Intrinsic and external noise in an auto-regulatory genetic network

A single gene auto-regulatory network is analysed. The main goal is to investigate the effects of the negative and positive feedbacks on the intrinsic and external noises. The central finding of this paper is that: for the intrinsic noise, both the negative and positive feedback regulations increase the fluctuation strength of mRNA levels (where the fluctuation strength is measured by the Fano factor for both the fluctuations of mRNAs and proteins), and the negative feedback decreases, but the positive feedback increases, the fluctuation strength of proteins; for the external noise, the negative feedback not only increase the fluctuation strength of mRNA levels but also the fluctuation strength of proteins, and though the effect of the positive feedback on the fluctuation strength of mRNA levels depends on the size of positive feedback parameter k, the positive feedback must decrease the fluctuation strength of proteins.     

Role of Relaxation Time Scale in Noisy Signal Transduction

Intra-cellular fluctuations, mainly triggered by gene expression, are an inevitable phenomenon observed in living cells. It influences generation of phenotypic diversity in genetically identical cells. Such variation of cellular components is beneficial in some contexts but detrimental in others. To quantify the fluctuations in a gene product, we undertake an analytical scheme for studying few naturally abundant linear as well as branched chain network motifs. We solve the Langevin equations associated with each motif under the purview of linear noise approximation and derive the expressions for Fano factor and mutual information in close analytical form. Both quantifiable expressions exclusively depend on the relaxation time (decay rate constant) and steady state population of the network components. We investigate the effect of relaxation time constraints on Fano factor and mutual information to indentify a time scale domain where a network can recognize the fluctuations associated with the input signal more reliably. We also show how input population affects both quantities. We extend our calculation to long chain linear motif and show that with increasing chain length, the Fano factor value increases but the mutual information processing capability decreases. In this type of motif, the intermediate components act as a noise filter that tune up input fluctuations and maintain optimum fluctuations in the output. For branched chain motifs, both quantities vary within a large scale due to their network architecture and facilitate survival of living system in diverse environmental conditions.     

Effect of feedback regulation on stochastic gene expression

Stochastic noise in gene expression arises as a result of species in small copy number undergoing transitions between discrete chemical states. Here the noise in a single gene network is investigated using the Omega-expansion techniques. We show that the linear noise approximation implies an invariant relationship between the normalized variances and normalized covariance in steady-state statistics. This invariant relationship provides an exactly statistical interpretation for why the stochastic noise in gene expression should be measured by the normalized variance. The nature of the normalized variance reveals the basic relationship between the stochasticity and system size in gene expression. The linear noise approximation implies also that for both mRNA and protein, the total noise can be decomposed into two basic components, one concerns the contribution of average number of molecules, and other the contribution of interactions between mRNA and protein. For the situation with linear feedback, our results clearly show that for two genes with the same average number of protein molecules, the gene with negative feedback will have a small protein noise, i.e., the negative feedback will reduce the protein noise. For the effect of the burst size on the protein noise, we show also that the protein intrinsic noise will decrease with the increase of the burst size, but the protein extrinsic noise is independent of the burst size.     

External noise and feedback regulation: steady-state statistics of auto-regulatory genetic network

The steady-state statistics of a single gene auto-regulatory genetic network with the additive external Gaussian white noises is investigated. The main result shows that the negative feedback will result in that the mRNA noise has a positive contribution to the protein noise, but the positive feedback will result in that the mRNA noise has a negative contribution to the protein noise. If there is no feed back, then the contribution of mRNA noise to protein noise is always positive. On the other hand, the analysis and numerical simulations of linear and nonlinear feedback show that it is possible that the negative feedback increases, but the positive feedback decreases, the protein noise.     

Multivariate analysis of noise in genetic regulatory networks

Stochasticity is an intrinsic property of genetic regulatory networks due to the low copy numbers of the major molecular species, such as, DNA, mRNA, and regulatory proteins. Therefore, investigation of the mechanisms that reduce the stochastic noise is essential in understanding the reproducible behaviors of real organisms and is also a key to design synthetic genetic regulatory networks that can reliably work. We use an analytical and systematic method, the linear noise approximation of the chemical master equation along with the decoupling of a stoichiometric matrix. In the analysis of fluctuations of multiple molecular species, the covariance is an important measure of noise. However, usually the representation of a covariance matrix in the natural coordinate system, i.e. the copy numbers of the molecular species, is intractably complicated because reactions change copy numbers of more than one molecular species simultaneously. Decoupling of a stoichiometric matrix, which is a transformation of variables, significantly simplifies the representation of a covariance matrix and elucidates the mechanisms behind the observed fluctuations in the copy numbers. We apply our method to three types of fundamental genetic regulatory networks, that is, a single-gene autoregulatory network, a two-gene autoregulatory network, and a mutually repressive network. We have found that there are multiple noise components differently originating. Each noise component produces fluctuation in the characteristic direction. The resulting fluctuations in the copy numbers of the molecular species are the sum of these fluctuations. In the examples, the limitation of the negative feedback in noise reduction and the trade-off of fluctuations in multiple molecular species are clearly explained. The analytical representations show the full parameter dependence. Additionally, the validity of our method is tested by stochastic simulations.     

Diffusion of transcription factors can drastically enhance the noise in gene expression

We study by Green's Function Reaction Dynamics the effect of the diffusive motion of repressor molecules on the noise in mRNA and protein levels for a gene that is under the control of a repressor. We find that spatial fluctuations due to diffusion can drastically enhance the noise in gene expression. After dissociation from the operator, a repressor can rapidly rebind to the DNA. Our results show that the rebinding trajectories are so short that, on this timescale, the RNA polymerase (RNAP) cannot effectively compete with the repressor for binding to the promoter. As a result, a dissociated repressor molecule will on average rebind many times, before it eventually diffuses away. These rebindings thus lower the effective dissociation rate, and this increases the noise in gene expression. Another consequence of the timescale separation between repressor rebinding and RNAP association is that the effect of spatial fluctuations can be described by a well-stirred, zero-dimensional, model by renormalizing the reaction rates for repressor-DNA (un) binding. Our results thus support the use of well-stirred, zero-dimensional models for describing noise in gene expression. We also show that for a fixed repressor strength, the noise due to diffusion can be minimized by increasing the number of repressors or by decreasing the rate of the open complex formation. Lastly, our results emphasize that power spectra are a highly useful tool for studying the propagation of noise through the different stages of gene expression.     

Fano Resonances Induced by Strong Interactions Between Dipole and Multipole Plasmons in T-Shaped Nanorod Dimer

A simple T-shaped plasmonic nanostructure composed of two perpendicular coupled nanorods is proposed to produce strong Fano resonances. By the near-field coupling between the “bright” dipole and “dark” quadrupole plasmons of the nanorods, a deep Fano dip is formed in the extinction spectrum, which can be well fitted by the Fano interference model. The effects of the geometry parameters including nanorod length, coupling gap size, and coupling location to the Fano resonances are analyzed in detail, and a very high refractive index sensitivity is achieved by the Fano resonance. Also by adjusting the incident polarization direction, double Fano resonances can be formed by the interferences of the dipole, quadrupole, and hexapole plasmons. The proposed nanorod dimer structure is agile, and a trimer which supports double Fano resonances can be easily formed by introducing a third perpendicular coupled nanorod. The proposed T-shaped nanorod dimer structure may have applications in the fields of biological sensing and plasmon-induced transparency.     

Covariation of Mitochondrial Genome Size with Gene Lengths: Evidence for Gene Length Reduction During Mitochondrial Evolution

Reduction of genome size and gene shortening have been observed in a number of parasitic and mutualistic intracellular symbionts. Reduction of coding capacity is also a unifying principle in the evolutionary history of mitochondria, but little is known about the evolution of gene length in mitochondria. The genes for cytochrome c oxidase subunits I–III, cytochrome b, and the large and small subunit rRNAs are, with very few exceptions, always found on the mitochondrial genome. These resident mitochondrial genes can therefore be used to test whether the reduction in gene lengths observed in a number of intracellular symbionts is also seen in mitochondria. Here we show that resident mitochondrial gene products are shorter than their corresponding counterparts in -proteobacteria and, furthermore, that the reduction of mitochondrial genome size is correlated with a reduction in the length of the corresponding resident gene products. We show that relative genomic AT content, which has been identified as a factor influencing gene lengths in other systems, cannot explain gene length/genome size covariance observed in mitochondria. Our data are therefore in agreement with the idea that gene length evolves as a consequence of selection for smaller genomes, either to avoid accumulation of deleterious mutations or triggered by selection for a replication advantage.     

Dynamic models of gene expression and classification

Powerful new methods, like expression profiles using cDNA arrays, have been used to monitor changes in gene expression levels as a result of a variety of metabolic, xenobiotic or pathogenic challenges. This potentially vast quantity of data enables, in principle, the dissection of the complex genetic networks that control the patterns and rhythms of gene expression in the cell. Here we present a general approach to developing dynamic models for analyzing time series of whole genome expression. In this approach, a self-consistent calculation is performed that involves both linear and non-linear response terms for interrelating gene expression levels. This calculation uses singular value decomposition (SVD) not as a statistical tool but as a means of inverting noisy and near-singular matrices. The linear transition matrix that is determined from this calculation can be used to calculate the underlying network reflected in the data. This suggests a direct method of classifying genes according to their place in the resulting network. In addition to providing a means to model such a large multivariate system this approach can be used to reduce the dimensionality of the problem in a rational and consistent way, and suppress the strong noise amplification effects often encountered with expression profile data. Non-linear and higher-order Markov behavior of the network are also determined in this self-consistent method. In data sets from yeast, we calculate the Markov matrix and the gene classes based on the linear-Markov network. These results compare favorably with previously used methods like cluster analysis. Our dynamic method appears to give a broad and general framework for data analysis and modeling of gene expression arrays. Electronic Publication     

Crystallographic analysis of Lac repressor bound to natural operator O1

Previous structures of Lac repressor bound to DNA used a fully symmetric "ideal" operator sequence that is missing the central G-C base-pair present in the three natural operator sequences. Here we have determined the X-ray crystal structure of a dimeric Lac repressor bound to a 22 base-pair DNA with the natural operator O1 sequence and the anti-inducer ONPF, at 4.0 A resolution. The natural operator is bent in the same way as the symmetric sequence, due to the binding of the hinge helices of the repressor to the minor groove at the central GCGG sequence of O1. Comparison of the structures of the repressor bound to the natural and symmetric operators shows very similar overall structures, with only slight rearrangements of the headpiece domains of the repressor. Analysis of crystals with iodinated DNA shows that the operator is uniquely positioned and allows for the sequence registration of the DNA relative to the repressor to be determined. The kink in the operator is centered between the left half-site and the central G-C base-pair of O1. Our results are most consistent with a previously proposed model in which, relative to the complex with the symmetric operator, the repressor accommodates binding to the natural operator sequence by shifting the position of the right headpiece by one base-pair step towards the center of O1.     

Tunable Multi-Fano Resonances in MDM-Based Side-Coupled Resonator System and its Application in Nanosensor

In this paper, two Fano resonances are achieved in the proposed plasmonic system. Theoretical analysis and simulation results show that two discrete states coupled with a continua lead to these Fano resonances. The discrete states are provided by the side-coupled square cavity, and a baffle plate placed in metal-dielectric-metal waveguide is used to produce a continuous transmission spectrum. The resonant wavelengths and the linewidth of these Fano resonances can be easily tuned by adjusting the parameters of system. This system exhibits high sensitivities as high as 850 and 1120 nm/RIU corresponding to two Fano resonances, and the figure of merit can reach to 1.7 × 10⁵ by optimizing the system. By introducing another square cavity, four Fano resonances are obtained which originate from four discrete states coupled with continua, and they can be tuned independently. The flexible multi-Fano resonances system has significant application bio-nanosensor, nonlinear, and slow light devices.