Octopamine effects mimick state-dependent changes in a proprioceptive feedback system

The modulatory actions of the biogenic amine octopamine on the femur tibia (FT) control loop in the stick insect Carausius morosus were examined. The response properties of the FT control loop were determined under open loop conditions. Mechanical stimulation of the femoral chordotonal organ (fCO) was the input and tibial movement and motoneuronal activity were measured as the output of the system. Following octopamine injection into the hemolymph of intact, inactive animals, two consecutive phases occurred at the behavioral level. Octopamine caused initially an activation of the animal. During this first phase (3.5–12 min duration) the response properties of the FT control loop were similar to those found in animals that were activated by tactile stimuli under normal conditions. Afterward, animals became inactive. During this second phase (15–20 min duration), the gain of the control loop was zero and no resistance reflex in the FT joint was generated in response to fCO stimulation. However, active movements of the tibia could still be elicited. As we could show in restrained animals, where dl-octopamine was applied topically onto the undesheated mesothoracic ganglion, the complete suppression of the resistance reflex on the motoneuronal level was dose dependent starting at concentrations of 5 ± 10^?3 M octopamine. We could show that octopamine specifically suppressed the pathways involved in the resistance reflex, while feedback loop responses to fCO stimuli typical for active animals could still be elicited. Our results indicate that an increase in the octopamine concentration mimicks activation of the animal: Properties being characteristic for the control of the FT joint in the inactive animal are inhibited by octopamine, while properties of the FT control loop typical for the active animal appear to be facilitated following octopamine injection. The results clearly demonstrate that different pathways in the neuronal network underlying the FT control loop are involved in the responses of the control loop to fCO stimuli in the inactive and active behavioral states of the stick insect. © 1993 John Wiley & Sons, Inc.     

Designing dynamical output feedback controllers for store-operated Ca entry

Store-operated calcium entry (SOCE) has been proposed as the main process controlling Ca²⁺ entry in non-excitable cells. Although recent breakthroughs in experimental studies of SOCE have been made, its mathematical modeling has not been developed. In the present work, SOCE is viewed as a feedback control system subject to an extracellular agonist disturbance and an extracellular calcium input. We then design a dynamic output feedback controller to reject the disturbance and track Ca²⁺ resting levels in the cytosol and the endoplasmic reticulum (ER). The constructed feedback control system is validated by published experimental data and its global asymptotic stability is proved by using the LaSalle’s invariance principle. We then simulate the dynamic responses of STIM1 and Orai1, two major components in the operation of the store-operated channels, to the depletion of Ca²⁺ in the ER with thapsigargin, which show that: (1) Upon the depletion of Ca²⁺ in the ER, the concentrations of activated STIM1 and STIM1-Orai1 cluster are elevated gradually, indicating that STIM1 is accumulating in the ER-PM junctions and that the cytosolic portion of the active STIM1 is binding to Orai1 and driving the opening of CRAC channels for Ca²⁺ entry; (2) after the extracellular Ca²⁺ addition, the concentrations of both STIM1 and STIM1-Orai1 cluster decrease but still much higher than the original levels. We also simulate the system responses to the agonist disturbance, which show that, when a sequence of periodic agonist pulses is applied, the system returns to its equilibrium after each pulse. This indicates that the designed feedback controller can reject the disturbance and track the equilibrium.     

Adaptive control for insect leg position: controller properties depend on substrate compliance

This paper concentrates on the system that controls the femur-tibia joint in the legs of the stick insect, Carausius morosus. Earlier investigations have shown that this joint is subject to a mixture of proportional and differential control whereby the differential part plays a prominent role. Experiments presented here suggest another interpretation: single legs of a stick insect were systematically perturbed using devices of different compliance and compensatory forces and movements monitored. When the compliance is high (soft spring), forces are generated that return the leg close to its original position. When the compliance is low (stiff spring), larger forces are generated but sustained changes in position occur that are proportional to the force that is applied. Selective ablation of leg sense organs showed that the leg did not maintain its position after elimination of afferents of the femoral chordotonal organ. Ablation of leg campaniform sensilla had no effect. These data support the idea that different control strategies are used, depending upon substrate compliance. In particular, what we and other authors have called a differential controller, is now considered as an integral controller that intelligently gives up when the correlation between motor output and movement of the leg is low.We would like to dedicate this article to Prof. Dr. Ulrich Bässler. Starting in the 1960s, his seminal work stimulated a long series of fruitful studies that, even today, reveal exciting insights into motor control.     

A model for improving microbial biofuel production using a synthetic feedback loop

Cells use feedback to implement a diverse range of regulatory functions. Building synthetic feedback control systems may yield insight into the roles that feedback can play in regulation since it can be introduced independently of native regulation, and alternative control architectures can be compared. We propose a model for microbial biofuel production where a synthetic control system is used to increase cell viability and biofuel yields. Although microbes can be engineered to produce biofuels, the fuels are often toxic to cell growth, creating a negative feedback loop that limits biofuel production. These toxic effects may be mitigated by expressing efflux pumps that export biofuel from the cell. We developed a model for cell growth and biofuel production and used it to compare several genetic control strategies for their ability to improve biofuel yields. We show that controlling efflux pump expression directly with a biofuel-responsive promoter is a straightforward way of improving biofuel production. In addition, a feed forward loop controller is shown to be versatile at dealing with uncertainty in biofuel production rates.     

A dynamic model of thoracic differentiation for the control of turning in the stick insect

Leg movements of stick insects (Carausius morosus) making turns towards visual targets are examined in detail, and a dynamic model of this behaviour is proposed. Initial results suggest that front legs shape most of the body trajectory, while the middle and hind legs just follow external forces (Rosano H, Webb B, in The control of turning in real and simulated stick insects, vol. 4095, pp 145–156, 2006). However, some limitations of this explanation and dissimilarities in the turning behaviour of the insect and the model were found. A second set of behavioural experiments was made by blocking front tarsi to further investigate the active role of the other legs for the control of turning. The results indicate that it is necessary to have different roles for each pair of legs to replicate insect behaviour. We demonstrate that the rear legs actively rotate the body while the middle legs move sideways tangentially to the hind inner leg. Furthermore, we show that on average the middle inner and hind outer leg contribute to turning while the middle outer leg and hind inner leg oppose body rotation. These behavioural results are incorporated into a 3D dynamic robot simulation. We show that the simulation can now replicate more precisely the turns made by the stick insect. This work was supported by CONACYT México and the European Commission under project FP6-2003-IST2-004690 SPARK.     

A feedback control system for the precise and continuous regulation of photosynthetic photon flux density

A simple and inexpensive feedback control system that provides continuous and precise control of photosynthetic photon flux density (PPFD) in a whole plant cuvette is described. A ‘Plexiglass’ tank is interposed between a light source and cuvette and PPFD changed by varying the level of dyed liquid in the tank. The amount of liquid pumped into or drained from the tank is a function of the difference (error) between a defined set point value of PPFD and that measured in the cuvette. The set point can be varied as a function of time, can follow the output of a quantum sensor measuring ambient PPFD or can be driven by values of PPFD read from a data file. Within the 0.4 to 0.64 μm waveband, the dye acts as a neutral density filter so that there is no change in spectral distribution with PPFD. Photosynthetic photon flux density in the cuvette was controlled to better than 20 μmol m⁻²s⁻¹ when the set point was varied from 200 to 1100 μmol m⁻²s⁻¹ over 3 min. When the set point was held constant or changed less rapidly, errors did not exceed 5 μmol m⁻²s⁻¹. Net photosynthesis of Western redcedar (Thuja plicata Donn.) seedlings held at 18 °C closely followed rapid changes in PPFD.     

Adrenergic neurons and short proprioceptive feedback loops involved in the integration of cardiac function in the rat

Summary Serial cryostat and paraffin-embedded sections through the atrioventricular junction of the rat heart were studied at the light-microscopic level after indirect immunohistochemical staining (tyrosine hydroxylase, neuropeptide Y, C-terminal flanking peptide of neuropeptide Y immunoreactivities) or silver impregnation. The distribution of these immunoreactivities in the Hissian ganglion (Moravec and Moravec 1984) as well as the relationships of the Hissian ganglion cells with the surrounding structures have been studied to assess its function. The results suggest that the Hissian ganglion is composed of large multipolar neurons displaying both tyrosine hydroxylase (TH) and related peptide (neuropeptide Y, C-terminal flanking peptide of neuropeptide Y) immunoreactivities. The dendritic projections of these adrenergic cells penetrate the reticular portion of the atrioventricular node and the upper segments of the interventricular septum where they constitute sensory-like corpuscles. The hypothesis that the adrenergic neurons of the atrioventricular junction are involved in short proprioceptive feedback loops necessary for beat-to-beat modulation of cardiac excitability and intracardiac conduction can thus be suggested.     

A flight cylinder bioassay as a simple,effective quality control test for Cydia pomonella

Assessment of quality of the sterile male insects that are being mass‐reared for release in area‐wide integrated pest management programmes that include a sterile insect technique component is crucial for the success of these programmes. Routine monitoring of sterile male quality needs to be carried out both in the mass‐rearing facility and in the field. Simple bioassays that can be conducted in the laboratory and that would be surrogates for laborious field tests would be a very cost‐effective way of monitoring sterile male field performance. Simple flight cylinders were used to assess whether these could detect differences in quality of male codling moth Cydia pomonella. The number of male and female codling moths that flew out of the cylinders was influenced by cylinder diameter, cylinder height and number of hours following the initiation of the test. The flight cylinder bioassay was capable of detecting differences in quality of codling moths induced by irradiation when moths were shipped, but no differences were found in flight ability when the moths were not transported. The tests also confirmed that handling and shipment reduced quality more for irradiated than for non‐treated codling moth, and that insect quality was significantly influenced by larval rearing protocols. The flight cylinder bioassay was therefore successful in detecting differences in codling moth quality induced by various treatments that had been identified previously by more complex laboratory bioassays and field trials. Treatment differences were most likely detected when flight cylinders were 16 cm high.     

Extracellular pH is under circadian control in Gonyaulax polyedra and forms a metabolic feedback loop

This study investigates the relationship between the circadian clock and metabolism based on recordings of the extracellular pH in cultures of the marine dinoflagellate, Gonyaulax polyedra. In light-dark cycles, pH of the medium rises during the light phase and declines in the dark. The amplitude of this pH-rhythm correlates with light intensity, indicating photosynthesis (and respiration) as the driving force. The recorded extracellular pH changes probably reflect the need to control intracellular pH in spite of pH-modifying reactions. The daily pH-changes are under control of the circadian clock because they continue to oscillate with a circa-24 h period in constant light, albeit with a smaller amplitude. Similar to other circadian output rhythms, the pH rhythm depends (amplitude and phase) on nitrate levels in the medium. Both the bioluminescence and the pH rhythm can also be shifted by extracellular pH-changes although Gonyaulax is rarely exposed to significant pH changes in its marine ecosystems (except for highly dense algal blooms). Because intracellular proton levels are both affecting circadian input and output they form a feedback loop with the Gonyaulax circadian system indicating complex interactions between metabolism and the circadian clock.     

Domain interaction in cyanobacterial phytochromes as a prerequisite for spectral integrity

Two phytochromes, CphA and CphB, from the cyanobacterium Calothrix PCC7601, with similar size (768 and 766 amino acids) and domain structure, were investigated for the essential length of their protein moiety required to maintain the spectral integrity. Both proteins fold into PAS-, GAF-, PHY-, and Histidine-kinase (HK) domains. CphA binds a phycocyanobilin (PCB) chromophore at a “canonical” cysteine within the GAF domain, identically as in plant phytochromes. CphB binds biliverdin IXα at cysteine24, positioned in the N-terminal PAS domain. The C-terminally located HK and PHY domains, present in both proteins, were removed subsequently by introducing stop-codons at the corresponding DNA positions. The spectral properties of the resulting proteins were investigated. The full-length proteins absorb at (CphA) 663 and 707 nm (red-, far red-absorbing P _r and P _fr forms of phytochromes) and at (CphB) 704 and 750 nm. Removal of the HK domains had no effect on the absorbance maxima of the resulting PAS–GAF–PHY constructs (CphA: 663/707 nm, CphB: 704/750 nm, P _r/P _fr, respectively). Further deletion of the “PHY” domains caused a blue-shift of the P _r and P _fr absorption of CphA (λ _max: 658/698 nm) and increased the amount of unproperly folded apoprotein, seen by a reduced capability to bind the chromophore in photoconvertible manner. In CphB, however, it practically impaired the formation of P _fr, i.e., showing a very low oscillator strength absorption band, whereas the P _r form remains unchanged (702 nm). This finding clearly indicates a different interaction between domains in the “typical”, PCB binding and in the biliverdin-binding phytochromes, and demonstrates a loss of oscillator strength for the latter, most probably due to a strong conformational distortion of the chromophore in the CphB P _fr form. Proceedings of the XVIII Congress of the Italian Society of Pure and Applied Biophysics (SIBPA), Palermo, Sicily, September 2006.     

Characterisation of Rubus niveus: a prerequisite to its biological control in oceanic islands

This study is intended to inform the search for a biocontrol solution to stem the spread of Rubus niveus, a morphologically-diverse and invasive Rubus species which has become an aggressive invader in areas of the world outside its native range. The fragile biodiversity of islands can be especially threatened by this plant – exemplars of this are the Galápagos archipelago and Hawaii. This report focuses on the morphological and molecular work carried out to establish the homogeneity or intra-specific variation of R. niveus populations within the Galápagos Islands, as well as their kinship with plants of the same name found in Asia. The premise of this study is that genetic closeness between these populations offers increased probability that pathogens of R. niveus in its native range will also provide effective control in the target environment. Increased knowledge of the genetic make-up of R. niveus in both its native and naturalised locations will also help to assess the feasibility of using organisms which have been found to be effective against other Rubus species, but not hitherto considered for R. niveus itself.     

A method for testing the stability of a steady-state system during the calculation of a response to large changes in regulator concentrations

A modification of the ‘finite decomposition’ method (Crabtree and Newsholme (1985) Curr. Top. Cell. Regul. 25, 21–76) for calculating physiological responses from sensitivities is described, to enable the system to be tested for stability at each step of the procedure. Instability is indicated by a change of sign of the determinant of the square matrix (N) in the governing equation for the system. The method cannot be used to predict responses beyond any step at which instability occurs.     

Analysis of protein synthesis dynamic model in eukaryotic cells: Input control

This paper presents the analysis of initiation control model of protein synthesis via eukaryotic initiation factor (eIF)-2 unit, introduced by [N.S. Bar, D.R. Morris, Dynamic model of the process of protein synthesis in eukaryoric cells, Bulletin of Mathematical Biology 69 (2007) 361-393, doi:10.1007/s11538-006-9128-2.] and propose methods to control it.Linearization of the model is presented as a measure to simplify the analysis and control application. The properties of the linear model were investigated and compared to the non-linear model using simulations. It was shown that the linear model is (marginally) stable and the states converge to a finite value. Linear optimal control theory can then be applied to the model under the value range where the linearized model is accurate. The effect of the input signals GCN2·tRNA and eIF-2 on the non-linear system was investigated. A few characteristics known from in vitro experiments of the initiation process were proven from a mathematical aspect and some conclusions about the function of the initiation complexes such as eIF2B and the ternary complex were derived. Consistent with published experiments, it was shown that overexpression of eIF-2 increases the concentration of 48S initiation complex and promote initiation rate. A state feedback control was applied in order to manipulate the initiation rate and it was proven that the 48S initiation complex can be driven to a desired value by calculating an input control law using measurement techniques available today. If this strategy can be implemented de facto, then a genuine control on protein synthesis process can be obtained.     

Negative feedback predominates over cross-regulation to control ERK MAPK activity in response to FGF signalling in embryos

Expression of the gene encoding the MKP-3/Pyst1 protein phosphatase, which inactivates ERK MAPK, is induced by FGF. However, which intracellular signalling pathway mediates this expression is unclear, with essential roles proposed for both ERK and PI(3)K in chick embryonic limb. Here, we report that MKP-3/Pyst1 expression is sensitive to inhibition of ERK or MAPKK, that endogenous MKP-3/Pyst1 co-localizes with activated ERK, and expression of MKP-3/Pyst1 in mice lacking PDK1, an essential mediator of PI(3)K signalling. We conclude that MKP-3/Pyst1 expression is mediated by ERK activation and that negative feedback control predominates in limiting the extent of FGF-induced ERK activity.     

Optimal choice between feedforward and feedback control in gene expression to cope with unpredictable danger

All organisms face risks of unpredictable danger caused by harmful physical environments, pathogens, parasites or predators. Organisms may have several alternative ways of coping with such dangers. These differ in cost, effectiveness and activation time. We study the conditions under which it is optimal to use different alternatives for damage control. As an example we consider a microbe (such as E. coli), which may experience heat shocks that cause denaturation of proteins in the cell. To restore the denatured proteins the organism produces heat-shock proteins (HSP). There are two different pathways for production of HSP. Some HSP are produced immediately after a heat shock (feedforward control), but additional HSP may be produced thereafter, stimulated by the presence of denatured proteins (feedback control). Feedforward is based solely on heat-shock intensity without accurate information on the resulting amount of denatured proteins. We examine the optimal combination of the two pathways that minimizes the sum of the damage caused by the presence of untreated denatured proteins and the production cost of HSP. The optimal response depends on the time delay for feedback control, the effectiveness of HSP in processing denatured proteins, the production cost of HSP, the severity of damage by denatured proteins and the probability distribution of the abundance of denatured protein conditional on heat-shock intensity. We find that feedforward control should always be used. Additional HSP may be produced by feedback control when the abundance of denatured protein is large whilst no feedback control should be used when it is small. All the HSP are produced by feedforward control when the maximum is close to the mean of denatured protein abundance conditional on the heat-shock intensity.     

Normal mode analysis as a prerequisite for drug design: application to matrix metalloproteinases inhibitors

We demonstrate the utility of normal mode analysis in correctly predicting the binding modes of inhibitors in the active sites of matrix metalloproteinases (MMPs). We show the accuracy in predicting the positions of MMP-3 inhibitors is strongly dependent on which structure is used as the target, especially when it has been energy minimized. This dependency can be overcome by using intermediate structures generated along one of the normal modes previously calculated for a given target. These results may be of prime importance for further in silico drug discovery.     

A mathematical modelling framework for elucidating the role of feedback control in translation termination

Translation is the final stage of gene expression where messenger RNA is used as a template for protein polymerization from appropriate amino acids. Release of the completed protein requires a release factor protein acting at the termination/stop codon to liberate it. In this paper we focus on a complex feedback control mechanism involved in the translation and synthesis of release factor proteins, which has been observed in different systems. These release factor proteins are involved in the termination stage of their own translation. Further, mutations in the release factor gene can result in a premature stop codon. In this case translation can result either in early termination and the production of a truncated protein or readthrough of the premature stop codon and production of the complete release factor protein. Thus during translation of the release factor mRNA containing a premature stop codon, the full length protein negatively regulates its production by its action on a premature stop codon, while positively regulating its production by its action on the regular stop codon. This paper develops a mathematical modelling framework to investigate this complex feedback control system involved in translation. A series of models is established to carefully investigate the role of individual mechanisms and how they work together. The steady state and dynamic behaviour of the resulting models are examined both analytically and numerically.