Model Reduction for the Chemical Master Equation: an Information-Theoretic Approach

The complexity of mathematical models in biology has rendered model reduction an essential tool in the quantitative biologist's toolkit. For stochastic reaction networks described using the Chemical Master Equation, commonly used methods include time-scale separation, the Linear Mapping Approximation and state-space lumping. Despite the success of these techniques, they appear to be rather disparate and at present no general-purpose approach to model reduction for stochastic reaction networks is known. In this paper we show that most common model reduction approaches for the Chemical Master Equation can be seen as minimising a well-known information-theoretic quantity between the full model and its reduction, the Kullback-Leibler divergence defined on the space of trajectories. This allows us to recast the task of model reduction as a variational problem that can be tackled using standard numerical optimisation approaches. In addition we derive general expressions for the propensities of a reduced system that generalise those found using classical methods. We show that the Kullback-Leibler divergence is a useful metric to assess model discrepancy and to compare different model reduction techniques using three examples from the literature: an autoregulatory feedback loop, the Michaelis-Menten enzyme system and a genetic oscillator

Absolute frequency measurements of 85Rb nF7/2 Rydberg states using purely optical detection

A three-step laser excitation scheme is used to make absolute frequency measurements of highly excited nF7/2 Rydberg states in 85Rb for principal quantum numbers n=33-100. This work demonstrates the first absolute frequency measurements of rubidium Rydberg levels using a purely optical detection scheme. The Rydberg states are excited in a heated Rb vapour cell and Doppler free signals are detected via purely optical means. All of the frequency measurements are made using a wavemeter which is calibrated against a GPS disciplined self-referenced optical frequency comb. We find that the measured levels have a very high frequency stability, and are especially robust to electric fields. The apparatus has allowed measurements of the states to an accuracy of 8.0MHz. The new measurements are analysed by extracting the modified Rydberg-Ritz series parameters.Comment: 12 pages, 5 figures, submitted to New. J. Phy

Picosecond Nonlinear Relaxation of Photoinjected Carriers in a Single GaAs/AlGaAs Quantum Dot

Photoemission from a single self-organized GaAs/AlGaAs quantum dot (QD) is temporally resolved with picosecond time resolution. The emission spectra consisting of the multiexciton structures are observed to depend on the delay time and the excitation intensity. Quantitative agreement is found between the experimental data and the calculation based on a model which characterizes the successive relaxation of multiexcitons. Through the analysis we can determine the carrier relaxation time as a function of population of photoinjected carriers. Enhancement of the intra-dot carrier relaxation is demonstrated to be due to the carrier-carrier scattering inside a single QD.Comment: 4 pages, 4 figures, to be published in Phys. Rev. B, Rapid

A rate splitting strategy for mitigating intra-cell pilot contamination in massive mimo

The spectral efficiency (SE) of Massive MIMO (MaMIMO) systems is affected by low quality channel estimates. Rate-Splitting (RS) has recently gained some interest in multiuser multiple antenna systems as an effective means to mitigate the multi-user interference due to imperfect channel state information. This paper investigates the benefits of RS in the downlink of a single-cell MaMIMO system when all the users use the same pilot sequence for channel estimation. Novel expressions for the SE achieved in the downlink by a single-layer RS strategy (that relies on a single successive interference cancellation at each user side) are derived and used to design precoding schemes and power allocation strategies for common and private messages. Numerical results are used to show that the proposed RS solution achieves higher spectral efficiency that conventional MaMIMO with maximum ratio precoding

Comparison of Bond Character in Hydrocarbons and Fullerenes

We present a comparison of the bond polarizabilities for carbon-carbon bonds in hydrocarbons and fullerenes, using two different models for the fullerene Raman spectrum and the results of Raman measurements on ethane and ethylene. We find that the polarizabilities for single bonds in fullerenes and hydrocarbons compare well, while the double bonds in fullerenes have greater polarizability than in ethylene.Comment: 7 pages, no figures, uses RevTeX. (To appear in Phys. Rev. B.

CydDC-mediated reductant export in Escherichia coli controls the transcriptional wiring of energy metabolism and combats nitrosative stress

The glutathione/cysteine exporter CydDC maintains redox balance in Escherichia coli. A cydD mutant strain was used to probe the influence of CydDC upon reduced thiol export, gene expression, metabolic perturbations, intracellular pH homeostasis, and tolerance to nitric oxide (NO). Loss of CydDC was found to decrease extracytoplasmic thiol levels, whereas overexpression diminished the cytoplasmic thiol content. Transcriptomic analysis revealed a dramatic up-regulation of protein chaperones, protein degradation (via phenylpropionate/phenylacetate catabolism), ?-oxidation of fatty acids, and genes involved in nitrate/nitrite reduction. 1H NMR metabolomics revealed elevated methionine and betaine and diminished acetate and NAD+ in cydD cells, which was consistent with the transcriptomics-based metabolic model. The growth rate and ?pH, however, were unaffected, although the cydD strain did exhibit sensitivity to the NO-releasing compound NOC-12. These observations are consistent with the hypothesis that the loss of CydDC-mediated reductant export promotes protein misfolding, adaptations to energy metabolism, and sensitivity to NO. The addition of both glutathione and cysteine to the medium was found to complement the loss of bd -type cytochrome synthesis in a cydD strain (a key component of the pleiotropic cydDC phenotype), providing the first direct evidence that CydDC substrates are able to restore the correct assembly of this respiratory oxidase. These data provide an insight into the metabolic flexibility of E. coli , highlight the importance of bacterial redox homeostasis during nitrosative stress, and report for the first time the ability of periplasmic low molecular weight thiols to restore haem incorporation into a cytochrome complex

Play, but not observing play, engages rat medial prefrontal cortex

Rats have elaborate cognitive capacities for playing Hide & Seek. Playing Hide & Seek strongly engages medial prefrontal cortex and the activity of prefrontal cortex neurons reflects the structure of the game. We wondered if prefrontal neurons would also show a mirroring of play‐related neural activity. Specifically, we asked how does the activity in the rat medial prefrontal cortex differ when the animal plays itself versus when it observes others playing. Consistent with our previous work, when the animal plays itself we observed medial prefrontal cortex activity that was sharply locked to game events. Observing play, however, did not lead to a comparable activation of rat medial prefrontal cortex. Firing rates during observing play were lower than during real play. The modulation of responses in medial prefrontal cortex by game events was strong during playing Hide & Seek, but weak during observing Hide & Seek. We conclude the rat prefrontal cortex does not mirror play events under our experimental conditions.Peer Reviewe

Electron-phonon interaction in C70

The matrix elements of the deformation potential of C$_{70}$ are calculated by means of a simple, yet accurate solution of the electron-phonon coupling problem in fullerenes, based on a parametrization of the ground state electronic density of the system in terms of $sp^{2+x}$ hybridized orbitals. The value of the calculated dimensionless total electron-phonon coupling constant is $\lambda\approx0.1$, an order of magnitude smaller than in C$_{60}$, consistent with the lack of a superconducting phase transition in C$_{70}$A$_3$ fullerite, and in overall agreement with measurements of the broadening of Raman peaks in C$_{70}$K$_4$. We also calculate the photoemission cross section of C$_{70}^-$, which is found to display less structure than that associated with C$_{60}^-$, in overall agreement with the experimental findings.Comment: To be published in Phys. Rev.

Two pup vocalization types are genetically and functionally separable in deer mice

Vocalization is a widespread vertebrate social behavior that is essential for fitness in the wild. While many vocal behaviors are highly conserved, heritable features of specific vocalization types can vary both within and between species, raising the questions of why and how some vocal behaviors evolve. Here, using new computational tools to automatically detect and cluster vocalizations into distinct acoustic categories, we compare pup isolation calls across neonatal development in eight taxa of deer mice (genusPeromyscus) and compare them to laboratory mice (C57Bl6/j strain) and free-living, wild house mice (Mus musculus musculus). Whereas bothPeromyscusandMuspups produce ultrasonic vocalizations (USVs),Peromyscuspups also produce a second call type with acoustic features, temporal rhythms, and developmental trajectories that are distinct from those of USVs. In deer mice, these tonal and low frequency “cries” are predominantly emitted in postnatal days one through nine, while USVs are primarily made after day nine. Using playback assays, we show that cries result in a more rapid approach byPeromyscusmothers than USVs, suggesting a role for cries in eliciting parental care early in neonatal development. Using genetic crosses between two sister species of deer mice exhibiting large, innate differences in the acoustic structure of cries and USVs, we find that variation in vocalization rate, duration, and pitch display different degrees of genetic dominance and that cry and USV features can be uncoupled in second-generation hybrids. Taken together, this work shows that vocal behavior can evolve quickly between closely related rodent species in which vocalization types, likely serving distinct functions in communication, are controlled by distinct genetic loci