switching the master-oscillator. We show the existence of working points at very close driving conditions with stable or unstable regimes caused by the compound cavity effects. The optical and radio-frequency spectra of stable and unstable operating points are analyzed.

Analysis of mode competition in a monolithic master- oscillator power‐amplifier emitting at 1.5 μm

The optical and radio-frequency spectra of a monolithic master-oscillator power-amplifier emitting at 1.5 ?m have been analyzed in a wide range of steady-state injection conditions. The analysis of the spectral maps reveals that, under low injection current of the master oscillator, the device operates in two essentially different operation modes depending on the current injected into the amplifier section. The regular operation mode with predominance of the master oscillator alternates with lasing of the compound cavity modes allowed by the residual reflectance of the amplifier front facet. The quasi-periodic occurrence of these two regimes as a function of the amplifier current has been consistently interpreted in terms of a thermally tuned competition between the modes of the master oscillator and the compound cavity modes.

Temperature-depnedent disruption of circadian oscillations in woody plants-A mathematical approach

Poster

Uncovering cold disruption of the circadian clock in poplar

Dormancy is an adaptive mechanism that allows woody plants to survive at low temperatures during the winter. Disruption of circadian clock genes in winter or under low temperatures, both in long days as in short days, were described in our group few years ago (Ramos et al., 2005). Basic mechanisms of the circadian clock function are similar in herbaceous as well as in woody plants although there are differences in their response to low temperatures (Bieniawska et al., 2008). Woody plants growing in daylight conditions should have a specific transcriptional control above the circadian clock genes, which is responsible of their constitutive transcriptional activation observed under low temperatures conditions. In order to understand this regulatory process, we are analyzing the behavior of a circadian clock gene in poplar. To this aim, we have isolated its promoter region and fused to the luciferase reporter gene. This construct has been transformed into Populus tremula x P. alba 717-1B4 INRA clone. Here we present the characterization of these transgenic lines under different conditions of light and temperature.

Emission regimes in a distributed feedback tapered master-oscillator power-amplifier at 1.5 µm

Integrated master-oscillator power amplifiers driven under steady-state injection conditions are known to show a complex dynamics resulting in a variety of emission regimes. We present experimental results on the emission characteristics of a 1.5 µm distributed feedback tapered master-oscillator power-amplifier in a wide range of steady-state injection conditions, showing different dynamic behaviors. The study combines the optical and radio-frequency spectra recorded under different levels of injected current into the master oscillator and the power amplifier sections. Under low injection current of the master oscillator the correlation between the optical and radio-frequency spectral maps allows to identify operation regimes in which the device emission arises from either the master oscillator mode or from the compound cavity modes allowed by the residual reflectance of the amplifier front facet. The quasi-periodic occurrence of these emission regimes as a function of the amplifier current is interpreted in terms of a thermally tuned competition between the modes of the master oscillator and the compound cavity modes. Under high injection current of the masteroscillator, two different regimes alternate quasi-periodically as a function of the injected current in the power amplifier: a stable regime with a single mode emission at the master oscillator frequency, and an unstable and complex self-pulsating regime showing strong peaks in the radio-frequency spectra as well as multiple frequencies in the optical spectra.

Monolithic master oscillator power amplifier at 1.58 µm for lidar measurements

Nowadays the interest in high power semiconductor devices is growing for applications such as telemetry, lidar system or free space communications. Indeed semiconductor devices can be an alternative to solid state lasers because they are more compact and less power consuming. These characteristics are very important for constrained and/or low power supply environment such as airplanes or satellites. Lots of work has been done in the 800-1200 nm range for integrated and free space Master Oscillator Power Amplifier (MOPA) [1]-[3]. At 1.5 ?m, the only commercially available MOPA is from QPC [4]: the fibred output power is about 700 mW and the optical linewidth is 500 kHz. In this paper, we first report on the simulations we have done to determine the appropriate vertical structure and architecture for a good MOPA at 1.58 ?m (section II). Then we describe the fabrication of the devices (section III). Finally we report on the optical and electrical measurements we have done for various devices (section IV).

Loss of the circadian clock-associated protein 1 in Arabidopsis results in altered clock-regulated gene expression

Little is known about plant circadian oscillators, in spite of how important they are to sessile plants, which require accurate timekeepers that enable the plants to respond to their environment. Previously, we identified a circadian clock-associated (CCA1) gene that encodes an Myb-related protein that is associated with phytochrome control and circadian regulation in plants. To understand the role CCA1 plays in phytochrome and circadian regulation, we have isolated an Arabidopsis line with a T DNA insertion that results in the loss of CCA1 RNA, of CCA1 protein, and of an Lhcb-promoter binding activity. This mutation affects the circadian expression of all four clock-controlled genes that we examined. The results show that, despite their similarity, CCA1 and LHY are only partially redundant. The lack of CCA1 also affects the phytochrome regulation of gene expression, suggesting that CCA1 has an additional role in a signal transduction pathway from light, possibly acting at the point of integration between phytochrome and the clock. Our results indicate that CCA1 is an important clock-associated protein involved in circadian regulation of gene expression.

The protein kinase CK2 is involved in regulation of circadian rhythms in Arabidopsis

A wide range of processes in plants, including expression of certain genes, is regulated by endogenous circadian rhythms. The circadian clock-associated 1 (CCA1) and the late elongated hypocotyl (LHY) proteins have been shown to be closely associated with clock function in Arabidopsis thaliana. The protein kinase CK2 can interact with and phosphorylate CCA1, but its role in the regulation of the circadian clock remains unknown. Here we show that plants overexpressing CKB3, a regulatory subunit of CK2, display increased CK2 activity and shorter periods of rhythmic expression of CCA1 and LHY. CK2 is also able to interact with and phosphorylate LHY in vitro. Additionally, overexpression of CKB3 shortened the periods of four known circadian clock-controlled genes with different phase angles, demonstrating that many clock outputs are affected. This overexpression also reduced phytochrome induction of an Lhcb gene. Finally, we found that the photoperiodic flowering response, which is influenced by circadian rhythms, was diminished in the transgenic lines, and that the plants flowered earlier on both long-day and short-day photoperiods. These data demonstrate that CK2 is involved in regulation of the circadian clock in Arabidopsis.

Pituitary adenylyl cyclase-activating peptide: A pivotal modulator of glutamatergic regulation of the suprachiasmatic circadian clock

The circadian clock in the suprachiasmatic nucleus (SCN) of the hypothalamus organizes behavioral rhythms, such as the sleep–wake cycle, on a near 24-h time base and synchronizes them to environmental day and night. Light information is transmitted to the SCN by direct retinal projections via the retinohypothalamic tract (RHT). Both glutamate (Glu) and pituitary adenylyl cyclase-activating peptide (PACAP) are localized within the RHT. Whereas Glu is an established mediator of light entrainment, the role of PACAP is unknown. To understand the functional significance of this colocalization, we assessed the effects of nocturnal Glu and PACAP on phasing of the circadian rhythm of neuronal firing in slices of rat SCN. When coadministered, PACAP blocked the phase advance normally induced by Glu during late night. Surprisingly, blocking PACAP neurotransmission, with either PACAP6–38, a specific PACAP receptor antagonist, or anti-PACAP antibodies, augmented the Glu-induced phase advance. Blocking PACAP in vivo also potentiated the light-induced phase advance of the rhythm of hamster wheel-running activity. Conversely, PACAP enhanced the Glu-induced delay in the early night, whereas PACAP6–38 inhibited it. These results reveal that PACAP is a significant component of the Glu-mediated light-entrainment pathway. When Glu activates the system, PACAP receptor-mediated processes can provide gain control that generates graded phase shifts. The relative strengths of the Glu and PACAP signals together may encode the amplitude of adaptive circadian behavioral responses to the natural range of intensities of nocturnal light.

Circadian clock-controlled genes isolated from Neurospora crassa are late night- to early morning-specific

An endogenous circadian biological clock controls the temporal aspects of life in most organisms, including rhythmic control of genes involved in clock output pathways. In the fungus Neurospora crassa, one pathway known to be under control of the clock is asexual spore (conidia) development. To understand more fully the processes that are regulated by the N. crassa circadian clock, systematic screens were carried out for genes that oscillate at the transcriptional level. Time-of-day-specific cDNA libraries were generated and used in differential screens to identify six new clock-controlled genes (ccgs). Transcripts specific for each of the ccgs preferentially accumulate during the late night to early morning, although they vary with respect to steady-state mRNA levels and amplitude of the rhythm. Sequencing of the ends of the new ccg cDNAs revealed that ccg-12 is identical to N. crassa cmt encoding copper metallothionein, providing the suggestion that not all clock-regulated genes in N. crassa are specifically involved in the development of conidia. This was supported by finding that half of the new ccgs, including cmt(ccg-12), are not transcriptionally induced by developmental or light signals. These data suggest a major role for the clock in the regulation of biological processes distinct from development.