Robust stability of linear systems: Some computational considerations

The cases of both additive and multiplicative perturbations were discussed and a number of relationships between the two cases were given. A number of computational aspects of the theory were also discussed, including a proposed new method for evaluating general transfer or frequency response matrices. The new method is numerically stable and efficient, requiring only operations to update for new values of the frequency parameter

Analysis techniques for multivariate root loci

Analysis and techniques are developed for the multivariable root locus and the multivariable optimal root locus. The generalized eigenvalue problem is used to compute angles and sensitivities for both types of loci, and an algorithm is presented that determines the asymptotic properties of the optimal root locus

Photonic band-gap properties for two-component slow light

We consider two-component "spinor" slow light in an ensemble of atoms coherently driven by two pairs of counterpropagating control laser fields in a double tripod-type linkage scheme. We derive an equation of motion for the spinor slow light (SSL) representing an effective Dirac equation for a massive particle with the mass determined by the two-photon detuning. By changing the detuning the atomic medium acts as a photonic crystal with a controllable band gap. If the frequency of the incident probe light lies within the band gap, the light tunnels through the sample. For frequencies outside the band gap, the transmission probability oscillates with increasing length of the sample. In both cases the reflection takes place into the complementary mode of the probe field. We investigate the influence of the finite excited state lifetime on the transmission and reflection coefficients of the probe light. We discuss possible experimental implementations of the SSL using alkali atoms such as Rubidium or Sodium.Comment: 7 figure

Selection and Certification of TPS: Constraints and Considerations of Venus Missions

This presentation was part of the session : Probe Missions to the Giant Planets, Titan and VenusSixth International Planetary Probe WorkshopThe science community currently has interest in planetary entry probe missions to improve our understanding of the atmosphere of Saturn [1], missions to Venus and also sample return missions from comets and asteroids. In addition, the In-Space Propulsion Program has completed aerocapture mission design studies that have defined the requirements for the Thermal protection System (TPS) to Venus, Mars, Titan and Neptune. There have been investments in new TPS materials and to revive flight qualified materials such as PICA (used on Stardust and currently baselined for MSL and Orion) and Carbon-Phenolic, the TPS material of choice for Venus and Outer Planet missions. Mission studies have shown the heating rates for the "shallow" Saturn probes are in the range of (2 - 5) KW/cm2 in its H(2)/He atmosphere. Venus entry probes will experience heat fluxes in the similar range of (3 - 7) kW/cm(2) in CO2. High-speed Earth reentry missions from comets and asteroids will experience heating of the range of (1 - 5) kW/cm(2) and at pressures equal to or higher than Stardust. Aerocapture during Venus missions will experience heat fluxes in the range of (2 - 4) kW/cm(2) in CO2. Titan aero-capture missions will experience far smaller heating fluxes in the N2/methane atmosphere. Since the flight times are longer during aerocapture missions, TPS design requirements involve much larger heatloads at relatively lower heat-fluxes compared to those for direct entry probe missions. It is clear that qualification and certification of the heritage ablative materials or the development of new, ablative Thermal Protection System (TPS) materials for entry or aerocapture probe missions is needed [2] and the challenges are in testing, especially in the appropriate atmospheric gases. NASA Ames has nearly completed the construction of a small, low cost, 5 MW arc jet facility, called the Development Arcjet Facility (DAF) that will permit testing of small models at high heat fluxes and in different gases. This paper will review the entry conditions from a collection of mission studies to various solar system destinations, the testing needs of both newer as well as heritage TPS for each destination and provide the approach, we at NASA Ames plan to adopt, in testing and analysis by making use of both existing arc jet facilities as well as an affordable, small 5 MW arc jet that can be used for TPS development in test gases appropriate for the Neptune, Titan, Saturn, Venus or Earth applications. [1] Atreya, S. K., et. al. "Formation of Giant Planets and Their Atmospheres: Entry Probes for Saturn and Beyond; 5 th International Planetary Probe Workshop, June 25-29, Bordeaux, France. [2] Venkatapathy, E. and Laub, B. "Requirements for Development of Thermal Protection Systems for Multiple Missions: 5th International Planetary Probe Workshop, June 25-29, Bordeaux, France.NASA In-Space Propulsion Progra

The statistical mechanics of complex signaling networks : nerve growth factor signaling

It is becoming increasingly appreciated that the signal transduction systems used by eukaryotic cells to achieve a variety of essential responses represent highly complex networks rather than simple linear pathways. While significant effort is being made to experimentally measure the rate constants for individual steps in these signaling networks, many of the parameters required to describe the behavior of these systems remain unknown, or at best, estimates. With these goals and caveats in mind, we use methods of statistical mechanics to extract useful predictions for complex cellular signaling networks. To establish the usefulness of our approach, we have applied our methods towards modeling the nerve growth factor (NGF)-induced differentiation of neuronal cells. Using our approach, we are able to extract predictions that are highly specific and accurate, thereby enabling us to predict the influence of specific signaling modules in determining the integrated cellular response to the two growth factors. We show that extracting biologically relevant predictions from complex signaling models appears to be possible even in the absence of measurements of all the individual rate constants. Our methods also raise some interesting insights into the design and possible evolution of cellular systems, highlighting an inherent property of these systems wherein particular ''soft'' combinations of parameters can be varied over wide ranges without impacting the final output and demonstrating that a few ''stiff'' parameter combinations center around the paramount regulatory steps of the network. We refer to this property -- which is distinct from robustness -- as ''sloppiness.''Comment: 24 pages, 10 EPS figures, 1 GIF (makes 5 multi-panel figs + caption for GIF), IOP style; supp. info/figs. included as brown_supp.pd

Translational control of the SigR-directed oxidative stress response in streptomyces via IF3-mediated repression of a noncanonical GTC start codon

The major oxidative stress response in Streptomyces is controlled by the sigma factor SigR and its cognate antisigma factor RsrA, and SigR activity is tightly controlled through multiple mechanisms at both the transcriptional and posttranslational levels. Here we show that sigR has a highly unusual GTC start codon and that this leads to another level of SigR regulation, in which SigR translation is repressed by translation initiation factor 3 (IF3). Changing the GTC to a canonical start codon causes SigR to be overproduced relative to RsrA, resulting in unregulated and constitutive expression of the SigR regulon. Similarly, introducing IF3* mutations that impair its ability to repress SigR translation has the same effect. Thus, the noncanonical GTC sigR start codon and its repression by IF3 are critical for the correct and proper functioning of the oxidative stress regulatory system. sigR and rsrA are cotranscribed and translationally coupled, and it had therefore been assumed that SigR and RsrA are produced in stoichiometric amounts. Here we show that RsrA can be transcribed and translated independently of SigR, present evidence that RsrA is normally produced in excess of SigR, and describe the factors that determine SigR-RsrA stoichiometry.IMPORTANCE In all sigma factor-antisigma factor regulatory switches, the relative abundance of the two proteins is critical to the proper functioning of the system. Many sigma-antisigma operons are cotranscribed and translationally coupled, leading to a generic assumption that the sigma and antisigma factors are produced in a fixed 1:1 ratio. In the case of sigR-rsrA, we show instead that the antisigma factor is produced in excess over the sigma factor, providing a buffer to prevent spurious release of sigma activity. This excess arises in part because sigR has an extremely rare noncanonical GTC start codon, and as a result, SigR translation initiation is repressed by IF3. This finding highlights the potential significance of noncanonical start codons, very few of which have been characterized experimentally. It also emphasizes the limitations of predicting start codons using bioinformatic approaches, which rely heavily on the assumption that ATG, GTG, and TTG are the only permissible start codons

Identification of direct residue contacts in protein-protein interaction by message passing

Understanding the molecular determinants of specificity in protein-protein interaction is an outstanding challenge of postgenome biology. The availability of large protein databases generated from sequences of hundreds of bacterial genomes enables various statistical approaches to this problem. In this context covariance-based methods have been used to identify correlation between amino acid positions in interacting proteins. However, these methods have an important shortcoming, in that they cannot distinguish between directly and indirectly correlated residues. We developed a method that combines covariance analysis with global inference analysis, adopted from use in statistical physics. Applied to a set of >2,500 representatives of the bacterial two-component signal transduction system, the combination of covariance with global inference successfully and robustly identified residue pairs that are proximal in space without resorting to ad hoc tuning parameters, both for heterointeractions between sensor kinase (SK) and response regulator (RR) proteins and for homointeractions between RR proteins. The spectacular success of this approach illustrates the effectiveness of the global inference approach in identifying direct interaction based on sequence information alone. We expect this method to be applicable soon to interaction surfaces between proteins present in only 1 copy per genome as the number of sequenced genomes continues to expand. Use of this method could significantly increase the potential targets for therapeutic intervention, shed light on the mechanism of protein-protein interaction, and establish the foundation for the accurate prediction of interacting protein partners.Comment: Supplementary information available on http://www.pnas.org/content/106/1/67.abstrac

Microstructural enrichment functions based on stochastic Wang tilings

This paper presents an approach to constructing microstructural enrichment functions to local fields in non-periodic heterogeneous materials with applications in Partition of Unity and Hybrid Finite Element schemes. It is based on a concept of aperiodic tilings by the Wang tiles, designed to produce microstructures morphologically similar to original media and enrichment functions that satisfy the underlying governing equations. An appealing feature of this approach is that the enrichment functions are defined only on a small set of square tiles and extended to larger domains by an inexpensive stochastic tiling algorithm in a non-periodic manner. Feasibility of the proposed methodology is demonstrated on constructions of stress enrichment functions for two-dimensional mono-disperse particulate media.Comment: 27 pages, 12 figures; v2: completely re-written after the first revie

Pulsed Feedback Defers Cellular Differentiation

Environmental signals induce diverse cellular differentiation programs. In certain systems, cells defer differentiation for extended time periods after the signal appears, proliferating through multiple rounds of cell division before committing to a new fate. How can cells set a deferral time much longer than the cell cycle? Here we study Bacillus subtilis cells that respond to sudden nutrient limitation with multiple rounds of growth and division before differentiating into spores. A well-characterized genetic circuit controls the concentration and phosphorylation of the master regulator Spo0A, which rises to a critical concentration to initiate sporulation. However, it remains unclear how this circuit enables cells to defer sporulation for multiple cell cycles. Using quantitative time-lapse fluorescence microscopy of Spo0A dynamics in individual cells, we observed pulses of Spo0A phosphorylation at a characteristic cell cycle phase. Pulse amplitudes grew systematically and cell-autonomously over multiple cell cycles leading up to sporulation. This pulse growth required a key positive feedback loop involving the sporulation kinases, without which the deferral of sporulation became ultrasensitive to kinase expression. Thus, deferral is controlled by a pulsed positive feedback loop in which kinase expression is activated by pulses of Spo0A phosphorylation. This pulsed positive feedback architecture provides a more robust mechanism for setting deferral times than constitutive kinase expression. Finally, using mathematical modeling, we show how pulsing and time delays together enable “polyphasic” positive feedback, in which different parts of a feedback loop are active at different times. Polyphasic feedback can enable more accurate tuning of long deferral times. Together, these results suggest that Bacillus subtilis uses a pulsed positive feedback loop to implement a “timer” that operates over timescales much longer than a cell cycle