Evolutionary dynamics of redundant regulatory control

Many complex regulatory processes concern tracking a constant or variable set point. Examples include temperature homeostasis, rhythmic oscillation, and the concentration of key metabolites and enzymes. Control over homeostatic or tracking phenotypes often depends on multiple, overlapping regulatory systems. In this paper, I develop a theory for the evolutionary dynamics of redundant regulatory control architecture. Prior theories analyzed the evolution of redundant control architectures by the balance between improved performance for additional redundant control weighed against the decay by germline mutation that arises in characters with overlapping function. By contrast, I argue that germline mutation is likely to be a very weak balancing force in evolutionary dynamics. Instead, I analyze the evolutionary dynamics of redundant control by a balance between the benefits of reduced tracking error and the costs of building and running the multiple control systems. In one particular mathematical model that highlights key features of evolutionary dynamics, additional redundant control reduces tracking error multiplicatively but contributes to costs additively. In that model, the performance landscape has multiple peaks of the same height, one peak for each level of redundancy and the associated optimal investment per control structure. The multipeak landscape imposes evolutionary stasis, in which control systems resist invasion by increased or decreased levels of redundancy. However, fluctuating environments likely favor a rise in redundancy over time. With greater redundancy, investment per individual control structure declines, causing a decay in the performance of each individual dimension of control. I conclude that the costs of control structures may influence regulatory architecture.     

Motion control of the ankle joint with a multiple contact nerve cuff electrode: a simulation study

The flat interface nerve electrode (FINE) has demonstrated significant capability for fascicular and subfascicular stimulation selectivity. However, due to the inherent complexity of the neuromuscular skeletal systems and nerve–electrode interface, a trajectory tracking motion control algorithm of musculoskeletal systems for functional electrical stimulation using a multiple contact nerve cuff electrode such as FINE has not yet been developed. In our previous study, a control system was developed for multiple-input multiple-output (MIMO) musculoskeletal systems with little prior knowledge of the system. In this study, more realistic computational ankle/subtalar joint model including a finite element model of the sciatic nerve was developed. The control system was tested to control the motion of ankle/subtalar joint angles by modulating the pulse amplitude of each contact of a FINE placed on the sciatic nerve. The simulation results showed that the control strategy based on the separation of steady state and dynamic properties of the system resulted in small output tracking errors for different reference trajectories such as sinusoidal and filtered random signals. The proposed control method also demonstrated robustness against external disturbances and system parameter variations such as muscle fatigue. These simulation results under various circumstances indicate that it is possible to take advantage of multiple contact nerve electrodes with spatial selectivity for the control of limb motion by peripheral nerve stimulation even with limited individual muscle selectivity. This technology could be useful to restore neural function in patients with paralysis.     

The study of neural network-based controller for controlling dissolved oxygen concentration in a sequencing batch reactor

The design and development of the neural network (NN)-based controller performance for the activated sludge process in sequencing batch reactor (SBR) is presented in this paper. Here we give a comparative study of various neural network (NN)-based controllers such as the direct inverse control, internal model control (IMC) and hybrid NN control strategies to maintain the dissolved oxygen (DO) level of an activated sludge system by manipulating the air flow rate. The NN inverse model-based controller with the model-based scheme represents the controller, which relies solely upon the simple NN inverse model. In the IMC, both the forward and inverse models are used directly as elements within the feedback loop. The hybrid NN control consists of a basic NN controller in parallel with a proportional integral (PI) controller. Various simulation tests involving multiple set-point changes, disturbances rejection and noise effects were performed to review the performances of these various controllers. From the results it can be seen that hybrid controller gives the best results in tracking set-point changes under disturbances and noise effects.     

Inferior olive mirrors joint dynamics to implement an inverse controller

To produce smooth and coordinated motion, our nervous systems need to generate precisely timed muscle activation patterns that, due to axonal conduction delay, must be generated in a predictive and feedforward manner. Kawato proposed that the cerebellum accomplishes this by acting as an inverse controller that modulates descending motor commands to predictively drive the spinal cord such that the musculoskeletal dynamics are canceled out. This and other cerebellar theories do not, however, account for the rich biophysical properties expressed by the olivocerebellar complex’s various cell types, making these theories difficult to verify experimentally. Here we propose that a multizonal microcomplex’s (MZMC) inferior olivary neurons use their subthreshold oscillations to mirror a musculoskeletal joint’s underdamped dynamics, thereby achieving inverse control. We used control theory to map a joint’s inverse model onto an MZMC’s biophysics, and we used biophysical modeling to confirm that inferior olivary neurons can express the dynamics required to mirror biomechanical joints. We then combined both techniques to predict how experimentally injecting current into the inferior olive would affect overall motor output performance. We found that this experimental manipulation unmasked a joint’s natural dynamics, as observed by motor output ringing at the joint’s natural frequency, with amplitude proportional to the amount of current. These results support the proposal that the cerebellum—in particular an MZMC—is an inverse controller; the results also provide a biophysical implementation for this controller and allow one to make an experimentally testable prediction.     

Computation of a Stabilizing Set of Feedback Matrices bf a Large-scale Nonlinear Musculoskeletal Dynamic Model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/ output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

Computation of a stabilizing set of feedback matrices of a large-scale nonlinear musculoskeletal dynamic model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

RankAggreg, an R package for weighted rank aggregation

Background

Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems.

Results

In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters.

Conclusion

The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.     

Modeling biological motor control for human locomotion with functional electrical stimulation

This paper develops a novel control system for functional electrical stimulation (FES) locomotion, which aims to generate normal locomotion for paraplegics via FES. It explores the possibility of applying ideas from biology to engineering. The neural control mechanism of the biological motor system, the central pattern generator, has been adopted in the control system design. Some artificial control techniques such as neural network control, fuzzy logic, control and impedance control are incorporated to refine the control performance. Several types of sensory feedback are integrated to endow this control system with an adaptive ability. A musculoskeletal model with 7 segments and 18 muscles is constructed for the simulation study. Satisfactory simulation results are achieved under this FES control system, which indicates a promising technique for the potential application of FES locomotion in future.     

Stiffness modulation of redundant musculoskeletal systems

This work presents a framework for computing the limbs’ stiffness using inverse methods that account for the musculoskeletal redundancy effects. The musculoskeletal task, joint and muscle stiffness are regulated by the central nervous system towards improving stability and interaction with the environment during movement. Many pathological conditions, such as Parkinson’s disease, result in increased rigidity due to elevated muscle tone in antagonist muscle pairs, therefore the stiffness is an important quantity that can provide valuable information during the analysis phase. Musculoskeletal redundancy poses significant challenges in obtaining accurate stiffness results without introducing critical modeling assumptions. Currently, model-based estimation of stiffness relies on some objective criterion to deal with muscle redundancy, which, however, cannot be assumed to hold in every context. To alleviate this source of error, our approach explores the entire space of possible solutions that satisfy the action and the physiological muscle constraints. Using the notion of null space, the proposed framework rigorously accounts for the effect of muscle redundancy in the computation of the feasible stiffness characteristics. To confirm this, comprehensive case studies on hand movement and gait are provided, where the feasible endpoint and joint stiffness is evaluated. Notably, this process enables the estimation of stiffness distribution over the range of motion and aids in further investigation of factors affecting the capacity of the system to modulate its stiffness. Such knowledge can significantly improve modeling by providing a holistic overview of dynamic quantities related to the human musculoskeletal system, despite its inherent redundancy.     

Internal models and intermittency: A theoretical account of human tracking behavior

This paper concerns the use of tracking studies to test a theoretical account of the information processing performed by the human CNS during control of movement. The theory provides a bridge between studies of reaction time and continuous tracking. It is proposed that the human CNS includes neuronal circuitry to compute inverse internal models of the multiple input, multiple output, dynamic, nonlinear relationships between outgoing motor commands and their resulting perceptual consequences. The inverse internal models are employed during movement execution to transform preplanned trajectories of desired perceptual consequences into appropriate outgoing motor commands to achieve them. A finite interval of time is required by the CNS to preplan the desired perceptual consequences of a movement and it does not commence planning a new movement until planning of the old one has been completed. This behavior introduces intermittency into the planning of movements. In this paper we show that the gain and phase frequency response characteristics of the human operator in a visual pursuit tracking task can be derived theoretically from these assumptions. By incorporating the effects of internal model inaccuracy and of speed-accuracy trade-off in performance, it is shown that various aspects of experimentally measured tracking behavior can be accounted for.     

Parameter adaptation and control in a biochemical reactor

A discrete optimally sensitive controller is developed which yields steady-state feedback control of a three-stage biochemical reactor system in spite of system parameter variations. A feedback law is implemented that estimates those variations which cause the output states to deviate from nominal, and adjusts the control policy in light of these variations.     

Advances in functional electrical stimulation (FES)

This review discusses the advancements that are needed to enhance the effects of electrical stimulation for restoring or assisting movement in humans with an injury/disease of the central nervous system. A complex model of the effects of electrical stimulation of peripheral systems is presented. The model indicates that both the motor and sensory systems are activated by electrical stimulation. We propose that a hierarchical hybrid controller may be suitable for functional electrical stimulation (FES) because this type of controller acts as a structural mimetic of its biological counterpart. Specific attention is given to the neural systems at the periphery with respect to the required electrodes and stimulators. Furthermore, we note that FES with surface electrodes is preferred for the therapy, although there is a definite advantage associated with implantable technology for life-long use. The last section of the review discusses the potential need to combine FES and robotic systems to provide assistance in some cases.     

Stabilization of human standing posture using functional neuromuscular stimulation

Functional neuromuscular stimulation (FNS)/functional electrical stimulation (FES) is a potential way to restore some functionality to the limbs of patients with spinal cord injury through direct/indirect stimulation of the motoneuron. One of the constraints for wider use of FNS on paraplegic patients is the lack of efficient control algorithm. Most of the published works on FNS/FES control are based on oversimplified models of human body dynamics. An innovative control strategy for stabilizing the standing posture of paraplegic patients is proposed here which is a combination of a proportional-plus-derivative controller for motions of the skeletal system and a control action prediction mechanism to produce musculotendon activation. The goal is to produce musculotendon torque which can approximate those demanded by the controller for the skeletal system. In computer simulations, using a detailed skeletal–musculotendon–muscle activation dynamics model of human body, this FNS/FES control approach can stabilize a paraplegic patient's standing posture with the minimum number of musculotendon groups. Also, it is found that this control strategy can maintain stability even in the presence of reasonable variations in the controller's musculotendon parameters.     

毒素在森林各分室循环的广义模型的变结构控制

利用广义系统变结构控制理论,研究了一个毒素在森林各分室循环的广义模型的变结构控制问题.首先,针对毒素在森林生态系统各分室的循环特征,构建了毒素在森林各分室循环的广义模型;其次,利用广义系统理论,对所建模型的平衡点进行了稳定性分析;最后,应用广义系统变结构控制理论设计了变结构控制器,使森林各分室中的毒素最终稳定到零点,使森林生态系统正常发展.     

Observer-based tracking control of abnormal oscillations in demyelination symptom

Fast axonal conduction of action potentials in mammals relies on myelin insulation. Demyelination can cause slowed, blocked, desynchronized, or paradoxically excessive spiking that underlies the symptoms observed in demyelination diseases. Feedback control via functional electrical stimulation (FES) seems to be a promising treatment modality in such diseases. However, there are challenges to implementing such method for neurons: high nonlinearity, biological tissue constrains and unobservable ion channel states. To address this problem, we propose an estimating and tracking control strategy for systems based on Kalman filter, in order to enhance the action potential propagation reliability of demyelinated neuron via FES. Unscented Kalman filter (UKF) is employed to estimate the unobservable states and parameters in the demyelination neuron model from membrane potential dynamics. Our method could promote the design of new closed-loop electrical stimulation systems for patients suffering from different nerve system dysfunctions.     

Current topics in clinical FES in Japan

This paper reviews recent topics of clinical application of functional electrical stimulation (FES) for the paralyzed extremities in Japan. Transcutaneous and percutaneous FES systems have been clinically used in Japan. Candidates of extremity FES arer mostly stroke and spinal cord injury patients. By using percutaneous FES system, all of the joints of the upper extremity including the shoulder have been controlled for activities of daily living in the hemiplegic patient. Simultaneous FES control of the hand and wrist and the bilateral hands have also been achieved in C5 and C6 quadriplegics, respectively. Hybrid FES systems using percutaneous and surface electrodes, where FES is used in combination with orthoses, have been applied to the paraplegics because they are highly practical for assisting their locomotive activities. Percutaneous FES have been also provided the amyotropic lateral sclerosis patients with standing up motion. A total implant FES system with 16 output channels is currently developing as a next generation FES system.     

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     

Maximization of learning speed in the motor cortex due to neuronal redundancy

Many redundancies play functional roles in motor control and motor learning. For example, kinematic and muscle redundancies contribute to stabilizing posture and impedance control, respectively. Another redundancy is the number of neurons themselves; there are overwhelmingly more neurons than muscles, and many combinations of neural activation can generate identical muscle activity. The functional roles of this neuronal redundancy remains unknown. Analysis of a redundant neural network model makes it possible to investigate these functional roles while varying the number of model neurons and holding constant the number of output units. Our analysis reveals that learning speed reaches its maximum value if and only if the model includes sufficient neuronal redundancy. This analytical result does not depend on whether the distribution of the preferred direction is uniform or a skewed bimodal, both of which have been reported in neurophysiological studies. Neuronal redundancy maximizes learning speed, even if the neural network model includes recurrent connections, a nonlinear activation function, or nonlinear muscle units. Furthermore, our results do not rely on the shape of the generalization function. The results of this study suggest that one of the functional roles of neuronal redundancy is to maximize learning speed.     

SIR传染病模型的混沌跟踪控制

研究了一类疾病传染率受季节因素影响的SIR传染病模型的混沌运动,并采用轨迹跟踪控制方法对传染病模型中的混沌运动进行控制,设计状态反馈控制器,控制系统输出跟踪某一理想状态,使染病者数量渐近趋于零,从而,达到消除疾病的目的．仿真结果表明该方法的有效性．     

The conservation of redundancy in genetic systems: effects of sexual and asexual reproduction

The relationship between probability of survival and the number of deleterious mutations in the genome is investigated using three different models of highly redundant systems that interact with a threatening environment. Model one is a system that counters a potentially lethal infection; it has multiple identical components that act in sequence and in parallel. Model two has many different overlapping components that provide three-fold coverage of a large number of vital functions. The third model is based on statistical decision theory: an ideal detector, following an optimum decision strategy, makes crucial decisions in an uncertain world. The probability of a fatal error is reduced by a redundant sampling system, but the chance of error rises as the system is impaired by deleterious mutations. In all three cases the survival profile shows a synergistic pattern in that the probability of survival falls slowly and then more rapidly. This is different than the multiplicative or independent survival profile that is often used in mathematical models. It is suggested that a synergistic profile is a property of redundant systems. Model one is then used to study the conservation of redundancy during sexual and asexual reproduction. A unicellular haploid organism reproducing asexually retains redundancy when the mutation rate is very low (0001 per cell division), but tends to lose high levels of redundancy if the mutation rate is increased (001 to 01 per cell division). If a similar unicellular haploid organism has a sexual phase then redundancy is retained for mutation rates between 0001 and 01 per cell division. The sexual organism outgrows the asexual organism when the above mutation rates apply. If they compete for finite resources the asexual organism will be extinguished. Variants of the sexual organism with increased redundancy will outgrow those with lower levels of redundancy and the sexual process facilitates the evolution of more complex forms. There is a limit to the extent that complexity can be increased by increasing the size of the genome and in asexual organisms this leads to progressive accumulation of mutations with loss of redundancy and eventual extinction. If complexity is increased by using genes in new combinations, the asexual form can reach a stable equilibrium, although it is associated with some loss of redundancy. The sexual form, by comparison, can survive, with retention of redundancy, even if the mutation rate is above one per generation. The conservation and evolution of redundancy, which is essential for complexity, depends on the sexual process of reproduction.