Delayed feedback control for a chemostat model

In this paper, we discuss asymptotic properties and numerical simulations of a chemostat model with delayed feedback control. A chemostat model with two organisms can be made coexistent by feedback control of the dilution rate which depends affinely on the concentrations of two organisms [P. De Leenher, H.L. Smith, Feedback control for chemostat models, J. Math. Biol. 46 (2003) 48]. Then the coexistence takes its simplest form; the equilibrium point in the non-negative orthant is globally asymptotically stable. We show that stability of the equilibrium point is changed by 'time-delay' caused in controlling the dilution rate after measuring the concentrations of two organisms.     

Neural control of Caenorhabditis elegans forward locomotion: the role of sensory feedback

This paper presents a simple yet biologically-grounded model for the neural control of Caenorhabditis elegans forward locomotion. We identify a minimal circuit within the C. elegans ventral cord that is likely to be sufficient to generate and sustain forward locomotion in vivo. This limited subcircuit appears to contain no obvious central pattern generated control. For that subcircuit, we present a model that relies on a chain of oscillators along the body which are driven by local and proximate mechano-sensory input. Computer simulations were used to study the model under a variety of conditions and to test whether it is behaviourally plausible. Within our model, we find that a minimal circuit of AVB interneurons and B-class motoneurons is sufficient to generate and sustain fictive forward locomotion patterns that are robust to significant environmental perturbations. The model predicts speed and amplitude modulation by the AVB command interneurons. An extended model including D-class motoneurons is included for comparison. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. John Bryden and Netta Cohen contributed equally to this work.     

Neuroendocrine control of thyroid secretion in living systems: A feedback control system model

A model of the regulation of thyroid hormone in the bloodstream of living systems is formulated and analyzed. The portion of this model defined as theregulator includes components representing the thyroid, anterior pituitary and hypothalamic organs and their intercommunicating channels, that is, the peripheral plasma and hypophysial portal circulations and certain neuro-secretory connections. The loss of hormones from the plasma in the living system associated with physiological mechanisms within the peripheral tissue space and the excretory pathways is represented in the model by a lumpedload on the regulator. The model is reduced to a system of differential equations involving eleven parameters and variables, all of which are identified with certain physiological structures and states. Five of these are currently observable by available laboratory techniques and two others are computable explicity from the equations of the model; the remaining four can be computed in the same way to within a multiplicative constant. Procedires for carrying out ten of these measurements and calculations are suggested. On the basis of the equations and parameters of the model, a discussion of the normal behavior and the response of this system to certain types of disturbances is presented. A systematic effort has been made in the development of this model to include all relevant physiological data and relationships reported in the biological literature. A summary of this literature, reflecting the views and interpretations made by the authors of this paper, is included for completeness and ease of reference.     

An age-dependent feedback control model of calcium dynamics in yeast cells

The functional decline of selected proteins or organelles leads to aging at the intracellular level. Identification of these proteins or organelles is usually challenging to traditional single-factor approaches since these factors are inter-connected via feedback or feedforward controls. Establishing a feedback control model to simulate the interactions of multiple factors is an insightful approach to guide the search for proteins involved in aging. However, there are only a few mathematical models describing the age-dependent accumulation of DNA mutations, which are directly or indirectly induced by deterioration of the intracellular environment including alteration of calcium homeostasis, a contributor of aging. Thus, based on Cui and Kaandorp’s model, we develop an age-dependent mathematical model for the calcium homeostasis in budding yeast Saccharomyces cerevisiae. Our model contains cell cycle-dependent aging factors and can qualitatively reproduce calcium shocks and calcium accumulations in cells observed in experiments. Using this model, we predict calcium oscillations in wild type, pmc1Δ, and pmr1Δ cells. This prediction suggests that Pmr1p plays a major role in regulating cytosolic calcium. Combining the model with our experimental lifespan data, we predict an upper-limit of cytosolic calcium tolerance for cell survival. This prediction indicates that, for aged cells (>35 generations), no pmr1 Δ can tolerate the cytosolic calcium concentration of 0.1 μM while a very small fraction (1%) of aged wild type cells (>50 generations) can tolerate a high cytosolic calcium concentration of 0.5 μM.     

A model of internal control may improve the response time of an automatic arterial pressure controller

A simplified model for the arterial pressure control system was implemented on a personal computer using Matlab Simulink. Model responses to variations of systemic vascular resistance were comparable to those predicted by physiology. Computer simulation suggested that including this model of the internal pressure control system within the design of an external controller would achieve better arterial pressure control and faster response than previous systems.     

A model of feedback control for the charge-balanced suppression of epileptic seizures

Here we present several refinements to a model of feedback control for the suppression of epileptic seizures. We utilize a stochastic partial differential equation (SPDE) model of the human cortex. First, we verify the strong convergence of numerical solutions to this model, paying special attention to the sharp spatial changes that occur at electrode edges. This allows us to choose appropriate step sizes for our simulations; because the spatial step size must be small relative to the size of an electrode in order to resolve its electrical behavior, we are able to include a more detailed electrode profile in the simulation. Then, based on evidence that the mean soma potential is not the variable most closely related to the measurement of a cortical surface electrode, we develop a new model for this. The model is based on the currents flowing in the cortex and is used for a simulation of feedback control. The simulation utilizes a new control algorithm incorporating the total integral of the applied electrical potential. Not only does this succeed in suppressing the seizure-like oscillations, but it guarantees that the applied signal will be charge-balanced and therefore unlikely to cause cortical damage.     

A computational model of limb impedance control based on principles of internal model uncertainty

Efficient human motor control is characterized by an extensive use of joint impedance modulation, which is achieved by co-contracting antagonistic muscles in a way that is beneficial to the specific task. While there is much experimental evidence available that the nervous system employs such strategies, no generally-valid computational model of impedance control derived from first principles has been proposed so far. Here we develop a new impedance control model for antagonistic limb systems which is based on a minimization of uncertainties in the internal model predictions. In contrast to previously proposed models, our framework predicts a wide range of impedance control patterns, during stationary and adaptive tasks. This indicates that many well-known impedance control phenomena naturally emerge from the first principles of a stochastic optimization process that minimizes for internal model prediction uncertainties, along with energy and accuracy demands. The insights from this computational model could be used to interpret existing experimental impedance control data from the viewpoint of optimality or could even govern the design of future experiments based on principles of internal model uncertainty.     

Rapid encoding of an internal model for imitative learning

As in human infant speech development, vocal imitation in songbirds involves sensory acquisition and memorization of adult-produced vocal signals, followed by a protracted phase of vocal motor practice. The internal model of adult tutor song in the juvenile male brain, termed ‘the template’, is central to the vocal imitation process. However, even the most fundamental aspects of the template, such as when, where and how it is encoded in the brain, remain poorly understood. A major impediment to progress is that current studies of songbird vocal learning use protracted tutoring over days, weeks or months, complicating dissection of the template encoding process. Here, we take the key step of tightly constraining the timing of template acquisition. We show that, in the zebra finch, template encoding can be time locked to, on average, a 2 h period of juvenile life and based on just 75 s of cumulative tutor song exposure. Crucially, we find that vocal changes occurring on the day of training correlate with eventual imitative success. This paradigm will lead to insights on how the template is instantiated in the songbird brain, with general implications for deciphering how internal models are formed to guide learning of complex social behaviours.     

Active muscle response using feedback control of a finite element human arm model

Mathematical human body models (HBMs) are important research tools that are used to study the human response in car crash situations. Development of automotive safety systems requires the implementation of active muscle response in HBM, as novel safety systems also interact with vehicle occupants in the pre-crash phase. In this study, active muscle response was implemented using feedback control of a nonlinear muscle model in the right upper extremity of a finite element (FE) HBM. Hill-type line muscle elements were added, and the active and passive properties were assessed. Volunteer tests with low impact loading resulting in elbow flexion motions were performed. Simulations of posture maintenance in a gravity field and the volunteer tests were successfully conducted. It was concluded that feedback control of a nonlinear musculoskeletal model can be used to obtain posture maintenance and human-like reflexive responses in an FE HBM.     

Prediction of muscle energy states at low metabolic rates requires feedback control of mitochondrial respiratory chain activity by inorganic phosphate

The regulation of the 100-fold dynamic range of mitochondrial ATP synthesis flux in skeletal muscle was investigated. Hypotheses of key control mechanisms were included in a biophysical model of oxidative phosphorylation and tested against metabolite dynamics recorded by ³¹P nuclear magnetic resonance spectroscopy (³¹P MRS). Simulations of the initial model featuring only ADP and Pi feedback control of flux failed in reproducing the experimentally sampled relation between myoplasmic free energy of ATP hydrolysis (ΔG_p = ΔG_p ^o′+RT ln ([ADP][Pi]/[ATP]) and the rate of mitochondrial ATP synthesis at low fluxes (<0.2 mM/s). Model analyses including Monte Carlo simulation approaches and metabolic control analysis (MCA) showed that this problem could not be amended by model re-parameterization, but instead required reformulation of ADP and Pi feedback control or introduction of additional control mechanisms (feed forward activation), specifically at respiratory Complex III. Both hypotheses were implemented and tested against time course data of phosphocreatine (PCr), Pi and ATP dynamics during post-exercise recovery and validation data obtained by ³¹P MRS of sedentary subjects and track athletes. The results rejected the hypothesis of regulation by feed forward activation. Instead, it was concluded that feedback control of respiratory chain complexes by inorganic phosphate is essential to explain the regulation of mitochondrial ATP synthesis flux in skeletal muscle throughout its full dynamic range.     

Regularity in an environment produces an internal torque pattern for biped balance control

In this paper, we present a control method for achieving biped static balance under unknown periodic external forces whose periods are only known. In order to maintain static balance adaptively in an uncertain environment, it is essential to have information on the ground reaction forces. However, when the biped is exposed to a steady environment that provides an external force periodically, uncertain factors on the regularity with respect to a steady environment are gradually clarified using learning process, and finally a torque pattern for balancing motion is acquired. Consequently, static balance is maintained without feedback from ground reaction forces and achieved in a feedforward manner.     

A holistic model for an internal representation to control the movement of a manipulator with redundant degrees of freedom

The paper proposes a model for the control of a multisegmented manipulator with redundant degrees of freedom. On the basis of an earlier model, the so-called MMC net, a simplified version is proposed here which has several advantages. First, it can easily be scaled up for the 3D case. Second, for the linear version a complete convergence proof is possible. Third, an easy way of implementing a damping parameter is shown. Fourth, the properties of the earlier model are unchanged, namely versatile control of the redundant system, immediate change from direct kinematics to inverse kinematics or any mixed control task, as well as robustness in the case of singularities. Received: 4 October 1997 / Accepted in revised form: 26 August 1998     

Efficient mobilization of mariner in vivo requires multiple internal sequences

Aberrant products of mariner excision that have an impaired ability to be mobilized often include internal deletions that do not encroach on either of the inverted repeats. Analysis of 13 such deletions, as well as 7 additional internal deletions obtained by various methods, has revealed at least three internal regions whose integrity is necessary for efficient mariner mobilization. Within the 1286-bp element, the essential regions are contained in the intervals bounded by coordinates 229-586, 735-765, and 939-1066, numbering in base pairs from the extreme 5' end of the element. These regions may contain sequences that are necessary for transposase binding or that are needed to maintain proper spacing between binding sites. The isolation of excision-defective elements with point mutations at nucleotide positions 993 and 161/179 supports the hypothesis of sequence requirements, but the reduced mobility of transformation vectors with insertions into the SacI site at position 790 supports the hypothesis of spacing requirements. The finding of multiple internal regions that are essential for efficient mariner mobilization in vivo contrasts with reports that mini-elements with as little as 43 bp of DNA between the inverted repeats can transpose efficiently in vitro.     

An internal survival standard for Salmonella typhimurium forward mutation assays

A novel S. typhimurium forward mutation assay which avoids plating density artifacts is described. The new method uses a pair of multiply drug-resistant substrains of TM677, a bacterial strain used in previous forward mutation studies. This technique permits the measurement of cell survival following mutagen treatment by plating the culture on specially supplemented plates at the same cell concentration used to measure mutant yield. Thus this method is both technically easier and theoretically superior to our previous method.     

Genomic selection requires genomic control of inbreeding

Background

In the past, pedigree relationships were used to control and monitor inbreeding because genomic relationships among selection candidates were not available until recently. The aim of this study was to understand the consequences for genetic variability across the genome when genomic information is used to estimate breeding values and in managing the inbreeding generated in the course of selection on genome-enhanced estimated breeding values.

Methods

These consequences were measured by genetic gain, pedigree- and genome-based rates of inbreeding, and local inbreeding across the genome. Breeding schemes were compared by simulating truncation selection or optimum contribution selection with a restriction on pedigree- or genome-based inbreeding, and with selection using estimated breeding values based on genome- or pedigree-based BLUP. Trait information was recorded on full-sibs of the candidates.

Results

When the information used to estimate breeding values and to constrain rates of inbreeding were either both pedigree-based or both genome-based, rates of genomic inbreeding were close to the desired values and the identical-by-descent profiles were reasonably uniform across the genome. However, with a pedigree-based inbreeding constraint and genome-based estimated breeding values, genomic rates of inbreeding were much higher than expected. With pedigree-instead of genome-based estimated breeding values, the impact of the largest QTL on the breeding values was much smaller, resulting in a more uniform genome-wide identical-by-descent profile but genomic rates of inbreeding were still higher than expected based on pedigree relationships, because they measure the inbreeding at a neutral locus not linked to any QTL. Neutral loci did not exist here, where there were 100 QTL on each chromosome. With a pedigree-based inbreeding constraint and genome-based estimated breeding values, genomic rates of inbreeding substantially exceeded the value of its constraint. In contrast, with a genome-based inbreeding constraint and genome-based estimated breeding values, marker frequencies changed, but this change was limited by the inbreeding constraint at the marker position.

Conclusions

To control inbreeding, it is necessary to account for it on the same basis as what is used to estimate breeding values, i.e. pedigree-based inbreeding control with traditional pedigree-based BLUP estimated breeding values and genome-based inbreeding control with genome-based estimated breeding values.     

A valine-resistant mutant ofArabidopsis thaliana displays an acetolactate synthase with altered feedback control

A valine-resistant mutant line, VAL-2, ofArabidopsis thaliana (L.) Heynh. was identified by screening M 2 populations of ethylmethane-sulfonate-mutagenized seeds. The resistance was found to be due to a single, dominant, nuclear gene mutation. Assay of acetolactate synthase (ALS) indicated that the valine resistance in this mutant is caused by decreased sensitivity of ALS to the branched-chain amino acids, valine, leucine andisoleucine. A two fold decrease in apparentK _m value for pyruvate of the mutant ALS enzyme was detected compared with that of the wild type. The sensitivity of the ALS enzyme to sulfonylurea, imidazolinone and triazolopyrimidine herbicides was not altered in the mutant. At the plant growth level the mutant was also resistant to valine plus leucine, but was sensitive to leucine orisoleucine alone. The mutant gene,var1, maps, or is very closely linked, toCSR1, the gene encoding acetolactate synthase inArabidopsis.Abbreviations ALS acetolactate synthase - BCAA branched-chain amino acid - CS chlorsulfuron - IM imidazolinone - SU sulfonylurea - TP triazolopyrimidine We thank Dr. George W. Haughn for providing Arabidopsis lines MSU12, MSU15, MSU21, MSU22 and MSU23. This work was supported by a Research Grant from the Natural Sciences and Engineering Research Council of Canada to J.K., K.W. is grateful for a University of Saskatchewan Graduate Scholarship.     

Ocular and stabilization feedback: an evaluation of two EMG biofeedback control procedures

This study evaluated the adequacy of two novel EMG biofeedback control procedures. During a single training session, 36 subjects received either contingent EMG feedback from the frontal region (Veridical), contingent feedback for vertical eye movements (Ocular), or a feedback condition where the signal increased with deviations in any direction from baseline EMG levels (Stabilization). The results supported the use of Ocular but not Stabilization feedback as a control procedure in frontalis EMG biofeedback studies. Ocular feedback did not produce reductions in frontalis EMG but did lead to changes in subjective measures of nonspecific treatment effects that were at least comparable to those obtained with Veridical feedback. Stabilization subjects produced small but significant reductions in EMG, felt the most bored as a result of their feedback training, and were the most likely to rate themselves as having received false feedback. The implications of attribution theory and multiprocess relaxation theory for the evaluation of nonspecific treatment effects are discussed.