Synthetic Circuits for Feedback and Detection in Bacteria

Synthetic biology, by co-opting molecular machinery from existing organisms, can be used as a tool for building new genetic systems from scratch, for understanding natural networks through perturbation, or for hybrid circuits that piggy-back on existing cellular infrastructure. Although the toolbox for genetic circuits has greatly expanded in recent years, it is still difficult to separate the circuit function from its specific molecular implementation. In this thesis, we discuss the function-driven design of two synthetic circuit modules, and use mathematical models to understand the fundamental limits of circuit topology versus operating regimes as determined by the specific molecular implementation. First, we describe a protein concentration tracker circuit that sets the concentration of an output protein relative to the concentration of a reference protein. The functionality of this circuit relies on a single negative feedback loop that is implemented via small programmable protein scaffold domains. We build a mass-action model to understand the relevant timescales of the tracking behavior and how the input/output ratios and circuit gain might be tuned with circuit components. Second, we design an event detector circuit with permanent genetic memory that can record order and timing between two chemical events. This circuit was implemented using bacteriophage integrases that recombine specific segments of DNA in response to chemical inputs. We simulate expected population-level outcomes using a stochastic Markov-chain model, and investigate how inferences on past events can be made from differences between single-cell and population-level responses. Additionally, we present some preliminary investigations on spatial patterning using the event detector circuit as well as the design of stationary phase promoters for growth-phase dependent activation. These results advance our understanding of synthetic gene circuits, and contribute towards the use of circuit modules as building blocks for larger and more complex synthetic networks.

Gene Expression Noise in Spatial Patterning: hunchback Promoter Structure Affects Noise Amplitude and Distribution in Drosophila Segmentation

Positional information in developing embryos is specified by spatial gradients of transcriptional regulators. One of the classic systems for studying this is the activation of the hunchback (hb) gene in early fruit fly (Drosophila) segmentation by the maternally-derived gradient of the Bicoid (Bcd) protein. Gene regulation is subject to intrinsic noise which can produce variable expression. This variability must be constrained in the highly reproducible and coordinated events of development. We identify means by which noise is controlled during gene expression by characterizing the dependence of hb mRNA and protein output noise on hb promoter structure and transcriptional dynamics. We use a stochastic model of the hb promoter in which the number and strength of Bcd and Hb (self-regulatory) binding sites can be varied. Model parameters are fit to data from WT embryos, the self-regulation mutant hb(14F), and lacZ reporter constructs using different portions of the hb promoter. We have corroborated model noise predictions experimentally. The results indicate that WT (self-regulatory) Hb output noise is predominantly dependent on the transcription and translation dynamics of its own expression, rather than on Bcd fluctuations. The constructs and mutant, which lack self-regulation, indicate that the multiple Bcd binding sites in the hb promoter (and their strengths) also play a role in buffering noise. The model is robust to the variation in Bcd binding site number across a number of fly species. This study identifies particular ways in which promoter structure and regulatory dynamics reduce hb output noise. Insofar as many of these are common features of genes (e. g. multiple regulatory sites, cooperativity, self-feedback), the current results contribute to the general understanding of the reproducibility and determinacy of spatial patterning in early development.

The influence of peripheral afferent signals on the rating of perceived exertion and time to exhaustion during exercise at different intensities

This study determined which peripheral variables would better predict the rating of perceived exertion (RPE) and time to exhaustion (TE) during exercise at different intensities. Ten men performed exercises at first lactate threshold (LT1), second lactate threshold (LT2), 50% of the distance from LT1 to LT2 (TT(50%)), and 25% of the distance from LT2 to maximal power output (TW(25%)). Lactate, catecholamines, potassium, pH, glucose, (V) over dotO(2), VE, HR, respiratory rate (RR) and RPE were measured and plotted against the exercise duration for the slope calculation. Glucose, dopamine, and noradrenaline predicted RPE in TT(50%) (88%), LT2 (64%), and TW(25%) (77%), but no variable predicted RPE in LT1. RPE (55%), RPE+HR (86%), and RPE+RR (92% and 55%) predicted TE in LT1, TT(50%), LT2, and TW(25%), respectively. At intensities from TT(50%) to TW(25%), variables associated with brain activity seem to explain most of the RPE slope, and RPE (+HR and+RR) seems to predict the TE.

Is acute static stretching able to reduce the time to exhaustion at power output corresponding to maximal oxygen uptake?

Samogin Lopes, FA, Menegon, EM, Franchini, E, Tricoli, V, and de M. Bertuzzi, RC. Is acute static stretching able to reduce the time to exhaustion at power output corresponding to maximal oxygen uptake? J Strength Cond Res 24(6): 1650-1656, 2010-This study analyzed the effect of an acute static stretching bout on the time to exhaustion (T(lim)) at power output corresponding to (V) over dotO(2)max. Eleven physically active male subjects (age 22.3 +/- 2.8 years, (V) over dotO(2)max 2.7 +/- 0.5 L . min(-1)) completed an incremental cycle ergometer test, 2 muscle strength tests, and 2 maximal tests to exhaustion at power output corresponding to (V) over dotO(2)max with and without a previous static stretching bout. The T(lim) was not significantly affected by the static stretching (164 +/- 28 vs. 150 +/- 26 seconds with and without stretching, respectively, p = 0.09), but the time to reach (V) over dotO(2)max (118 +/- 22 vs. 102 +/- 25 seconds), blood-lactate accumulation immediately after exercise (10.7 +/- 2.9 vs. 8.0 +/- 1.7 mmol . L(-1)), and oxygen deficit (2.4 +/- 0.9 vs. 2.1 +/- 0.7 L) were significantly reduced (p <= 0.02). Thus, an acute static stretching bout did not reduce T(lim) at power output corresponding to (V) over dotO(2)max possibly by accelerating aerobic metabolism activation at the beginning of exercise. These results suggest that coaches and practitioners involved with aerobic dependent activities may use static stretching as part of their warm-up routines without fear of diminishing high-intensity aerobic exercise performance.

Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller. (C) 2009 Elsevier Ltd. All rights reserved.

Performance analysis of a single-user MISO ultra-wideband time reversal system with DFE

This paper presents an analysis of the performance of a baseband multiple-input single-output (MISO) time reversal ultra-wideband system (TR-UWB) incorporating a symbol spaced decision feedback equalizer (DFE). A semi-analytical performance analysis based on a Gaussian approach is considered, which matched well with simulation results, even for the DFE case. The channel model adopted is based on the IEEE 802.15.3a model, considering correlated shadowing across antenna elements. In order to provide a more realistic analysis, channel estimation errors are considered for the design of the TR filter. A guideline for the choice of equalizer length is provided. The results show that the system`s performance improves with an increase in the number of transmit antennas and when a symbol spaced equalizer is used with a relatively small number of taps compared to the number of resolvable paths in the channel impulse response. Moreover, it is possible to conclude that due to the time reversal scheme, the error propagation in the DFE does not play a role in the system`s performance.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

A Class of Channels Resulting in Ill-Convergence for CMA in Decision Feedback Equalizers

This paper analyzes the convergence of the constant modulus algorithm (CMA) in a decision feedback equalizer using only a feedback filter. Several works had already observed that the CMA presented a better performance than decision directed algorithm in the adaptation of the decision feedback equalizer, but theoretical analysis always showed to be difficult specially due to the analytical difficulties presented by the constant modulus criterion. In this paper, we surmount such obstacle by using a recent result concerning the CM analysis, first obtained in a linear finite impulse response context with the objective of comparing its solutions to the ones obtained through the Wiener criterion. The theoretical analysis presented here confirms the robustness of the CMA when applied to the adaptation of the decision feedback equalizer and also defines a class of channels for which the algorithm will suffer from ill-convergence when initialized at the origin.

Some remarks on static-feedback linearization for time-varying systems

This work summarizes some results about static state feedback linearization for time-varying systems. Three different necessary and sufficient conditions are stated in this paper. The first condition is the one by [Sluis, W. M. (1993). A necessary condition for dynamic feedback linearization. Systems & Control Letters, 21, 277-283]. The second and the third are the generalizations of known results due respectively to [Aranda-Bricaire, E., Moog, C. H., Pomet, J. B. (1995). A linear algebraic framework for dynamic feedback linearization. IEEE Transactions on Automatic Control, 40, 127-132] and to [Jakubczyk, B., Respondek, W. (1980). On linearization of control systems. Bulletin del` Academie Polonaise des Sciences. Serie des Sciences Mathematiques, 28, 517-522]. The proofs of the second and third conditions are established by showing the equivalence between these three conditions. The results are re-stated in the infinite dimensional geometric approach of [Fliess, M., Levine J., Martin, P., Rouchon, P. (1999). A Lie-Backlund approach to equivalence and flatness of nonlinear systems. IEEE Transactions on Automatic Control, 44(5), 922-937]. (C) 2008 Elsevier Ltd. All rights reserved.

Predation and reproductive output of the ladybird beetle Stethorus tridens preying on tomato red spider mite Tetranychus evansi

Predatory behaviour and reproductive output of the ladybird beetle Stethorus tridens Gordon as function of the tomato red spider mite (TRSM), Tetranychus evansi Baker & Pritchard, densities was investigated in the laboratory. Adult female of S. tridens were isolated in cylindrical plastic arenas, containing a leaf disc of Solanum americanum Mill. with 5, 20, 40, 60, 80 or 100 T. evansi nymphs. The number of prey consumed and eggs laid were evaluated daily for ten consecutive days, starting at the oviposition. Oviposition of S. tridens was positively correlated with prey consumption and lower threshold prey consumption for S. tridens laying eggs was 16.3 mites per day. The instantaneous rate of attack (ca. discovery area) and the handling time were 0.0062 h(-1) and 0.83 h, and 0.00254 h(-1) and 0.78 h, respectively, for predators at the 1st- and 10th-oviposition day. The predator exhibited a type II functional response at 1st- and 10th-oviposition day with a maximum consumption per predator of 33 T. evansi nymphs per day at the highest prey density. The ladybird beetle S. tridens is often collected associated with red spider mite colonies on solanaceous wild plants and the results suggest the potential of this ladybird beetle to control T. evansi in tomatoes crops.

An unexpected role for visual feedback in vehicle steering control

Some motor tasks can be completed, quite literally, with our eyes shut. Most people can touch their nose without looking or reach for an object after only a brief glance at its location. This distinction leads to one of the defining questions of movement control: is information gleaned prior to starting the movement sufficient to complete the task (open loop), or is feedback about the progress of the movement required (closed loop)? One task that has commanded considerable interest in the literature over the years is that of steering a vehicle, in particular lane-correction and lane-changing tasks. Recent work has suggested that this type of task can proceed in a fundamentally open loop manner [1 and 2], with feedback mainly serving to correct minor, accumulating errors. This paper reevaluates the conclusions of these studies by conducting a new set of experiments in a driving simulator. We demonstrate that, in fact, drivers rely on regular visual feedback, even during the well-practiced steering task of lane changing. Without feedback, drivers fail to initiate the return phase of the maneuver, resulting in systematic errors in final heading. The results provide new insight into the control of vehicle heading, suggesting that drivers employ a simple policy of “turn and see,” with only limited understanding of the relationship between steering angle and vehicle heading.

Frequency stabilised grating feedback laser diode for atom cooling applications

The free running linewidth of an external cavity grating feedback diode laser is on the order of a few megahertz and is limited by the mechanical and acoustic vibrations of the external cavity. Such frequency fluctuations can be removed by electronic feedback. We present a hybrid stabilisation technique that uses both a Fabry-Perot confocal cavity and an atomic resonance to achieve excellent short and long term frequency stability. The system has been shown to reduce the laser linewidth of an external cavity diode laser by an order of magnitude to 140 kHz, while limiting frequency excursions to 60 kHz relative to an absolute reference over periods of several hours. The scheme also presents a simple way to frequency offset two lasers many gigahertz apart which should find a use in atom cooling experiments, where hyperfine ground-state frequency separations are often required.

Tension regulation during lengthening and shortening actions of the human soleus muscle

In the present study we investigated tension regulation in the human soleus (SOL) muscle during controlled lengthening and shortening actions. Eleven subjects performed plantar flexor efforts on an ankle torque motor through 30 degrees of ankle displacement (75 degrees-105 degrees internal ankle angle) at lengthening and shortening velocities of 5, 15 and 30 degrees s(-1). To isolate the SOL from the remainder of the triceps surae, the subject's knee was flexed to 60 degrees during all trials. Voluntary plantar flexor efforts were performed under two test conditions: (1) maximal voluntary activation (MVA) of the SOL, and (2) constant submaximal voluntary activation (SVA) of the SOL. SVA trials were performed with direct visual feedback of the SOL electromyogram (EMG) at a level resulting in a torque output of 30% of isometric maximum. Angle-specific (90 degrees ankle angle) torque and EMG of the SOL, medial gastrocnemius (MG) and tibialis anterior (TA) were recorded. In seven subjects from the initial group, the test protocol was repeated under submaximal percutaneous electrical activation (SEA) of SOL (to 30% isometric maximal effort). Lengthening torques were significantly greater than shortening torques in all test conditions. Lengthening torques in MVA and SVA were independent of velocity and remained at the isometric level, whereas SEA torques were greater than isometric torques and increased at higher lengthening velocities. Shortening torques were lower than the isometric level for all conditions. However, whereas SVA and SEA torques decreased at higher velocities of shortening, MVA torques were independent of velocity. These results indicate velocity- and activation-type-specific tension regulation in the human SOL muscle.