Analysis of interaction for mixtures of agents using the linear isobole

The linear isobole that is commonly used as a reference for the study of interaction is derived from the interaction of an agent with itself. It is shown that the general use of the linear isobole in the study of the combined effects of mixtures of agents implies interaction between the agents whether the dose-effect curves of the agents are the same or not. It is difficult to generalize the interaction between two doses of the same agent to the interaction between two doses of different agents with different action mechanisms without the use of a mechanistic model. Predictions using non-interaction defined as independent action are generally different from those using linear isobole. A simple mechanistic framework based on the concept of common intermediate lesions is introduced in this paper to relate these two methods used for the analysis of synergism and antagonism. In this framework of lesion development, two agents that have no common intermediate lesion in their action will be non-interactive (referred to as independent action). When the two agents share a common intermediate, it is shown that the combined effect will follow the linear isobole (referred to as common action). This simple framework of analysis is applicable to the general study of interaction between two agents with different types of dose-effect curves.     

Evaluation of interaction in olfactory and taste mixtures

Models for the evaluation of interaction in olfactory and tastemixtures are compared to the isobole approach, which is widelyused in other fields of biomedical research. Analogies and differencesare described in detail. The isobole approach has a profoundtheoretical basis and can be applied to all possible types ofconcentration–response relationships, in particular toall values of exponents in the widely used power function, andeven if analytical expression of concentration–responserelationships are not known. Due to this generality it leadsto a substantial simplification of the evaluation proceduresas compared to other methods used in taste and olfaction research.It can be applied to any number of components of a mixture.Response surface modeling and computer graphics is recommededin appropriate cases because it can provide information on theconcentration dependence of interaction. Even though it hasto be pointed out that there is no general consensus on themost appropriate approach for the evaluation of interactionbetween biologically active agents so far, we are led to theconclusion that good arguments can be made in supporting theapplication of the isobole method for taste and olfactory mixtures.     

Culture instability of auxotrophic amino acid producers

The long-term dynamic characteristics of the L-lysine producer Corynebcterium glutamicum in continuous culture were studied over a range of specific growth rates. The double-auxotroph parent strain was found to be susceptible to a back mutation, or reversion, which negated the regulatory bypass that allows this strain to accumulate L-lysine in culture but also gives rise to a L-threonine auxotrophic requirement. Consequently, the revertant cells no longer over-produced L-lysine, nor were they limited in their growth by the low levels of L-threonine in the medium. All continuous culture experiments were enventually taken over by these revertants. The instability of the culture was found to be primarily due to the growth rate differential between the two competing populations, the (productive) parent auxotrophs and the (nonproductive) revertants. A deterministic mathematical model of the culture dynamics, incoroporating two limiting-substrate balances, satisfactorily described the takeover profiles. A linear stability analysis of the model equations identified that although long-term culture demise is inevitable, the dimensionless ratio of the two limiting substrates controls the rate of takeover by nonproductive cells. The anslysis further demonstrated the importance of proper medium design in delaying the onset of takeover in cultures of this double-auxotroph strain. The theoretical medium design criterion was then confirmed experimentally by the stabilization of a fed-batch culture against revertant takeover for an extended fermentation time.     

A general formulation of the concept of independent action for the combined effects of agents

Analysis schemes for the classification of synergism and antagonism for mixed agents operate on the discrepancies between observed and calculated results. As such they cannot be confirmed by experiments and therefore have to be tested in terms of mathematical and logical self-consistency. The concept of independent action is close to the literal meaning of the term “non-interaction”. Since this concept does not depend on the mechanisms of actions nor on the type of effect scale used, it is suitable as one of the basic criterion for the definition of synergism and antagonism. A general mathematical framework of independent action is presented in this paper based on the concept of “relative effect” as used in the literature. The, different equations for independent action currently used in various areas are shown to be manifestations, of a general formula under different sets of boundary conditions, which are the natural limiting values of the effects of the corresponding system observed at low and at high doses of the agents. The framework can, be generalized to the combined action ofn-agents as well as to the interaction of an agent with itself. In addition, the differential form of the formula for independent action is derived. This framework of systematic definitions and derived equations enable a more in-depth study of the implications of the concept of independent action and its relation to other concepts of non-interaction.     

A simple function for full‐subsets multiple regression in ecology with R

Full‐subsets information theoretic approaches are becoming an increasingly popular tool for exploring predictive power and variable importance where a wide range of candidate predictors are being considered. Here, we describe a simple function in the statistical programming language R that can be used to construct, fit, and compare a complete model set of possible ecological or environmental predictors, given a response variable of interest and a starting generalized additive (mixed) model fit. Main advantages include not requiring a complete model to be fit as the starting point for candidate model set construction (meaning that a greater number of predictors can potentially be explored than might be available through functions such as dredge); model sets that include interactions between factors and continuous nonlinear predictors; and automatic removal of models with correlated predictors (based on a user defined criterion for exclusion). The function takes continuous predictors, which are fitted using smoothers via either gam, gamm (mgcv) or gamm4, as well as factor variables which are included on their own or as two‐level interaction terms within the gam smooth (via use of the “by” argument), or with themselves. The function allows any model to be constructed and used as a null model, and takes a range of arguments that allow control over the model set being constructed, including specifying cyclic and linear continuous predictors, specification of the smoothing algorithm used, and the maximum complexity allowed for smooth terms. The use of the function is demonstrated via case studies that highlight how appropriate model sets can be easily constructed and the broader utility of the approach for exploratory ecology.     

EFFICIENT DESIGNS FOR STUDYING SYNERGISTIC DRUG COMBINATIONS

Distinguishing between pharmacologically additive and synergistic drug combinations requires experimental designs and statistical analyses that often require appreciable numbers of animals and much experimenter time. The current study employed a design in which individual dose-effect data from each drug were translated into theoretically additive total dose combinations, in a fixed drug proportion, in order to produce a composite additive dose-effect relation that could be compared with that of an actual mixture having the same proportion. Results from this approach, using a combination of intrathecal doses of morphine and clonidine, were virtually identical to those using isobolographic analysis of the same data set. Both analyses showed significant synergism for this combination and, in each method, it was not necessary to constrain the drug regression lines to parallelism. In contrast to the isobole approach, the use of the composite additive dose-effect relation also allows observation of the interaction over a range of effects while reducing the size of the data sets needed. © 1997 Elsevier Science Inc.     

A note on mathematical models for the interaction of neural elements

By introducing a plausible model for the initiation of axonal impulses the output is obtained as a function of the input incoming impulses. If the temporal aspects of the excitatory process resulting from the afferent impulses are sufficiently rapid one obtains the discontinuous or microscopic model of McCulloch-Pitts. If these are sufficiently slow a continuous model, such as Rashevsky’s one or two factor theory, is a natural model. But the linear relation between the strength of excitation of one axon and excitatory factor of the next will not in general hold. However, under conditions which are not too restrictive the linear relation with threshold can be considered as satisfactory approximation over a fairly wide range of values. This research was supported in whole or in part by the U. S. Air Force under Contract AF 49(638)-414 monitored by the Air Force Office of Scientific Research.     

New modeling approach for bounding flight in birds

A new modeling approach is presented which accounts for the unsteady motion features and dynamics characteristics of bounding flight. For this purpose, a realistic mathematical model is developed to describe the flight dynamics of a bird with regard to a motion which comprises flapping and bound phases involving acceleration and deceleration as well as, simultaneously, pull-up and push-down maneuvers. Furthermore, a mathematical optimization method is used for determining that bounding flight mode which yields the minimum energy expenditure per range. Thus, it can be shown to what extent bounding flight is aerodynamically superior to continuous flapping flight, yielding a reduction in the energy expenditure in the speed range practically above the maximum range speed. Moreover, the role of the body lift for the efficiency of bounding flight is identified and quantified. Introducing an appropriate non-dimensionalization of the relations describing the bird’s flight dynamics, results of generally valid nature are derived for the addressed items.     

A new kinetic model of protein adsorption on suspended anion-exchange resin particles.

The kinetics of adsorption of bovine serum albumin on an anion-exchange resin were measured in a batch system using a flow cell and ultraviolet absorbance, as a function of initial liquid-phase protein concentration and solid-to-liquid phase ratio. A new mathematical model for adsorption kinetics is presented that fits the experimental data to give a highly linear relationship with time, following a short transient period. Numerical integration of the differential form of the new composite nonlinear (CNL) kinetic model, containing three independent parameters, is shown to describe the dynamics of batch adsorption much better than alternative lumped parameter models. Although the new model is phenomenological rather than mechanistic, its principal parameter is shown to be a direct linear function of a physically measurable quantity. This study demonstrates that the model can accurately simulate protein concentration-time profiles using parameter estimates derived from correlations over a wide range of initial protein concentrations and phase ratios. The new CNL model is shown to be considerably superior to the Langmuir and solid-film linear kinetic models in this regard, having the additional advantage that an equilibrium isotherm for the system is not required.     

Resistance to extinction and behavioral momentum

In the metaphor of behavioral momentum, reinforcement is assumed to strengthen discriminated operant behavior in the sense of increasing its resistance to disruption, and extinction is viewed as disruption by contingency termination and reinforcer omission. In multiple schedules of intermittent reinforcement, resistance to extinction is an increasing function of reinforcer rate, consistent with a model based on the momentum metaphor. The partial-reinforcement extinction effect, which opposes the effects of reinforcer rate, can be explained by the large disruptive effect of terminating continuous reinforcement despite its strengthening effect during training. Inclusion of a term for the context of reinforcement during training allows the model to account for a wide range of multiple-schedule extinction data and makes contact with other formulations. The relation between resistance to extinction and reinforcer rate on single schedules of intermittent reinforcement is exactly opposite to that for multiple schedules over the same range of reinforcer rates; however, the momentum model can give an account of resistance to extinction in single as well as multiple schedules. An alternative analysis based on the number of reinforcers omitted to an extinction criterion supports the conclusion that response strength is an increasing function of reinforcer rate during training.     

Respiratory system dynamical mechanical properties: modeling in time and frequency domain

The mechanical properties of the respiratory system are important determinants of its function and can be severely compromised in disease. The assessment of respiratory system mechanical properties is thus essential in the management of some disorders as well as in the evaluation of respiratory system adaptations in response to an acute or chronic process. Most often, lungs and chest wall are treated as a linear dynamic system that can be expressed with differential equations, allowing determination of the system’s parameters, which will reflect the mechanical properties. However, different models that encompass nonlinear characteristics and also multicompartments have been used in several approaches and most specifically in mechanically ventilated patients with acute lung injury. Additionally, the input impedance over a range of frequencies can be assessed with a convenient excitation method allowing the identification of the mechanical characteristics of the central and peripheral airways as well as lung periphery impedance. With the evolution of computational power, the airway pressure and flow can be recorded and stored for hours, and hence continuous monitoring of the respiratory system mechanical properties is already available in some mechanical ventilators. This review aims to describe some of the most frequently used models for the assessment of the respiratory system mechanical properties in both time and frequency domain.     

Application of the isobologram technique for the analysis of combined effects with respect to additivity as well as independence

Combined actions of two substances with similar effects are frequently expressed by pairs of doses that produce a fixed response, usually 50%, in so-called isobolograms (ED50 isobolograms). In addition to the dose scales in such graphs we propose the addition of effect scales, where possible, to indicate the effect at certain doses, e.g., the ED30. We further propose to construct isoboles for expected independent interaction, in addition to the additivity line, for which purpose a simple procedure is delineated. In practice, an independent isobole for 50% effect passes through the point formed by the ED30s of A and of B in ED50 isobolograms. Thus, the ED30s constitute the "zenith" of an independent isobole in ED50 isobolograms. It is shown that theoretical independent isoboles can either represent additive, overadditive, or underadditive interactions, depending on the steepness of the dose-response curves of the components. Hence, drugs with shallow dose-response curves exhibit overadditive independent effects, compounds with exponentially steep curves show additive independent interactions. Substances with very steep dose-response curves, producing lethal effects, exhibited marked underadditive effects which could be ascribed largely to an independent mechanism of action of the components. Hence, the inclusion of independent isoboles into conventional isobolograms provides new insights into the mechanisms of interactions and into the actions of the components. Interactions can thus be characterized better and more completely, and misinterpretations appear less likely than with conventional isoboles.     

The study of combined action of agents using differential geometry of dose-effect surfaces

Although graphic surfaces have been used routinely in the study of combined action of agents, they are mainly used for display purposes. In this paper, it is shown that useful mechanistic information can be obtained from an analytical study of these surfaces using the tools of differential geometry. From the analysis of some simple dose-effect surfaces, it is proposed that the intrinsic curvature, referred to in differential geometry as the Gaussian curvature, of a dose-effect surface can be used as a general criterion for the classification of interaction between different agents. This is analogous to the interpretation of the line curvature of a dose-effect curve as an indication of self-interaction between doses for an agent. In this framework, the dose-effect surface would have basic uniform fabric with zero curvature in the absence of interaction, tentatively referred to as null-interaction. Pictorially speaking, this fabric is distorted locally or globally like the stretching and shrinking of a rubber sheet by the presence of interaction mechanisms between different agents. Since self-interaction with dilution dummies does not generate intrinsic curvature, this criterion of null-interaction would describe the interaction between two trulydifferent agents. It is shown that many of the published interaction mechanisms give rise to dose-effect surfaces with characteristic curvatures. This possible correlation between the intrinsic geometric curvature of dose-effect surfaces and the biophysical mechanism of interaction presents an interesting philosophical viewpoint for the study of combined action of agents.     

Biological age in children who practise swimming.

In the estimation of the developmental regularity among children it is important to know the relation between the developmental and the calendar age. It is particularly important in the estimation of the level of development among children with an increased level of guided motor activity. It takes place, for instance, in the case of children practising swimming. In auxology there are many morphological, physiological and motor features which are regarded as the measure of the developmental age. For several years researches have been conducted on the EMN index as the determinant of the biological age. The EMN index shows continuous changes during ontogeny, proves the existence of stages in the developmental age and is also considerably correlated with the calendar age. This is an ecosensitive factor. The EMN index differentiates individuals from another as well as groups isolated with regard to the effect of the environmental factors, for instance, the different levels of motor activity. The aim of this investigation is to estimate the standard of biological maturity (the body height and mass, the EMN index) among children, who went through a guided swimming training. Morphological features are most often used as the measures of development. However, they can become unreliable when they themselves establish the criterion of selection to a sports discipline or when some ranges of values are optimal on some given standards. The EMN index is not burdened with these features. The children who go through training show the higher level of the EMN index values than the children who do not go. The effect of this is the fact that young swimmers are biologically older than their peers. However, the shape of the curve of development of the EMN index in swimmers goes at a different level depending on the seniority of training.     

On the application of wave scattering theory for the diagnosis of muscle diseases

This investigation is concerned with a scattering matrix approach which is proposed for the non-destructive, differential diagnosis of muscle diseases. A number of muscle diseases are classified according to their various pathological indications and appropriate material parameters are derived for utilization as input data for a theoretical model. In the mathematical analysis phase of the model, Waterman's T-matrix approach in conjunction with statistical averaging for both position and orientation of muscle fibers are employed to obtain the attenuation due to geometric dispersion for a wide range of frequencies. The numerical results not only exhibit qualitative agreement with existing experimental data for normal muscle but also display differentiable patterns for the various muscle disease cases. The formulation is an improvement over the previously applied scattering theory in that it obtains the attenuation over a continuous frequency spectrum.     

Electrogenerated chemiluminescence biosensor incorporating ruthenium complex-labelled Concanavalin A as a probe for the detection of Escherichia coli

The interaction of riboflavin with salmon sperm double-stranded DNA based on the decreasing of the oxidation signal of guanine and adenine bases was studied electrochemically with a pencil graphite electrode (PGE) using differential pulse voltammetry. The decrease in the intensity of the guanine and adenine oxidation signals after interaction with riboflavin was used as an indicator signals for the sensitive determination of riboflavin. Under the optimum conditions, a linear dependence of the guanine and adenine oxidation signals was observed for the riboflavin concentration in the range of 0.5-70 μg mL(-1) with a detection limit of 0.34 μg mL(-1) at ds-DNA modified PGE. The reproducibility and applicability of the analysis to pharmaceutical dosage forms and urine sample were also investigated. These results showed that this DNA biosensor could be used for the sensitive, rapid, simple and cost effective detection and determination of riboflavin-ds-DNA interaction. Pretreated pencil graphite electrode (PPGE) was also used for the determination of riboflavin by differential pulse adsorptive stripping voltammetry. With PPGE, a linear relationship was obtained for riboflavin over the concentration range of 0.003-0.88 μg mL(-1) with differential pulse adsorptive stripping voltammetric signal and with a detection limit of 0.076 ng mL(-1). Both determination methods were fully validated and applied for the analysis of riboflavin.     

Mineral oil and aliphatic alcohols: toxicity and analysis of synergistic effects on German cockroaches (Dictyoptera: Blattellidae)

Two mineral oils and 12 linear primary alcohols were studied, alone and in combination, to determine their contact toxicity to adult German cockroaches, Blattella germanica (L.) (Dictyoptera: Blattellidae). The more toxic oil, PD23 (LD50 = 1.45 mg per cockroach) was used for combination studies. Alcohols with carbon chain lengths of C3 and C8 through C12 were the most toxic, with LD50 values ranging from 0.3 to 0.6 mg. C1 (methanol) and C14 (1-tetradecanol) were least toxic, with LD50 values of 2.35 and 1.75 mg, respectively. Eight of the 12 combinations of a nonlethal dose of PD23 oil with an LD10 dose of alcohol produced significantly greater mortality than predicted under the assumption of additive effects. A sample of five synergistic oil + alcohol combinations, covering most of the alcohol carbon chain length range over which synergy occurred, was further studied by calculating LD50 values for three fixed mixture ratios (80:20, 50:50, and 20:80) of each combination. Results were analyzed using both graphical techniques (isobole analysis) and by nonlinear regression. At least one, but not necessarily all, of the three fixed ratio combinations of each oil + alcohol pairing indicated synergy. The conclusions drawn from the isobole and regression analyses were consistent.     

Kinetics and stoichiometry of growth of plant cell cultures of Catharanthus roseus and Nicotiana tabacum in batch and continuous fermentors

Plant cell suspension cultures of Catharanthus roseus and Nicotiana tabacum were grown in stirred tank bioreactors operated in batch and continuous mode. The stoichiometry of growth of both species in steady-state glucose limited chemostats was studied at a range of different dilution rates. A linear relation was applied to describe specific glucose uptake, oxygen consumption, and carbon dioxide production as a function of the growth rate. Specific respiration deviated greatly from the linear relation. An unstructured mathematical model, based on the observed stoichiometry in the glucose limited chemostats, was applied to describe the growth in batch culture. From a comparison between the observed growth pattern in batch fermentors and computer simulations it appeared that the stoichiometry of growth of the C. roseus culture was different under steady-state and dynamic conditions. It was concluded that a mathematical model for the growth of suspension culture plant cells in which the biomass is considered to be a single compound with an average chemical composition is of limited value because large changes in the conmposition of the biomass may occur. (c) 1992 John Wiley & Sons, Inc.     

Stability analysis of a continuum-based constrained mixture model for vascular growth and remodeling

A stabilizing criterion is derived for equations governing vascular growth and remodeling. We start from the integral state equations of the continuum-based constrained mixture theory of vascular growth and remodeling and obtain a system of time-delayed differential equations describing vascular growth. By employing an exponential form of the constituent survival function, the delayed differential equations can be reduced to a nonlinear ODE system. We demonstrate the degeneracy of the linearized system about the homeostatic state, which is a fundamental cause of the neutral stability observations reported in prior studies. Due to this degeneracy, stability conclusions for the original nonlinear system cannot be directly inferred. To resolve this problem, a sub-system is constructed by recognizing a linear relation between two states. Subsequently, Lyapunov’s indirect method is used to connect stability properties between the linearized system and the original nonlinear system, to rigorously establish the neutral stability properties of the original system. In particular, this analysis leads to a stability criterion for vascular expansion in terms of growth and remodeling kinetic parameters, geometric quantities and material properties. Numerical simulations were conducted to evaluate the theoretical stability criterion under broader conditions, as well as study the influence of key parameters and physical factors on growth properties. The theoretical results are also compared with prior numerical and experimental findings in the literature.