Memory elements in the electrical network of Mimosa pudica L.

The fourth basic circuit element, a memristor, is a resistor with memory that was postulated by Chua in 1971. Here we found that memristors exist in vivo. The electrostimulation of the Mimosa pudica by bipolar sinusoidal or triangle periodic waves induce electrical responses with fingerprints of memristors. Uncouplers carbonylcyanide-3-chlorophenylhydrazone and carbonylcyanide-4-trifluoromethoxy-phenyl hydrazone decrease the amplitude of electrical responses at low and high frequencies of bipolar sinusoidal or triangle periodic electrostimulating waves. Memristive behavior of an electrical network in the Mimosa pudica is linked to the properties of voltage gated ion channels: the channel blocker TEACl reduces the electric response to a conventional resistor. Our results demonstrate that a voltage gated K⁺ channel in the excitable tissue of plants has properties of a memristor. The discovery of memristors in plants creates a new direction in the modeling and understanding of electrical phenomena in plants.     

Memristors: Memory elements in potato tubers

A memristor is a nonlinear element because its current-voltage characteristic is similar to that of a Lissajous pattern for nonlinear systems. This element was postulated recently and researchers are looking for it in different biosystems. We investigated electrical circuitry of red Irish potato tubers (Solanum tuberosum L.). The goal was to discover if potato tubers might have a new electrical component - a resistor with memory. The analysis was based on a cyclic current-voltage characteristic where the resistor with memory should manifest itself. We found that the electrostimulation by bipolar sinusoidal or triangle periodic waves induces electrical responses in the potato tubers with fingerprints of memristors. Tetraethylammonium chloride, an inhibitor of voltage gated K⁺ channels, transforms a memristor to a resistor in potato tubers. Our results demonstrate that a voltage gated K⁺ channel in the excitable tissue of potato tubers has properties of a memristor. Uncoupler carbonylcyanide-4-trifluoromethoxy-phenyl hydrazone decreases the amplitude of electrical responses at low and high frequencies of bipolar periodic sinusoidal or triangle electrostimulating waves. The discovery of memristors in plants creates a new direction in the understanding of electrical phenomena in plants.     

An analytical model of memristors in plants

The memristor, a resistor with memory, was postulated by Chua in 1971 and the first solid-state memristor was built in 2008. Recently, we found memristors in vivo in plants. Here we propose a simple analytical model of 2 types of memristors that can be found within plants. The electrostimulation of plants by bipolar periodic waves induces electrical responses in the Aloe vera and Mimosa pudica with fingerprints of memristors. Memristive properties of the Aloe vera and Mimosa pudica are linked to the properties of voltage gated K⁺ ion channels. The potassium channel blocker TEACl transform plant memristors to conventional resistors. The analytical model of a memristor with a capacitor connected in parallel exhibits different characteristic behavior at low and high frequency of applied voltage, which is the same as experimental data obtained by cyclic voltammetry in vivo.     

Back-Propagation Operation for Analog Neural Network Hardware with Synapse Components Having Hysteresis Characteristics

To realize an analog artificial neural network hardware, the circuit element for synapse function is important because the number of synapse elements is much larger than that of neuron elements. One of the candidates for this synapse element is a ferroelectric memristor. This device functions as a voltage controllable variable resistor, which can be applied to a synapse weight. However, its conductance shows hysteresis characteristics and dispersion to the input voltage. Therefore, the conductance values vary according to the history of the height and the width of the applied pulse voltage. Due to the difficulty of controlling the accurate conductance, it is not easy to apply the back-propagation learning algorithm to the neural network hardware having memristor synapses. To solve this problem, we proposed and simulated a learning operation procedure as follows. Employing a weight perturbation technique, we derived the error change. When the error reduced, the next pulse voltage was updated according to the back-propagation learning algorithm. If the error increased the amplitude of the next voltage pulse was set in such way as to cause similar memristor conductance but in the opposite voltage scanning direction. By this operation, we could eliminate the hysteresis and confirmed that the simulation of the learning operation converged. We also adopted conductance dispersion numerically in the simulation. We examined the probability that the error decreased to a designated value within a predetermined loop number. The ferroelectric has the characteristics that the magnitude of polarization does not become smaller when voltages having the same polarity are applied. These characteristics greatly improved the probability even if the learning rate was small, if the magnitude of the dispersion is adequate. Because the dispersion of analog circuit elements is inevitable, this learning operation procedure is useful for analog neural network hardware.     

Transcranial Extracellular Impedance Control (tEIC) Modulates Behavioral Performances

Electric brain stimulations such as transcranial direct current stimulation (tDCS), transcranial random noise stimulation (tRNS), and transcranial alternating current stimulation (tACS) electrophysiologically modulate brain activity and as a result sometimes modulate behavioral performances. These stimulations can be viewed from an engineering standpoint as involving an artificial electric source (DC, noise, or AC) attached to an impedance branch of a distributed parameter circuit. The distributed parameter circuit is an approximation of the brain and includes electric sources (neurons) and impedances (volume conductors). Such a brain model is linear, as is often the case with the electroencephalogram (EEG) forward model. Thus, the above-mentioned current stimulations change the current distribution in the brain depending on the locations of the electric sources in the brain. Now, if the attached artificial electric source were to be replaced with a resistor, or even a negative resistor, the resistor would also change the current distribution in the brain. In light of the superposition theorem, which holds for any linear electric circuit, attaching an electric source is different from attaching a resistor; the resistor affects each active electric source in the brain so as to increase (or decrease in some cases of a negative resistor) the current flowing out from each source. From an electrophysiological standpoint, the attached resistor can only control the extracellular impedance and never causes forced stimulation; we call this technique transcranial extracellular impedance control (tEIC). We conducted a behavioral experiment to evaluate tEIC and found evidence that it had real-time enhancement and depression effects on EEGs and a real-time facilitation effect on reaction times. Thus, tEIC could be another technique to modulate behavioral performance.     

A model for repetitive firing in neurons

This paper describes a model for the generation of repetitive firing patterns in single neurons to be used as a module in large-scale network simulation studies. The model is based on the combination of extended versions of Hill's model for accomodation and of Kernell's model for adaptation. Both digital computer and electronic circuit realizations of the model are presented. The model is shown to produce strength-duration curves for accomodation which are compatible with available data from real neurons. Both “high ceiling” and “low ceiling” cell types can be matched by adjusting parameters in the model. An equation relating steady-state firing rate to amplitude of applied steady current is presented which includes the accumulation of potassium conductance changes with repetitive firing. The occurence of phasic and tonic responses to step stimulation is mapped in the parameter space of the model. Several representative response patterns to irregular inputs are presented.     

A resistor interpretation of general anisotropic cardiac tissue

This paper describes a spatial discretization scheme for partial differential equation systems that contain anisotropic diffusion. The discretization method uses unstructured finite volumes, or the boxes, that are formed as a secondary geometric structure from an underlying triangular mesh. We show how the discretization can be interpreted as a resistive circuit network, where each resistor is assigned at each edge of the triangular element. The resistor is computed as an anisotropy dependent geometric quantity of the local mesh structure. Finally, we show that under certain conditions, the discretization gives rise to negative resistors that can produce non-physical hyperpolarizations near depolarizing stimuli. We discuss how the proper choice of triangulation (anisotropic Delaunay triangulation) can ensure monotonicity (i.e. all resistors are positive).     

Simulation of the cardiovascular system using equivalent electronic system

This paper describes simulation of the cardiovascular system using a complex electronic circuit. In this study we have taken a slightly different approach to the modeling of the system and tried to advance existing electrical models by increasing more segments and parameters. The model consists of 42 segments representing the arterial system. Anatomical and physiological data for circuit parameters have been extracted from medical articles and textbooks. The frequency of heart is 1 Hz and the system operates in steady state condition. Each artery is modeled by one capacitor, resistor and inductor. The left and right ventricles are modeled using AC power suppliers and diodes. The results of the simulation including pressure and volume graphs exhibit operation of the cardiovascular system under normal condition. The results of the simulation have been compared with the relevant experimental observation and are in good agreement with them.     

A simple distensible vessel model for interpreting pulmonary vascular pressure-flow curves.

A simple distensible vessel model was developed for the purpose of interpreting the vascular pressure-flow curve in the zone 3 lung. The model-governing equation has two parameters: R0, representing the hemodynamic resistance of the undistended pulmonary vascular bed, and alpha, representing the distensibility of the resistance vessels. To evaluate the model, the governing equation was used in a nonlinear regression analysis of the pressure-flow data from isolated dog lung lobes. The dependency of the estimates of the model parameters in response to changes in perfusate viscosity (hematocrit) was determined. The distensible vessel model provided reasonable fits to the data, and, as predicted, R0, but not alpha, was hematocrit dependent. On the other hand, the traditional linear ohmic-Starling resistor model fit to the same pressure-flow data generally provided fits approaching those of the distensibility model only if the pressure intercept (the mean "critical closing pressure") was allowed to increase with hematocrit. Because the ohmic-Starling resistor concept does not predict a hematocrit dependence of the critical closing pressure, this latter observation is evidence that the distensible vessel model offers an alternative conceptualization of the pulmonary circulation worthy of additional study with respect to the interpretation of experimental pressure-flow data.     

Molecular dynamics simulation of film size and vacancy defect effects on the thermal conductivities of argon thin films

It is well known that there is a size effect for the thermal conductivity of thin films and that vacancy defects in film reduce the film's thermal conduction. In this paper, the film size and vacancy defect effects on the thermal conductivities of argon thin films were studied by molecular dynamics simulations. The results show the existence of phonon boundary scattering. The results also confirm that the theoretical model based on the Boltzmann equation can accurately model the thermal conduction of thin argon films. Both the theoretical and MD results illustrate that, although, both the defect and the thickness of the thin film deduce the thermal conductivity, their physical mechanisms differ.     

An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series

In this paper, the extended Kalman filter (EKF) algorithm is applied to model the gene regulatory network from gene time series data. The gene regulatory network is considered as a nonlinear dynamic stochastic model that consists of the gene measurement equation and the gene regulation equation. After specifying the model structure, we apply the EKF algorithm for identifying both the model parameters and the actual value of gene expression levels. It is shown that the EKF algorithm is an online estimation algorithm that can identify a large number of parameters (including parameters of nonlinear functions) through iterative procedure by using a small number of observations. Four real-world gene expression data sets are employed to demonstrate the effectiveness of the EKF algorithm, and the obtained models are evaluated from the viewpoint of bioinformatics.     

A microscopic model of enzyme kinetics.

Many in vivo enzymatic processes, such as those of the tissue factor pathway of blood coagulation, occur in environments with facilitated substrate delivery or enzymes bound to cellular or lipid surfaces, which are quite different from the ideal fluid environment for which the Michaelis-Menten equation was derived. To describe the kinetics of such reactions, we propose a microscopic model that focuses on the kinetics of a single-enzyme molecule. This model provides the foundation for macroscopic models of the system kinetics of reactions occurring in both ideal and nonideal environments. For ideal reaction systems, the corresponding macroscopic models thus derived are consistent with the Michaelis-Menten equation. It is shown that the apparent Km is in fact a function of the mechanism of substrate delivery and should be interpreted as the substrate level at which the enzyme vacancy time equals the residence time of ES-complexes; it is suggested that our microscopic model parameters characterize more accurately an enzyme and its catalytic efficiency than does the classical Km. This model can also be incorporated into computer simulations of more complex reactions as an alternative to explicit analytical formulation of a macroscopic model.     

Searching preference of the parasitoid,Anisopteromalus calandrae (Howard) for different stages of the host,Callosobruchus maculatus (F.) in the laboratory

The functional response parameters of the parasitoid, Anisopteromalus calandrae (Howard ) to the third instar, the fourth instar and the pupae of Callosobruchus maculatus (F.) were estimated from the Random Parasitoid Equation. By modifying this equation for a two host situation and using the parameters estimated above, a no switch model could be obtained. This model was then used to test for switching. In the preference experiments where two stages of the host were presented to the female parasitoid, a definite preference for the fourth instar followed by the pupa and the third instar, respectively was shown. There was, however, no evidence of switching. There was also no evidence that the data fitted the no switch models which suggests that when the parasitoid is searching in an environment with two or more hosts, its searching behaviour is more complex.     

Plant growth and respiration re-visited: maintenance respiration defined - it is an emergent property of, not a separate process within, the system - and why the respiration : photosynthesis ratio is conservative

Background and Aims

Plant growth and respiration still has unresolved issues, examined here using a model. The aims of this work are to compare the model''s predictions with McCree''s observation-based respiration equation which led to the ‘growth respiration/maintenance respiration paradigm’ (GMRP) – this is required to give the model credibility; to clarify the nature of maintenance respiration (MR) using a model which does not represent MR explicitly; and to examine algebraic and numerical predictions for the respiration:photosynthesis ratio.

Methods

A two-state variable growth model is constructed, with structure and substrate, applicable on plant to ecosystem scales. Four processes are represented: photosynthesis, growth with growth respiration (GR), senescence giving a flux towards litter, and a recycling of some of this flux. There are four significant parameters: growth efficiency, rate constants for substrate utilization and structure senescence, and fraction of structure returned to the substrate pool.

Key Results

The model can simulate McCree''s data on respiration, providing an alternative interpretation to the GMRP. The model''s parameters are related to parameters used in this paradigm. MR is defined and calculated in terms of the model''s parameters in two ways: first during exponential growth at zero growth rate; and secondly at equilibrium. The approaches concur. The equilibrium respiration:photosynthesis ratio has the value of 0·4, depending only on growth efficiency and recycling fraction.

Conclusions

McCree''s equation is an approximation that the model can describe; it is mistaken to interpret his second coefficient as a maintenance requirement. An MR rate is defined and extracted algebraically from the model. MR as a specific process is not required and may be replaced with an approach from which an MR rate emerges. The model suggests that the respiration:photosynthesis ratio is conservative because it depends on two parameters only whose values are likely to be similar across ecosystems.     

Biochemical switching device: how to turn on (off) the switch

We previously showed with computer simulations that cyclic enzyme systems have the reliability of ON-OFF types of operation (McCulloch-Pitts' neuronic equation) and the applicability for a switching circuit in a biocomputer. The switching time was inevitably determined in accordance with the difference in amount between two inputs of the system. This characteristic is, however, a disadvantage for practical use of a switching device; we need to improve the system in order for the switching time to optionally be changed. We shall present here how to turn on (off) the switch independently of the modes of two inputs. By introducing pulse perturbation, we could optionally set up the switching time of a cyclic enzyme system (biochemical switching device).     

Modeling error and stability of endothelial cytoskeletal membrane parameters based on modeling transendothelial impedance as resistor and capacitor in series

Transendothelial impedance across an endothelial monolayer grown on a microelectrode has previously been modeled as a repeating pattern of disks in which the electrical circuit consists of a resistor and capacitor in series. Although this numerical model breaks down barrier function into measurements of cell-cell adhesion, cell-matrix adhesion, and membrane capacitance, such solution parameters can be inaccurate without understanding model stability and error. In this study, we have evaluated modeling stability and error by using a ² evaluation and Levenberg-Marquardt nonlinear least-squares (LM-NLS) method of the real and/or imaginary data in which the experimental measurement is compared with the calculated measurement derived by the model. Modeling stability and error were dependent on current frequency and the type of experimental data modeled. Solution parameters of cell-matrix adhesion were most susceptible to modeling instability. Furthermore, the LM-NLS method displayed frequency-dependent instability of the solution parameters, regardless of whether the real or imaginary data were analyzed. However, the LM-NLS method identified stable and reproducible solution parameters between all types of experimental data when a defined frequency spectrum of the entire data set was selected on the basis of a criterion of minimizing error. The frequency bandwidth that produced stable solution parameters varied greatly among different data types. Thus a numerical model based on characterizing transendothelial impedance as a resistor and capacitor in series and as a repeating pattern of disks is not sufficient to characterize the entire frequency spectrum of experimental transendothelial impedance. cell-cell adhesion; cell-matrix adhesion; cell membrane capacitance; mathematical computation     

SeinFit,a Computer Program for the Estimation of the Seinhorst Equation

A computer program, "SeinFit," was created to determine the Seinhorst equation that best fits experimental data on the relationship between preplant nematode densities and plant growth. Data, which can be entered manually or imported from a text file, are displayed in a data window while the corresponding graph is shown in a graph window. Various options are available to manipulate the data and the graph settings. The best-fitting Seinhorst equation can be calculated by two methods that are both based on the evaluation of the residual sum of squares. Depending on the method, a range of values for different parameters of the Seinhorst equation can be chosen, as well as the number of steps in each range. Data, graphs, and values of the parameters of the Seinhorst equation can be printed. The program allows for quick calculation of the danaage threshold density - one of the parameters of the Seinhorst model. Versions written for Macintosh or DOS-compatible machines are currently available through the Society of Nematologists'' World Wide Web site (http://ianrwww.unl.edu/ianr/plntpath/ nematode/SOFTWARE/nemasoft.htm).     

Decrease in net photosynthesis caused by respiration

CO₂ exchange between air and leaf is conceived as a current along a resistor with a respiratory current, unaffected by CO₂ concentration, entering the resistor. The conclusion follows that a plant placed in an atmosphere free of CO₂ will increase the CO₂ concentration to the compensation concentration along a curve determined by the resistor and the volume of the atmosphere. This was verified. Also a photosynthesis rate calculated from the parameters of the observed curve agreed with an independent observation of photosynthesis in CO₂-free air. The decrease in net photosynthesis caused by respiration is, according to the model, the CO₂ compensation concentration divided by the concentration in the atmosphere.