Optimal production of glutathione by controlling the specific growth rate of yeast in fed-batch culture

The optimal of the specific growth rate was obtained with simple mathematical model in a yeast fed-batch cultures. The model was based on the mass balance around the fed-batch system and the relationship between the specific growth rate, mu, and the specific production rate of glutathione, rho(G). The optimal profile of mu was calculated as a bang-bang type, That is mu, should start from the maximum value, mu(max) and should be kept at mu(max); then mu should be switched to mu(c), which gives a maximum value of rho(G). It was proven from the maximum principle that switching was needed only once, with the switching time from mu(max) to mu(c) depending on the final required glutathione content. Finally, this ideal profile of mu for the maximum production of glutathione was realized by manipulating the substrates feed rate in the fed-batch culture. Using the extended Kalman filter and a programmed-controller/feedback-compensator (PF) system, mu could be controlled at the optimal profile obtained. As a result, the maximum production of glutathione was accomplished fairly successfully. However, further improvement in the controller performance for mu is desired. The control strategy employed here can be applied to other batch reaction processes.     

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.     

Effectiveness of social distancing interventions in containing COVID-19 incidence: International evidence using Kalman filter

The epidemiological literature has widely documented the importance of social distancing interventions in containing the spread of the COVID-19 pandemic. However, the epidemiological measure of virus reproduction, R₀, provides a myopic view of containment, especially when the absolute number of cases is still high. The paper investigates cross-country variations concerning the impact of social distancing interventions on COVID-19 incidence by employing a statistical measure of containment, which models the daily number of cases as a structural time-series, state-space vector. Countries that adopt strict lockdown policies and provide economic support in the form of income augmentations and debt relief improve the response towards the pandemic. Countries like China and South Korea have been most influential in containing the spread of infections. European nations of France, Italy, Spain and the UK are witnessing a second wave of the virus, indicating that re-opening the European economy perhaps has instigated an exponential spread.     

Real‐time model based process monitoring of enzymatic biodiesel production

In this contribution we extend our modelling work on the enzymatic production of biodiesel where we demonstrate the application of a Continuous‐Discrete Extended Kalman Filter (a state estimator). The state estimator is used to correct for mismatch between the process data and the process model for Fed‐batch production of biodiesel. For the three process runs investigated, using a single tuning parameter, q_x = 2 × 10^?2 which represents the uncertainty in the process model, it was possible over the entire course of the reaction to reduce the overall mean and standard deviation of the error between the model and the process data for all of the five measured components (triglycerides, diglycerides, monoglycerides, fatty acid methyl esters, and free fatty acid). The most significant reduction for the three process runs, were for the monoglyceride and free fatty acid concentration. For those components, there was over a ten‐fold decrease in the overall mean error for the state estimator prediction compared with the predictions from the pure model simulations. It is also shown that the state estimator can be used as a tool for detection of outliers in the measurement data. For the enzymatic biodiesel process, given the infrequent and sometimes uncertain measurements obtained we see the use of the Continuous‐Discrete Extended Kalman Filter as a viable tool for real time process monitoring. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:585–595, 2015     

基于Unscented卡尔曼滤波器的信号转导通路参数与不可观测状态估计

系统生物学的一个主要目的是建立细胞信号转导通路的数学模型。然而细胞信号转导通路多具有较强非线性、参与生化反应物质多等特点,同时测量数据往往不完备,并且混有来自实验各个阶段的各种噪声,这些都给模型参数估计带来很大困难。该文采用Unscented卡尔曼滤波器估计信号转导通路未知参数与模型不可观测状态。以肿瘤坏死因子诱导的核转录因子κB信号转导通路为例进行了仿真,结果表明,采用该方法可以在噪声干扰下较准确地的估计系统未知参数和不能观测状态。     

生理信号回归问题的一种解法

一自适应在线过程可通过Kalman滤波表示为时间变多变量的的自回归模型。时变模型的参数的估计能被用以计算线相关的瞬时测量,此方法对生理信号的分析非常有用。本文着重讨论了在呼吸运动,心率波动,血压的分析中的应用。     

Optimal spatio‐temporal hybrid sampling designs for ecological monitoring

Question: Static sampling designs for collecting spatial data efficiently are being readily utilized by ecologists, however, most ecological systems involve a multivariate spatial process that evolves dynamically over time. Efficient monitoring of such spatio‐temporal systems can be achieved by modeling the dynamic system and reducing the uncertainty associated with the effect of design choice at future observation times. However, can we combine traditional techniques with dynamic methods to find optimal dynamic sampling designs for monitoring the succession of a herbaceous community? Location: Lower Hamburg Bend Conservation Area, Missouri, USA (40°34′42″ lat. 95°45′38″ long.). Methods: The dynamic nature of the system under study is modeled in such a way that uncertainty in the measurements and temporal process can both be accounted for. Both fixed and roving monitoring locations were used in conjunction with a spatio‐temporal statistical model to efficiently determine optimal locations of roving monitors over time based on the reduction of uncertainty in predictions. Results: During the first 3 years of the study, roving monitors where held at fixed locations to allow for statistical parameter estimation from which to make predictions. Optimal monitoring locations for the remaining 2 years were selected based on the overall reduction in prediction uncertainty. Conclusions: The dynamic and adaptive vegetation monitoring scheme allowed for the efficient collection of data that will be utilized for many future ecological studies. By optimally placing an additional set of monitoring locations, we were able to utilize information about the system dynamics when informing the data collection process.     

The Unscented Kalman Filter estimates the plasma insulin from glucose measurement

Understanding the simultaneous interaction within the glucose and insulin homeostasis in real-time is very important for clinical treatment as well as for research issues. Until now only plasma glucose concentrations can be measured in real-time. To support a secure, effective and rapid treatment e.g. of diabetes a real-time estimation of plasma insulin would be of great value. A novel approach using an Unscented Kalman Filter that provides an estimate of the current plasma insulin concentration is presented, which operates on the measurement of the plasma glucose and Bergman's Minimal Model of the glucose insulin homeostasis. We can prove that process observability is obtained in this case. Hence, a successful estimator design is possible. Since the process is nonlinear we have to consider estimates that are not normally distributed. The symmetric Unscented Kalman Filter (UKF) will perform best compared to other estimator approaches as the Extended Kalman Filter (EKF), the simplex Unscented Kalman Filter (UKF), and the Particle Filter (PF). The symmetric UKF algorithm is applied to the plasma insulin estimation. It shows better results compared to the direct (open loop) estimation that uses a model of the insulin subsystem.     

An improved analysis of forest carbon dynamics using data assimilation

There are two broad approaches to quantifying landscape C dynamics – by measuring changes in C stocks over time, or by measuring fluxes of C directly. However, these data may be patchy, and have gaps or biases. An alternative approach to generating C budgets has been to use process‐based models, constructed to simulate the key processes involved in C exchange. However, the process of model building is arguably subjective, and parameters may be poorly defined. This paper demonstrates why data assimilation (DA) techniques – which combine stock and flux observations with a dynamic model – improve estimates of, and provide insights into, ecosystem carbon (C) exchanges. We use an ensemble Kalman filter (EnKF) to link a series of measurements with a simple box model of C transformations. Measurements were collected at a young ponderosa pine stand in central Oregon over a 3‐year period, and include eddy flux and soil CO₂ efflux data, litterfall collections, stem surveys, root and soil cores, and leaf area index data. The simple C model is a mass balance model with nine unknown parameters, tracking changes in C storage among five pools; foliar, wood and fine root pools in vegetation, and also fresh litter and soil organic matter (SOM) plus coarse woody debris pools. We nested the EnKF within an optimization routine to generate estimates from the data of the unknown parameters and the five initial conditions for the pools. The efficacy of the DA process can be judged by comparing the probability distributions of estimates produced with the EnKF analysis vs. those produced with reduced data or model alone. Using the model alone, estimated net ecosystem exchange of C (NEE)=?251±197 g C m^?2 over the 3 years, compared with an estimate of ?419±29 g C m^?2 when all observations were assimilated into the model. The uncertainty on daily measurements of NEE via eddy fluxes was estimated at 0.5 g C m^?2 day^?1, but the uncertainty on assimilated estimates averaged 0.47 g C m^?2 day^?1, and only exceeded 0.5 g C m^?2 day^?1 on days where neither eddy flux nor soil efflux data were available. In generating C budgets, the assimilation process reduced the uncertainties associated with using data or model alone and the forecasts of NEE were statistically unbiased estimates. The results of the analysis emphasize the importance of time series as constraints. Occasional, rare measurements of stocks have limited use in constraining the estimates of other components of the C cycle. Long time series are particularly crucial for improving the analysis of pools with long time constants, such as SOM, woody biomass, and woody debris. Long‐running forest stem surveys, and tree ring data, offer a rich resource that could be assimilated to provide an important constraint on C cycling of slow pools. For extending estimates of NEE across regions, DA can play a further important role, by assimilating remote‐sensing data into the analysis of C cycles. We show, via sensitivity analysis, how assimilating an estimate of photosynthesis – which might be provided indirectly by remotely sensed data – improves the analysis of NEE.