Sensitivity analysis of a model of mammalian neural membrane

The sensitivity of the strength-duration (S-D) relationship to changes in the parameters describing the sodium channel of mammalian neuronal membrane was determined by computer simulation. A space-clamped patch of neuronal membrane was modeled by a parallel nonlinear sodium conductance, linear leakage conductance, and membrane capacitance. Each parameter that governs the activation (m) and inactivation (h) variables of the sodium channel was varied from −50% to +50% of its default value, and for each variation a S-D relationship was generated. Individual changes in six of the eleven parameters (α _m A, α _m D, α _h A, β _m A, β _m B, and β _h B) generated substantial changes in the rheobase current and chronaxie time (Tch) of the model. Changing the parameter values individually did not correct for the model's failure to generate excitation after the release from a long duration hyperpolarization (anode break excitation). Scaling a combination of five parameters (α _m A, α _m B, α _h A, β _m A, and β _h B) by an equal amount produced a model that generated anode break excitation and increased Tch, but also decreased the amplitude of the action potential. To reproduce the amplitude of the action potential, the maximum sodium conductance and sodium Nernst potential were increased. These modifications generated a model that had S-D properties closer to experimental results, could produce anode break excitation, and reproduced the action potential amplitude. Received: 6 October 1997 / Accepted in revised form: 3 April 1998     

A mathematical model for insulin kinetics. III. Sensitivity analysis of the model

A non-linear mathematical model involving four variables and several constants incorporating beta-cell kinetics, a glucose-insulin feedback system and a gastrointestinal absorption term had been applied in earlier papers to various forms of diabetes mellitus. In this paper, we examine the response of the system to variations in the parameters and to initial conditions using sensitivity analysis. It is found that such a method leads to results that are consistent with clinical findings. Further, it is suggested that such an analysis could help in making some predictions regarding future directions in the therapy of diabetes mellitus.     

Sensitivity analysis and optimization for a head movement model

A sixth order nonlinear model for horizontal head rotations in humans is analyzed using an extended parameter sensitivity analysis and a global optimization algorithm. The sensitivity analysis is used in both the direct sense, as a model fitting tool, and in the indirect sense, as a guide to experimental design. Resolution is defined in terms of the sensitivity table, and is used to interpret the sensitivity results. Using sensitivity analyses, the head and eye movement systems are compared and contrasted. Controller signal parameters are the most influential. Their variations and effects on head movement trajectories and accelerations are investigated, and the conclusions are compared with clinical neurological findings. The global optimization algorithm, in addition to automating the fitting of various types of data, is combined with time optimality theory to give theoretical time-optimal inputs to the model.On leave from Department of Neurology, University of Hamburg, FRG; supported by Deutsche Forschungsgemeinschaft Bonn, FRG     

Two-mutation model for carcinogenesis: joint analysis of premalignant and malignant lesions.

A model for carcinogenesis that postulates two rate-limiting events for malignant transformation is a generalization of the recessive oncogenesis hypothesis, according to which inactivation of homologous tumor suppressor genes leads to cancer. This model has been shown to be consistent with a large body of epidemiologic and experimental data and has recently been used for the analysis of altered hepatic foci in rodents. These foci are considered to be premalignant lesions. In this paper the necessary mathematics for the joint analysis of premalignant and malignant lesions are developed within the framework of this model.     

Sensitivity analysis and reduction of a dynamic model of a bioproduction of fructo-oligosaccharides

Bioprocess and Biosystems Engineering - Starting from a relatively detailed model of a bioprocess producing fructo-oligosaccharides, a set of experimental data collected in batch and fed-batch...     

Environmental carcinogenesis: an integrative model.

An integrative theory is proposed in which environmental carcinogenesis is viewed as a process by which the genetic control of cell division and differentiation is altered by carcinogens. In this theory, carcinogens include physical, chemical, and viral "mutagens," as well as chemical and viral gene modulators. Existing explanations of carcinogenesis can be considered either as somatic mutation theories or as epigenetic theories. Evidence seems to support the hypothesis that both mutations and epigenetic processes are components of carcinogenesis. The mutational basis of cancer is supported by the clonal nature of tumors, the mutagenicity of most carcinogens, high mutation frequencies in cells of cancer-prone human fibroblasts lacking DNA repair enzymes, the correlation of in vitro DNA damage and in vitro mutation and transformation frequencies with in vivo tumorigenesis, age-related incidences of various hereditary tumors, and the correlation between photoreactivation of DNA damage and the biological amelioration of UV-induced neoplasms. Since both mutagens and gene modulators can be carcinogenic it may be that carcinogens affect genes which control cell division. An integration of the mutation and epigenetic theories of cancer with the "two-stage" theory and Comings's general theory of carcinogenesis is proposed. This integrative theory postulates that carcinogens can affect regulatory genes which control a series of "transforming genes." A general hypothesis is advanced that involves a common mechanism of somatic mutagenesis via error-prone repair of DNA damage which links carcinogenesis, teratogenesis, atherosclerosis and aging. Various concepts are presented to provide a framework for evaluating the scientific, medical, and social implications of cancer.     

Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics

A formal sensitivity analysis is performed on a delay differential equation model for the viral dynamics of an in vivo HIV infection during protease inhibitor therapy. We present results of both a differential analysis as well as a principle component based analysis and provide evidence that suggests the exact times at which specific parameters have the most influence over the solution. We offer insight into the pairwise mathematical relationships between the productively infected T-cell death rate δ, the viral plasma clearance rate c, and the time delay τ between infection and viral production as they relate to the viral dynamics. The results support the claim that the presence of a nonzero delay has a major impact on the model dynamics. Lastly, we comment upon the inadequacies of an alternative principle component based analysis.     

Sensitivity analysis of a biofilm model describing a one-stage completely autotrophic nitrogen removal (CANON) process.

A mathematical model for nitrification and anaerobic ammonium oxidation (ANAMMOX) processes in a single biofilm reactor (CANON) was developed. This model describes completely autotrophic conversion of ammonium to dinitrogen gas. Aerobic ammonium and nitrite oxidation were modeled together with ANAMMOX. The sensitivity of kinetic constants and biofilm and process parameters to the process performance was evaluated, and the total effluent concentrations were, in general, found to be insensitive to affinity constants. Increasing the amount of biomass by either increasing biofilm thickness and density or decreasing porosity had no significant influence on the total effluent concentrations, provided that a minimum total biomass was present in the reactor. The ANAMMOX process always occurred in the depth of the biofilm provided that the oxygen concentration was limiting. The optimal dissolved oxygen concentration level at which the maximum nitrogen removal occurred is related to a certain ammonium surface load on the biofilm. An ammonium surface load of 2 g N/m2. d, associated with a dissolved oxygen concentration level of 1.3 g O2/m3 in the bulk liquid and with a minimum biofilm depth of 1 mm seems a proper design condition for the one-stage ammonium removal process. Under this condition, the ammonium removal efficiency is 94% (82% for the total nitrogen removal efficiency) (30 degrees C). Better ammonium removal could be achieved with an increase in the dissolved oxygen concentration level, but this would strongly limit the ANAMMOX process and decrease total nitrogen removal. It can be concluded that a one-stage process is probably not optimal if a good nitrogen effluent is required. A two-stage process like the combined SHARON and ANAMMOX process would be advised for complete nitrogen removal.     

A stochastic two-stage carcinogenesis model: a new approach to computing the probability of observing tumor in animal bioassays.

A new definition of probability of observing tumor in animal bioassay is developed. It is derived from a two-stage stochastic model for carcinogenesis with time-dependent birth and death rates for cell proliferation. The model takes into account the method of collecting data on preneoplastic and neoplastic lesions. The new definition is appropriate for analyzing the presence or absence of tumors in animal bioassays.     

Efficient simulation under a population genetics model of carcinogenesis

MOTIVATION: Cancer is well known to be the end result of somatic mutations that disrupt normal cell division. The number of such mutations that have to be accumulated in a cell before cancer develops depends on the type of cancer. The waiting time T(m) until the appearance of m mutations in a cell is thus an important quantity in population genetics models of carcinogenesis. Such models are often difficult to analyze theoretically because of the complex interactions of mutation, drift and selection. They are also computationally expensive to simulate because of the large number of cells and the low mutation rate. RESULTS: We develop an efficient algorithm for simulating the waiting time T(m) until m mutations under a population genetics model of cancer development. We use an exact algorithm to simulate evolution of small cell populations and coarse-grained τ-leaping approximation to handle large populations. We compared our hybrid simulation algorithm with the exact algorithm in small populations and with available asymptotic results for large populations. The comparison suggested that our algorithm is accurate and computationally efficient. We used the algorithm to study the waiting time for up to 20 mutations under a Moran model with variable population sizes. Our new algorithm may be useful for studying realistic models of carcinogenesis, which incorporates variable mutation rates and fitness effects.     

Sensitivity of a Hill-based muscle model to perturbations in model parameters

Musculoskeletal simulations of human movement commonly use Hill muscle models to predict muscle forces, but their sensitivity to model parameter values is not well understood. The purpose of this study was to evaluate muscle model sensitivity to perturbations in 14 Hill muscle model parameters in forward dynamic simulations of running and walking by varying each by +/-50%. Three evaluations of the muscle model were performed based on: (1) calculating the sensitivity of the muscle model only, (2) determining the continuous partial derivatives of the muscle equations with respect to each parameter, and (3) evaluating the effects on the running and walking simulations. Model evaluations were found to be very sensitive (percent change in outputs greater than parameter perturbation) to parameters defining the series elastic component (tendon), force-length curve of the contractile element and maximum isometric force. For some parameters, the range of literature values was larger than the model sensitivity. Model evaluations were insensitive to parameters defining the parallel elastic element, force-velocity curve of the contractile element and muscle activation time constants. The derivative method provided similar results, but also provided a generic, continuous equation that can easily be applied to other motions. The sensitivities of the running and walking simulations were reduced compared to the sensitivity of the muscle model alone. Results demonstrate the importance of evaluating sensitivity of a musculoskeletal simulation in a controlled manner and provide an indication of which parameters must be selected most carefully based on the sensitivity of a given movement.     

Explanation of enigmas of the Lynch syndrome thanks to a new carcinogenesis model characterized by an unorthodox initiation process

The genotype-phenotype relationship of Lynch syndrome displays many enigmatic features which cannot be explained satisfactorily by the prevailing concepts of carcinogenesis and genetic predisposition to cancer. We propose here a new model of carcinogenesis divided into two and only two evolutive phases: a) a preliminary phase starting with the counter-selective loss of mismatch repair function, in which most clones with the RER mutator phenotype are eliminated through apoptosis or an accelerated ageing process; b) an explosive phase that is initiated only if mutations blocking apoptosis and senescence, rapidly acquired during the short life span of the non-transformed RER+ clones, eventually rescue one mismatch repair-deficient cell that gives rise to the malignant clone. Carcinogenesis is proposed here to progress irreversibly and very rapidly once initiated. We shall show how this model provides a meaningful etiologic and pathogenic interpretation of all the curious features of Lynch syndrome.     

Sensitivity of plant functional types to climate change: classification tree analysis of a simulation model

Question: The majority of studies investigating the impact of climate change on local plant communities ignores changes in regional processes, such as immigration from the regional seed pool. Here we explore: (i) the potential impact of climate change on composition of the regional seed pool, (ii) the influence of changes in climate and in the regional seed pool on local community structure, and (iii) the combinations of life history traits, i.e. plant functional types (PFTs), that are most affected by environmental changes. Location: Fire‐prone, Mediterranean‐type shrublands in southwestern Australia. Methods: Spatially explicit simulation experiments were conducted at the population level under different rainfall and fire regime scenarios to determine the effect of environmental change on the regional seed pool for 38 PFTs. The effects of environmental and seed immigration changes on local community dynamics were then derived from community‐level experiments. Classification tree analyses were used to investigate PFT‐specific vulnerabilities to climate change. Results: The classification tree analyses revealed that responses of PFTs to climate change are determined by specific trait characteristics. PFT‐specific seed production and community patterns responded in a complex manner to climate change. For example, an increase in annual rainfall caused an increase in numbers of dispersed seeds for some PFTs, but decreased PFT diversity in the community. Conversely, a simulated decrease in rainfall reduced the number of dispersed seeds and diversity of PFTs. Conclusions: PFT interactions and regional processes must be considered when assessing how local community structure will be affected by environmental change.     

Activation of multiple oncogene pathways: a model for experimental carcinogenesis

Evidence from experimental animal tumor models suggests that in many instances, the identity and mechanism of activation of cellular oncogenes is a function of both carcinogen and tissue specificity. In addition, the activation of no single oncogene has yet been found to be either sufficient or necessary for tumorigenesis in any particular experimental system. A hypothesis to account for these and other molecular and biological observations of experimental tumorigenesis has been developed. The hypothesis is based on the premise that multiple tissue specific groups or pathways of oncogenes exist in each cell, and that activation of all the oncogenes in any of these alternative pathways leads to transformation. It is assumed that each oncogene (which may be a member of one or more pathways) has a spontaneous and a carcinogen specific probability of activation. The latter value will vary from carcinogen to carcinogen. By modelling the spontaneous and carcinogen specific probabilities of activation of each gene, the number and identity of genes in each pathway, and the number of pathways in a particular cell type, it is possible to calculate the relative potency of carcinogens, the percentage of tumors containing each activated oncogene, the dose-response relationship, and other parameters. Use of this hypothetical model gives results consistent with experimental observations on oncogene activation in carcinogen-induced animal tumors.     

Receptor-mediated transport of vacuolar proteins: a critical analysis and a new model

In this article we challenge the widely accepted view that receptors for soluble vacuolar proteins (VSRs) bind to their ligands at the trans-Golgi network (TGN) and transport this cargo via clathrin-coated vesicles (CCV) to a multivesicular prevacuolar compartment. This notion, which we term the “classical model” for vacuolar protein sorting, further assumes that low pH in the prevacuolar compartment causes VSR–ligand dissociation, resulting in a retromer-mediated retrieval of the VSRs to the TGN. We have carefully evaluated the literature with respect to morphology and function of the compartments involved, localization of key components of the sorting machinery, and conclude that there is little direct evidence in its favour. Firstly, unlike mammalian cells where the sorting receptor for lysosomal hydrolases recognizes its ligand in the TGN, the available data suggests that in plants VSRs interact with vacuolar cargo ligands already in the endoplasmic reticulum. Secondly, the evidence supporting the packaging of VSR–ligand complexes into CCV at the TGN is not conclusive. Thirdly, the prevacuolar compartment appears to have a pH unsuitable for VSR–ligand dissociation and lacks the retromer core and the sorting nexins needed for VSR recycling. We present an alternative model for protein sorting in the TGN that draws attention to the much overlooked role of Ca²⁺ in VSR–ligand interactions and which may possibly also be a factor in the sequestration of secretory proteins.     

Sensitivity analysis of a mathematical model of phytoplankton growth and nutrient distribution in the Pacific Ocean off the northwestern U.S. coast

In a recent publication (Jamart el al., Deep-Sea Research, 24,753–773, 1977) we describe a numerical two-dimensional(time and depth) model of phytoplankton growth and nutrientdistribution in the Pacific Ocean off the northwestern U.S.coast. The numerical model consists of coupled integro-partialdifferential equations expressing conservation of chlorophyll, nitrate, and ammonium. The relevant physical and biologicalprocesses are represented by conventional functions and parameters.The system is "closed" by specification of grazing pressureand light intensity. A long-term simulation ova spring and summermonths (for convenience, called the "standard run") representswell the main features of observed chemical data and biologicalvariables, including the formation and deepening of a subsurfacechlorophyll maximum. In this paper, a sensitivity analysis of the system is carriedout by comparing the "standard run" with the results of twentynumerical experiments, in each of which a single function orparameter in the model is modified. The formation of the subsurfacechlorophyll maximum is simulated, more or less realistically,in all experiments. Moreover, the results suggest that the chlorophylldistribution adjusts in time and depth so as to optimize thetransfer of carbon to secondary producers. The level of thecarbon output is determined mainly by the resources availableto the primary producers.