Indistinguishability and identifiability analysis of linear compartmental models.

Two compartmental model structures are said to be indistinguishable if they have the same input-output properties. In cases in which available a priori information is not sufficient to specify a unique compartmental model structure, indistinguishable model structures may have to be generated and their attributes examined for relevance. An algorithm is developed that, for a given compartmental model, investigates the complete set of models with the same number of compartments and the same input-output structure as the original model, applies geometrical rules necessary for indistinguishable models, and test models meeting the geometrical criteria for equality of transfer functions. Identifiability is also checked in the algorithm. The software consists of three programs. Program 1 determines the number of locally identifiable parameters. Program 2 applies several geometrical rules that eliminate many (generally most) of the candidate models. Program 3 checks the equality between system transfer functions of the original model and models being tested. Ranks of Jacobian matrices and submatrices and other criteria are used to check patterns of moment invariants and local identifiability. Structural controllability and structural observability are checked throughout the programs. The approach was successfully used to corroborate results from examples investigated by others.     

Non-linear Membrane Properties in Entorhinal Cortical Stellate Cells Reduce Modulation of Input-Output Responses by Voltage Fluctuations

The presence of voltage fluctuations arising from synaptic activity is a critical component in models of gain control, neuronal output gating, and spike rate coding. The degree to which individual neuronal input-output functions are modulated by voltage fluctuations, however, is not well established across different cortical areas. Additionally, the extent and mechanisms of input-output modulation through fluctuations have been explored largely in simplified models of spike generation, and with limited consideration for the role of non-linear and voltage-dependent membrane properties. To address these issues, we studied fluctuation-based modulation of input-output responses in medial entorhinal cortical (MEC) stellate cells of rats, which express strong sub-threshold non-linear membrane properties. Using in vitro recordings, dynamic clamp and modeling, we show that the modulation of input-output responses by random voltage fluctuations in stellate cells is significantly limited. In stellate cells, a voltage-dependent increase in membrane resistance at sub-threshold voltages mediated by Na⁺ conductance activation limits the ability of fluctuations to elicit spikes. Similarly, in exponential leaky integrate-and-fire models using a shallow voltage-dependence for the exponential term that matches stellate cell membrane properties, a low degree of fluctuation-based modulation of input-output responses can be attained. These results demonstrate that fluctuation-based modulation of input-output responses is not a universal feature of neurons and can be significantly limited by subthreshold voltage-gated conductances.     

Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their input-output equations

When examining the structural identifiability properties of dynamic system models, some parameters can take on an infinite number of values and yet yield identical input-output data. These parameters and the model are then said to be unidentifiable. Finding identifiable combinations of parameters with which to reparameterize the model provides a means for quantitatively analyzing the model and computing solutions in terms of the combinations. In this paper, we revisit and explore the properties of an algorithm for finding identifiable parameter combinations using Gröbner Bases and prove useful theoretical properties of these parameter combinations. We prove a set of M algebraically independent identifiable parameter combinations can be found using this algorithm and that there exists a unique rational reparameterization of the input-output equations over these parameter combinations. We also demonstrate application of the procedure to a nonlinear biomodel.     

An efficient model development strategy for bioprocesses based on neural networks in macroscopic balances

In the serial gray box modeling strategy, generally available knowledge, represented in the macroscopic balance, is combined naturally with neural networks, which are powerful and convenient tools to model the inaccurately known terms in the macroscopic balance. This article shows, for a typical biochemical conversion, that in the serial gray box modeling strategy the identification data only have to cover the input-output space of the inaccurately known term in the macroscopic balances and that the accurately known terms can be used to achieve reliable extrapolation. The strategy is demonstrated successfully on the modeling of the enzymatic (repeated) batch conversion of penicillin G, for which real-time results are presented. Compared with a more data-driven black box strategy, the serial gray box strategy leads to models with reliable extrapolation properties, so that with the same number of identification experiments the model can be applied to a much wider range of different conditions. Compared to a more knowledge-driven white box strategy, the serial gray box model structure is only based on readily available or easily obtainable knowledge, so that the development time of serial gray box models still may be short in a situation where there is no detailed knowledge of the system available. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 549-566, 1997.     

Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity

We present a novel formulation for biochemical reaction networks in the context of protein signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of “source” species, which are interpreted as input signals. Signals are transmitted to all other species in the system (the “target” species) with a specific delay and with a specific transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and even recalled to build dynamical models on the basis of state changes. By separating the temporal and the magnitudinal domain we can greatly simplify the computational model, circumventing typical problems of complex dynamical systems. The transfer function transformation of biochemical reaction systems can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant novel insights while remaining a fully testable and executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modularizations that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. Remarkably, we found that overall interconnectedness depends on the magnitude of inputs, with higher connectivity at low input concentrations and significant modularization at moderate to high input concentrations. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.     

Time series modeling of neuromuscular system

The dynamic response of the human ankle joint to a bandlimited random torque perturbation superimposed on a constant bias torque is observed in normal human subjects. The applied torque input, the joint angular rotation output, and the electromyographic activity using surface electrodes from the extensor and the flexor muscles of the ankle joint were recorded. Transfer function models using time series techniques were developed for the torque — angular rotation input-output pair and for the angular rotation — electromyographic activity input-output pair. A parameter constraining technique was applied to develop more reliable models. It is shown that the asymptotic behavior of the system must be taken into account during parameter optimization to develop better predictive models.This work was supported in part by National Science Foundation grant ENG-7608754 and grants from the National Institutes of Health NS-12877 and NS-00196     

Statistical approach in search for optimal signal in simple olfactory neuronal models

Several models (concentration detectors and a flux detector) for coding of odor intensity in olfactory sensory neurons are investigated. Behavior of the system is described by different stochastic processes of binding the odorant molecules to the receptors and their activation. Characteristics how well the odorant concentration can be estimated from the knowledge of response, the number of activated neurons, are studied. The approach is based on the Fisher information and analogous measures. These measures of optimality are computed and applied to locate the odorant concentration which is most suitable for coding. The results are compared with the classical deterministic approach which judges the optimal odorant concentration via steepness of the input-output function.     

On the identifiability of linear compartmental systems: a revisited transfer function approach based on topological properties

This work deals with the problem of the a priori identifiability of compartmental systems from input-output experiments. A new approach is presented, in which, having associated a directed graph with the matrix to be identified, a set of “forms” is defined which are functions of the elements of matrix itself. It is shown how, by exploiting the topological properties of the graph and its subgraphs, the problem can be simplified into one of smaller dimensions. Examples are provided to illustrate this new approach.     

Model versus model or model versus data? A commentary on Berg and McDowell's "Quantitative, steady-state properties of Catania's computational model of the operant reserve"

Berg and McDowell's (2011) systematic exploration of some parameters of Catania's (2005) operant reserve model generated significant departures from the data predicted by matching models, especially in the form of an inflection point at the low end of the input-output function. The models need to be compared not only with each other but also with data. Much of the data to which both models have been fitted was obtained decades ago using equipment that constrained procedures and created unanalyzed contingencies. For example, in those days scheduled but unobtained reinforcers could not accumulate. To do justice to the sophistication of contemporary models, we need new data sets based on schedules that do not include such artifacts. Without such data, it is impossible to say whether the Berg/McDowell inflections are properties of behavior revealed by the model or are instead deviations of the model from real behavior and from other models.     

A new approach to reconstruction models of dendritic branching patterns

Quantitative models for characterising the detailed branching patterns of dendritic trees aim to explain these patterns either in terms of growth models based on principles of dendritic development or reconstruction models that describe an existing structure by means of a canonical set of elementary properties of dendritic morphology, which when incorporated into an algorithmic procedure will generate samples of dendrites that are statistically indistinguishable in both canonical and emergent features from those of the original sample of real neurons. This article introduces a conceptually new approach to reconstruction modelling based on the single assumption that dendritic segments are built from sequences of units of constant diameter, and that the distribution of the lengths of units of similar diameter is independent of location within a dendritic tree. This assumption in combination with non-parametric methods for estimating univariate and multivariate probability densities leads to an algorithm that significantly reduces the number of basic parameters required to simulate dendritic morphology. It is not necessary to distinguish between stem and terminal segments or to specify daughter branch ratios or dendritic taper. The procedure of sampling probability densities conditioned on local morphological features eliminates the need, for example, to specify daughter branch ratios and dendritic taper since these emerge naturally as a consequence of the conditioning process. Thus several basic parameters of previous reconstruction algorithms become emergent parameters of the new reconstruction process. The new procedure was applied successfully to a sample of 51 interneurons from lamina II/III of the spinal dorsal horn.     

Infinite number of solutions to the hemodynamic inverse problem

Investigators have had much success solving the "hemodynamic forward problem," i.e., predicting pressure and flow at the entrance of an arterial system given knowledge of specific arterial properties and arterial system topology. Recently, the focus has turned to solving the "hemodynamic inverse problem," i.e., inferring mechanical properties of an arterial system from measured input pressure and flow. Conventional methods to solve the inverse problem rely on fitting to data simple models with parameters that represent specific mechanical properties. Controversies have arisen, because different models ascribe pressure and flow to different properties. However, an inherent assumption common to all model-based methods is the existence of a unique set of mechanical properties that yield a particular pressure and flow. The present work illustrates that there are, in fact, an infinite number of solutions to the hemodynamic inverse problem. Thus a measured pressure-flow pair can result from an infinite number of different arterial systems. Except for a few critical properties, conventional approaches to solve the inverse problem for specific arterial properties are futile.     

The mechanism distinguishability problem in biochemical kinetics: the single-enzyme, single-substrate reaction as a case study

A theoretical analysis of the distinguishability problem of two rival models of the single enzyme-single substrate reaction, the Michaelis-Menten and Henri mechanisms, is presented. We also outline a general approach for analysing the structural indistinguishability between two mechanisms. The approach involves constructing, if possible, a smooth mapping between the two candidate models. Evans et al. [N.D. Evans, M.J. Chappell, M.J. Chapman, K.R. Godfrey, Structural indistinguishability between uncontrolled (autonomous) nonlinear analytic systems, Automatica 40 (2004) 1947-1953] have shown that if, in addition, either of the mechanisms satisfies a particular criterion then such a transformation always exists when the models are indistinguishable from their experimentally observable outputs. The approach is applied to the single enzyme-single substrate reaction mechanism. In principle, mechanisms can be distinguished using this analysis, but we show that our ability to distinguish mechanistic models depends both on the precise measurements made, and on our knowledge of the system prior to performing the kinetics experiments.     

环境投入产出分析在产业生态学中的应用

综述了环境投入产出分析的基本知识及其在产业生态学领域的应用。环境投入产出分析的核心是投入产出模型,包括价值型投入产出模型、实物型投入产出模型和混合型投入产出模型。环境投入产出分析在产业生态学领域主要用于环境压力核算、生命周期评估、社会经济因素相对贡献分析、产业链路径分析、风险影响分析和环境网络分析。同时,相关学者进行环境投入产出数据库开发,给环境投入产出分析提供便捷、标准化的数据渠道。讨论了环境投入产出分析的若干发展趋势。     

The analysis of nonlinear synaptic transmission

In order to characterize synaptic transmission at a unitary facilitating synapse in the lobster cardiac ganglion, a new nonlinear systems analysis technique for discrete-input systems was developed and applied. From the output of the postsynaptic cell in response to randomly occurring presynaptic nerve impulses, a set of kernels, analogous to Wiener kernels, was computed. The kernels up to third order served to characterize, with reasonable accuracy, the input-output properties of the synapse. A mathematical model of the synapse was also tested with a random impulse train and model predictions were compared with experimental synaptic output. Although the model proved to be even more accurate overall than the kernel characterization, there were slight but consistent errors in the model's performance. These were also reflected as differences between model and experimental kernels. It is concluded that a random train analysis provides a comprehensive and objective comparison between model and experiment and automatically provides an arbitrarily accurate characterization of a system's input-output behavior, even in complicated cases where other approaches are impractical.     

Stochastic automaton models for the temporal pattern discrimination of nerve impulse sequences

The application of stochastic automata to the input-output relations of single neurons is considered. For this, some stochastic properties of temporal pattern discrimination in single synaptic cells are used to suggest stochastic automaton models. The models have only three possible states, the active, the absolute refractory and the relative refractory states, which are sufficient for temporal pattern sensitivity. From such an application, it was found that the temporal pattern discriminating structures in the models are similar to those used for experimental data and computer simulation (real-time neuron models). Extensions related to temporal pattern learning are discussed.     

Econometric models for biohydrogen development

Biohydrogen is considered as an attractive clean energy source due to its high energy content and environmental-friendly conversion. Analyzing various economic scenarios can help decision makers to optimize development strategies for the biohydrogen sector. This study surveys econometric models of biohydrogen development, including input-out models, life-cycle assessment approach, computable general equilibrium models, linear programming models and impact pathway approach. Fundamentals of each model were briefly reviewed to highlight their advantages and disadvantages. The input-output model and the simplified economic input-output life-cycle assessment model proved most suitable for economic analysis of biohydrogen energy development. A sample analysis using input-output model for forecasting biohydrogen development in the United States is given.     

Erasing Sensorimotor Memories via PKMζ Inhibition

Sensorimotor cortex has a role in procedural learning. Previous studies suggested that this learning is subserved by long-term potentiation (LTP), which is in turn maintained by the persistently active kinase, protein kinase Mzeta (PKMζ). Whereas the role of PKMζ in animal models of declarative knowledge is established, its effect on procedural knowledge is not well understood. Here we show that PKMζ inhibition, via injection of zeta inhibitory peptide (ZIP) into the rat sensorimotor cortex, disrupts sensorimotor memories for a skilled reaching task even after several weeks of training. The rate of relearning the task after the memory disruption by ZIP was indistinguishable from the rate of initial learning, suggesting no significant savings after the memory loss. These results indicate a shared molecular mechanism of storage for declarative and procedural forms of memory.     

Model Identification of a Micro Air Vehicle

This paper is focused on the model identification of a Micro Air Vehicle （MAV） in straight steady flight condition. The identification is based on input-output data collected from flight tests using both frequency and time dorrtain techniques. The vehicle is an in-house 40 cm wingspan airplane. Because of the complex coupled, multivariable and nonlinear dynamics of the aircraft, linear SISO structures for both the lateral and longitudinal models around a reference state were derived. The aim of the identification is to provide models that can be used in future development of control techniques for the MAV.