The magnitude and colour of noise in genetic negative feedback systems

This is the final version of the article. Available from OUP via the DOI in this record.The comparative ability of transcriptional and small RNA-mediated negative feedback to control fluctuations or 'noise' in gene expression remains unexplored. Both autoregulatory mechanisms usually suppress the average (mean) of the protein level and its variability across cells. The variance of the number of proteins per molecule of mean expression is also typically reduced compared with the unregulated system, but is almost never below the value of one. This relative variance often substantially exceeds a recently obtained, theoretical lower limit for biochemical feedback systems. Adding the transcriptional or small RNA-mediated control has different effects. Transcriptional autorepression robustly reduces both the relative variance and persistence (lifetime) of fluctuations. Both benefits combine to reduce noise in downstream gene expression. Autorepression via small RNA can achieve more extreme noise reduction and typically has less effect on the mean expression level. However, it is often more costly to implement and is more sensitive to rate parameters. Theoretical lower limits on the relative variance are known to decrease slowly as a measure of the cost per molecule of mean expression increases. However, the proportional increase in cost to achieve substantial noise suppression can be different away from the optimal frontier-for transcriptional autorepression, it is frequently negligible.Funding for open access charge: MRC-EPSRC funded Fellowship in Bioinformatics (to C.G.B.)

Preferential duplication graphs

We consider a preferential duplication model for growing random graphs, extending previous models of duplication graphs by selecting the vertex to be duplicated with probability proportional to its degree. We show that a special case of this model can be analysed using the same stochastic approximation as for vertex-reinforced random walks, and show that 'trapping' behaviour can occur, such that the descendants of a particular group of initial vertices come to dominate the graph

Evidence of polariton induced transparency in a single organic quantum wire

The resonant interaction between quasi-one dimensional excitons and photons is investigated. For a single isolated organic quantum wire, embedded in its single crystal monomer matrix, the strong exciton-photon coupling regime is reached. This is evidenced by the suppression of the resonant excitonic absorption arising when the system eigenstate is a polariton. These observations demonstrate that the resonant excitonic absorption in a semiconductor can be understood in terms of a balance between the exciton coherence time and the Rabi period between exciton-like and photon-like states of the polariton.Comment: 9 pages and 4 figure

Mutual information and conditional mean prediction error

This version: arXiv:1407.7165v1. Available from arXiv.org via the link in this recordMutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for physical models of such mechanisms and to estimate reliably from data. Furthermore, its relationship to better known statistical procedures is still poorly understood. Here we explore new connections between mutual information and regression-based dependence measures, $\nu^{-1}$, that utilise the determinant of the second-moment matrix of the conditional mean prediction error. We examine convergence properties as $\nu\rightarrow0$ and establish sharp lower bounds on mutual information and capacity of the form $\mathrm{log}(\nu^{-1/2})$. The bounds are tighter than lower bounds based on the Pearson correlation and ones derived using average mean square-error rate distortion arguments. Furthermore, their estimation is feasible using techniques from nonparametric regression. As an illustration we provide bootstrap confidence intervals for the lower bounds which, through use of a composite estimator, substantially improve upon inference about mutual information based on $k$-nearest neighbour estimators alone

Mutual information and conditional mean prediction error

This version: arXiv:1407.7165v1. Available from arXiv.org via the link in this recordMutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for physical models of such mechanisms and to estimate reliably from data. Furthermore, its relationship to better known statistical procedures is still poorly understood. Here we explore new connections between mutual information and regression-based dependence measures, $\nu^{-1}$, that utilise the determinant of the second-moment matrix of the conditional mean prediction error. We examine convergence properties as $\nu\rightarrow0$ and establish sharp lower bounds on mutual information and capacity of the form $\mathrm{log}(\nu^{-1/2})$. The bounds are tighter than lower bounds based on the Pearson correlation and ones derived using average mean square-error rate distortion arguments. Furthermore, their estimation is feasible using techniques from nonparametric regression. As an illustration we provide bootstrap confidence intervals for the lower bounds which, through use of a composite estimator, substantially improve upon inference about mutual information based on $k$-nearest neighbour estimators alone

Influence of exciton spin relaxation on the photoluminescence spectra of semimagnetic quantum dots

We present a comprehensive experimental and theoretical studies of photoluminescence of single CdMnTe quantum dots with Mn content x ranging from 0.01 to 0.2. We distinguish three stages of the equilibration of the exciton-Mn ion spin system and show that the intermediate stage, in which the exciton spin is relaxed, while the total equilibrium is not attained, gives rise to a specific asymmetric shape of the photoluminescence spectrum. From an excellent agreement between the measured and calculated spectra we are able to evaluate the exciton localization volume, number of paramagnetic Mn ions, and their temperature for each particular dot. We discuss the values of these parameters and compare them with results of other experiments. Furthermore, we analyze the dependence of average Zeeman shifts and transition linewidths on the Mn content and point out specific processes, which control these values at particular Mn concentrations.Comment: submitted to Phys. Rev.

Mathematical modeling of gonadotropin-releasing hormone signaling.

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.Gonadotropin-releasing hormone (GnRH) acts via G-protein coupled receptors on pituitary gonadotropes to control of reproduction. These are Gq-coupled receptors that mediate acute effects of GnRH on the exocytotic secretion of luteinizing hormone (LH) and follicle-stimulating hormone (FSH), as well as the chronic regulation of their synthesis. GnRH is secreted in short pulses and GnRH effects on its target cells are dependent upon the dynamics of these pulses. Here we overview GnRH receptors and their signaling network, placing emphasis on pulsatile signaling, and how mechanistic mathematical models and an information theoretic approach have helped further this field.This work was funded Project Grants from MRC (93447) and the BBSRC (J014699). KTA and MV gratefully acknowledge the financial support of the EPSRC via grant EP/N014391/1 and an MRC Biomedical Informatics Fellowship (MR/K021826/1), respectively

On the exciton binding energy in a quantum well

We consider a model describing the one-dimensional confinement of an exciton in a symmetrical, rectangular quantum-well structure and derive upper and lower bounds for the binding energy $E_b$ of the exciton. Based on these bounds, we study the dependence of $E_b$ on the width of the confining potential with a higher accuracy than previous reports. For an infinitely deep potential the binding energy varies as expected from $1 Ry$ at large widths to $4 Ry$ at small widths. For a finite potential, but without consideration of a mass mismatch or a dielectric mismatch, we substantiate earlier results that the binding energy approaches the value $1 Ry$ for both small and large widths, having a characteristic peak for some intermediate size of the slab. Taking the mismatch into account, this result will in general no longer be true. For the specific case of a $Ga_{1-x}Al_{x}As/GaAs/Ga_{1-x}Al_{x}As$ quantum-well structure, however, and in contrast to previous findings, the peak structure is shown to survive.Comment: 32 pages, ReVTeX, including 9 figure

Information Transfer via Gonadotropin-Releasing Hormone Receptors to ERK and NFAT: Sensing GnRH and Sensing Dynamics

This is the final version of the article. Available from Oxford University Press via the DOI in this record.Information theoretic approaches can be used to quantify information transfer via cell signaling networks. In this study, we do so for gonadotropin-releasing hormone (GnRH) activation of extracellular signal-regulated kinase (ERK) and nuclear factor of activated T cells (NFAT) in large numbers of individual fixed LβT2 and HeLa cells. Information transfer, measured by mutual information between GnRH and ERK or NFAT, was <1 bit (despite 3-bit system inputs). It was increased by sensing both ERK and NFAT, but the increase was <50%. In live cells, information transfer via GnRH receptors to NFAT was also <1 bit and was increased by consideration of response trajectory, but the increase was <10%. GnRH secretion is pulsatile, so we explored information gained by sensing a second pulse, developing a model of GnRH signaling to NFAT with variability introduced by allowing effectors to fluctuate. Simulations revealed that when cell–cell variability reflects rapidly fluctuating effector levels, additional information is gained by sensing two GnRH pulses, but where it is due to slowly fluctuating effectors, responses in one pulse are predictive of those in another, so little information is gained from sensing both. Wet laboratory experiments revealed that the latter scenario holds true for GnRH signaling; within the timescale of our experiments (1 to 2 hours), cell–cell variability in the NFAT pathway remains relatively constant, so trajectories are reproducible from pulse to pulse. Accordingly, joint sensing, sensing of response trajectories, and sensing of repeated pulses can all increase information transfer via GnRH receptors, but in each case the increase is small.This work was supported by Biochemical and Biophysical Science Research Council Grant BBSRC BB/J014699/1 (to C.A.M. and K.T.-A.). M.V. acknowledges the support of the Medical Research Council (a strategic skills development fellowship in biomedical informatics) and the Engineering and Physical Sciences Research Council via Grant EP/N014391/1

Information Transfer in Gonadotropin-Releasing Hormone (GnRH) Signaling:Extracellular Signal-Regulated Kinase (ERK)-Mediated Feedback Loops Control Hormone Sensing

Cell signaling pathways are noisy communication channels, and statistical measures derived from information theory can be used to quantify the information they transfer. Here we use single cell signaling measures to calculate mutual information as a measure of information transfer via gonadotropin-releasing hormone (GnRH) receptors (GnRHR) to extracellular signal-regulated kinase (ERK) or nuclear factor of activated T-cells (NFAT). This revealed mutual information values <1 bit, implying that individual GnRH-responsive cells cannot unambiguously differentiate even two equally probable input concentrations. Addressing possible mechanisms for mitigation of information loss, we focused on the ERK pathway and developed a stochastic activation model incorporating negative feedback and constitutive activity. Model simulations revealed interplay between fast (min) and slow (min-h) negative feedback loops with maximal information transfer at intermediate feedback levels. Consistent with this, experiments revealed that reducing negative feedback (by expressing catalytically inactive ERK2) and increasing negative feedback (by Egr1-driven expression of dual-specificity phosphatase 5 (DUSP5)) both reduced information transfer from GnRHR to ERK. It was also reduced by blocking protein synthesis (to prevent GnRH from increasing DUSP expression) but did not differ for different GnRHRs that do or do not undergo rapid homologous desensitization. Thus, the first statistical measures of information transfer via these receptors reveals that individual cells are unreliable sensors of GnRH concentration and that this reliability is maximal at intermediate levels of ERK-mediated negative feedback but is not influenced by receptor desensitization