Multiple binding sites for transcriptional repressors can produce regular bursting and enhance noise suppression

Cells may control fluctuations in protein levels by means of negative autoregulation, where transcription factors bind DNA sites to repress their own production. Theoretical studies have assumed a single binding site for the repressor, while in most species it is found that multiple binding sites are arranged in clusters. We study a stochastic description of negative autoregulation with multiple binding sites for the repressor. We find that increasing the number of binding sites induces regular bursting of gene products. By tuning the threshold for repression, we show that multiple binding sites can also suppress fluctuations. Our results highlight possible roles for the presence of multiple binding sites of negative autoregulators

Turing Instability in a Boundary-fed System

The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations (Turing instability) in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis which neglects longitudinal diffusion is inappropriate for predicting the linear stability of these patterns. Using a fully nonuniform analysis, we investigate the structure of the patterns formed along the gradients and their stability to transverse Turing pattern formation as a function of the values of two control parameters: the malonic acid feed concentration and the size of the reactor in the dimension along the gradients. The results from this investigation are compared with existing experiments.Comment: 41 pages, 18 figures, to be published in Physical Review

Effect of Co doping and hydrostatic pressure on SrFe2As2

We report a pressure study on electron doped SrFe$_{2-x}$Co$_x$As$_2$ by electrical-resistivity ($\rho$) and magnetic-susceptibility ($\chi$) experiments. Application of either external pressure or Co substitution rapidly suppresses the spin-density wave ordering of the Fe moments and induces superconductivity in SrFe$_2$As$_2$. At $x=0.2$ the broad superconducting (SC) dome in the $T-p$ phase diagram exhibits its maximum $T_{c,{\rm max}}=20$ K at a pressure of only $p_{\rm max}\approx 0.75$ GPa. In SrFe$_{1.5}$Co$_{0.5}$As$_2$ no superconductivity is observed anymore up to 2.8 GPa. Upon increasing the Co concentration the maximum of the SC dome shifts toward lower pressure accompanied by a decrease in the value of $T_{c,{\rm max}}$. Even though, superconductivity is induced by both tuning methods, Co substitution leads to a much more robust SC state. Our study evidences that in SrFe$_{2-x}$Co$_x$As$_2$ both, the effect of pressure and Co-substitution, have to be considered in order to understand the SC phase-diagram and further attests the close relationship of SrFe$_2$As$_2$ and its sister compound BaFe$_2$As$_2$.Comment: 6 pages, 6 figure

Temperature - pressure phase diagram of CeCoSi: Pressure induced high-temperature phase

We have studied the temperature-pressure phase diagram of CeCoSi by electrical-resistivity experiments under pressure. Our measurements revealed a very unusual phase diagram. While at low pressures no dramatic changes and only a slight shift of the Ne\'{e}l temperature $T_N$ ($\approx 10$ K) are observed, at about 1.45 GPa a sharp and large anomaly, indicative of the opening of a spin-density-wave (SDW) gap, appears at a comparatively high temperature $T_S \approx 38$ K. With further increasing pressure $T_S$ shifts rapidly to low temperatures and disappears at about 2.15 GPa, likely continuously in a quantum critical point, but without evidence for superconductivity. Even more surprisingly, we observed a clear shift of $T_S$ to higher temperatures upon applying a magnetic field. We discuss two possible origins for $T_S$, either magnetic ordering of Co or a meta-orbital type of transition of Ce.Comment: 6 pages, 5 figure

Oscillations and noise in gene expression: a dialogue between theory and experiments

El carácter estocástico de las reacciones bioquímicas y las fluctuaciones del ambiente celular introducen variabilidad en la expresión y regulación genética como en todos los procesos a nivel celular. Sin embargo a pesar de las fluctuaciones, las células son capaces de realizar tareas complejas y funcionar en forma confiable y reproducible. A través de redes de regulación genética, las células toman decisiones y generan patrones precisos de actividad temporal y espacial. Un ejemplo en el que confluyen las redes de regulación, la dinámica en la expresión, la formación de patrones, y el control del ruido es el surgimiento de las estructuras que dan origen a las vertebras durante el desarrollo embrioario de los vertebrados, en el que se genera un patrón oscilatorio de expresión genética controlado por un reloj de segmentación. En esta tesis nos centramos en distintos aspectos que surgen del diálogo entre la teoría y los experimentos cuyos ingredientes en común son las redes de regulación genética, las oscilaciones, el ruido y el reloj de segmentación. Las células pueden controlar las fluctuaciones en los niveles de proteína por medio del feedback negativo, donde las proteínas se unen a sitios en el ADN para reprimir su propia producción. Los estudios teóricos usualmente asumen la existencia de un único sitio de unión para el represor, mientras que en la mayoría de las especies existen múltiples sitios de unión. En la primer parte de esta tesis, estudiamos una descripción estocástica de una red de feedback negativo con múltiples sitios de unión para el represor. Encontramos que el aumento del número de sitios de unión induce la expresión regular de los productos genéticos.. Al ajustar el umbral de la represión, mostramos que los múltiples sitios de unión también pueden suprimir las fluctuaciones en la expresión genética. Los resultados de este trabajo abren posibles aplicaciones en la biología sintética así como un marco teórico para entender la existencia de múltiples sitios de unión en diversos genes. Un ejemplo paradigmático de las redes de regulación y la dinámica en la expresión, la formación de patrones, y control del ruido es la estructura segmentada y repetitiva en los vertebrados en la que los segmentos que dan origen a las vertebras se originan durante el desarrollo embrionario de manera secuencial y rítmica. El ritmo de formación de los segmentos es controlado por un reloj de segmentación, basado en la idea de que existe una red genética que tiene una expresión oscilatoria y que es capaz de generar oscilaciones autónomas en las células del reloj. Si bien la evidencia es consistente con la idea de un reloj celular, debido a las altas fluctuaciones y a la complejidad y limitaciones del proceso de medición como a la cuantificación de dicho patrón de expresión, aún no es claro que exista una red genética capaz de generar oscilaciones a nivel autónomo. En la segunda parte de esta tesis estudiamos si las células individuales son capaces de producir oscilaciones. Para ello estudiamos series temporales de la concentración de las proteínas del reloj de segmentación obtenidas de células individuales de un reportero transgénico en zebrafish. A partir de la estadística de las series temporales y una forma normal de Hopf con ruido de color en la amplitud logramos mostrar que las células individuales se comportan como osciladores y que exhiben una dinámica heterogénea oscilatoria. Las fluctuaciones limitan la precisión temporal de un oscilador. Esta precisión puede ser caracterizada por el quality factor que cuantifica el número de ciclos en los cuál la serie es coherente. En una serie temporal, esta precisión puede ser determinada a partir de la función de autocorrelación o del periodograma. Sin embargo, una característica de todas las series temporales experimentales es que tienen una longitud finita, y en particular en biología, las series oscilatorias suelen tener un número pequeño de ciclos. Esto introduce grandes limitaciones para cuantificar la precisión de las oscilaciones a través del quality factor. En este trabajo mostramos que el valor del quality factor de las series temporales depende del método usado y para series temporales cortas puede haber grandes discrepancias entre el valor estimado y el valor real, limitando la precisión de la cuantificación. A partir de un oscilador de fases con ruido, y utilizando una teoría de First Passage Time encontramos un estimador para el quality factor que se basa en la estadística de los periodos y que converge rápidamente al valor real y es robusto inclusive en series temporales cortas. Mostramos que este estimador es robusto y preciso para distintos modelos de osciladores no lineales e inclusive en presencia de fluctuaciones de amplitud. Si bien el quality factor puede ser un estimador robusto de la precisión, cuando los periodos de la serie oscilatoria se encuentran correlacionados temporalmente, este estimador no logra capturar completamente la precision de las oscilaciones. A partir de un oscilador de fase con ruido de color, generamos series de tiempo oscilatorias con el periodo correlacionado y generalizamos la noción de quality factor definiendo un quality factor generalizado. En el cuarto capítulo mostramos que este estimador logra cuantificar correctamente la precisión temporal en series temporales cuyos periodos se encuentran correlacionados en el tiempo inclusive cuando las series temporales son cortas. Por último utilizando el método propuesto para calcular el quality factor basado en la estadística de los periodos, revisamos los resultados previos y discutimos las diferencias entre los distintos métodos de cuantificación. Para concluir, en esta tesis estudiamos aspectos complementarios para avanzar sobre el entendimiento y la cuantificación de la regulación genética, las fluctuaciones, las oscilaciones, y el reloj de segmentación a partir de un enfoque teórico.The stochastic nature of biochemical reactions and fluctuations in the cellular environment introduce variability in genetic expression and regulation as in all processes at the cellular level. However, despite fluctuations, the cells are able to perform complex tasks and function reliably. By means of gene regulatory networks, cells take decisions and generate precise patterns of temporal and spatial activity. An example where the regulatory networks, the dynamics of expression, the formation of patterns, and the control of noise converge is the emergence of the structures that give rise to vertebrae during the embryonic development of vertebrates controlled by the segmentation clock. In this thesis we study aspects that arise from the dialogue between theory and experiments whose common ingredients are the gene regulatory networks, oscillations,noise and the segmentation clock. Cells can control protein level fluctuations through negative feedback, in which proteins bind to specific sites in DNA and suppress their own production. Theoretical studies usually assume the existence of a single binding site for the repressor, while most species have multiple binding sites. In the first part of this thesis, we study a stochastic description of a negative feedback network with multiple sites for the repressor. We find that the increase in the number of binding sites induces the regular expression of gene products. By adjusting the repression threshold, we show that multiple binding sites can also enhance noise suppression in gene expression. These results open up possible applications in synthetic biology as well as a theoretical framework for understanding the existence of multiple binding sites in different genes. A paradigmatic example of regulatory networks and dynamics in gene expression, pattern formation, and noise control is the segmented and repetitive structure in vertebrates, in which the segments that give rise to vertebrae originate during embryonic development in a sequential and rhythmic manner. The rhythm of the formation of the segments is controlled by a segmentation clock, based on the idea that there is a genetic network that has an oscillatory expression and that is able to generate autonomous oscillations in the cells of the clock. Although the evidence is consistent with the idea of a cellular clock, due to the fluctuations and the complexity and limitations of the measurement process as well as the quantification of this pattern of expression, it is yet not clear whether there is a genetic network capable of generate autonomous oscillations at cellular level. In the second part of this thesis we study whether individual cells are capable of producing oscillations autonomously. We analyse time series of the concentration of the segmentation clock proteins obtained from individual cells of a transgenic reporter in zebrafish. By analysing the time series and using a Hopf normal form with colour noise in the amplitude we show that single cells behave like oscillators and exhibit a heterogeneous oscillatory dynamics. Fluctuations limit the temporal precision of an oscillator. Temporal precision can be characterised by a quality factor, which quantifies the number of coherent cycles. For an experimental time series, the quality factor can be determined either from the autocorrelation function or the periodogram. A feature of experimental time series is that they have a finite duration, and particularly in biology, oscillatory series usually have a small number of cycles. This introduces major limitations for quantifying the properties of time series, such as quantifying the accuracy of oscillations through quality factor. We show that the quality factor value of time series depends on the method used and for short time series there can be large discrepancies between the estimated value and the actual value, limiting the accuracy of quantification. From a phase oscillator with noise, and using a First Passage Time theory we find an estimator for the quality factor that is based on the statistics of the periods and that converges quickly to the real value and is robust even in short time series. We show that this estimator is robust and accurate for different models of non-linear oscillators and even in the presence of amplitude fluctuations. While the quality factor can be a robust precision estimator, when the periods of the oscillatory series are time correlated, this estimator fails to fully capture the precision of the oscillations.From a phase oscillator with additive colour noise, we generate oscillatory time series with correlated period and we generalise the notion of quality factor by defining a generalized quality factor. We show that this estimator correctly quantifies time accuracy in time series whose periods are correlated in time even when time series are short. Finally, using the proposed method to calculate the quality factor based on the period statistics, we review the previous results and we discuss the differences between the different methods of quantification. To conclude, in this thesis we study complementary aspects to advance on the understanding and quantification of gene regulation, gene expression dynamics, fluctuations, oscillations, and the segmentation clock using a theoretical approach.Fil: Lengyel, Iván M.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Nonlinearity arising from noncooperative transcription factor binding enhances negative feedback and promotes genetic oscillations

We study the effects of multiple binding sites in the promoter of a genetic oscillator. We evaluate the regulatory function of a promoter with multiple binding sites in the absence of cooperative binding, and consider different hypotheses for how the number of bound repressors affects transcription rate. Effective Hill exponents of the resulting regulatory functions reveal an increase in the nonlinearity of the feedback with the number of binding sites. We identify optimal configurations that maximize the nonlinearity of the feedback. We use a generic model of a biochemical oscillator to show that this increased nonlinearity is reflected in enhanced oscillations, with larger amplitudes over wider oscillatory ranges. Although the study is motivated by genetic oscillations in the zebrafish segmentation clock, our findings may reveal a general principle for gene regulation.Comment: 11 pages, 8 figure

Avoided ferromagnetic quantum critical point in CeRuPO

CeRuPO is a rare example of a ferromagnetic (FM) Kondo-lattice system. External pressure suppresses the ordering temperature to zero at about $p_c\approx3$ GPa. Our ac-susceptibility and electrical-resistivity investigations evidence that the type of magnetic ordering changes from FM to antiferromagnetic (AFM) at about $p^*\approx0.87$ GPa. Studies in applied magnetic fields suggest that ferromagnetic and antiferromagnetic correlations compete for the ground state at $p>p^*$, but finally the AFM correlations win. The change in the magnetic ground-state properties is closely related to the pressure evolution of the crystalline-electric-field level (CEF) scheme and the magnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction. The N\'{e}el temperature disappears abruptly in a first-order-like fashion at $p_c$, hinting at the absence of a quantum critical point. This is consistent with the low-temperature transport properties exhibiting Landau-Fermi-liquid (LFL) behavior in the whole investigated pressure range up to 7.5 GPa.Comment: 12 figure