The matrix representation of pharmacokinetic models.

An equation is developed from the matrix of rate constants which describes the behaviour of linear pharmacokinetic models for any initial condition as a function of time. This general matrix equation is then used to derive analogous expressions for drug distribution after a period of infusion, at the steady state, or during a multiple constant-dosage regimen. Matrix expressions are also derived for areas under drug concentration curves for any compartment after single doses or during multiple dosing. General matrix equations are shown to yield loading dosage schedules to achieve plateau concentrations throughout any open system.It is suggested that matrix methods have advantages over previously used mathematical techniques in pharmacokinetics in the simplicity of the algebraic expressions, and their ease of manipulation. An algebraic example of an open two-compartment model is worked to indicate the applicability of the general expressions.     

Spatial multistate transitional models for longitudinal event data

Summary .   Follow-up medical studies often collect longitudinal data on patients. Multistate transitional models are useful for analysis in such studies where at any point in time, individuals may be said to occupy one of a discrete set of states and interest centers on the transition process between states. For example, states may refer to the number of recurrences of an event, or the stage of a disease. We develop a hierarchical modeling framework for the analysis of such longitudinal data when the processes corresponding to different subjects may be correlated spatially over a region. Continuous-time Markov chains incorporating spatially correlated random effects are introduced. Here, joint modeling of both spatial dependence as well as dependence between different transition rates is required and a multivariate spatial approach is employed. A proportional intensities frailty model is developed where baseline intensity functions are modeled using parametric Weibull forms, piecewise-exponential formulations, and flexible representations based on cubic B-splines. The methodology is developed within the context of a study examining invasive cardiac procedures in Quebec. We consider patients admitted for acute coronary syndrome throughout the 139 local health units of the province and examine readmission and mortality rates over a 4-year period.     

Linear fuzzy gene network models obtained from microarray data by exhaustive search

Background  

Recent technological advances in high-throughput data collection allow for experimental study of increasingly complex systems on the scale of the whole cellular genome and proteome. Gene network models are needed to interpret the resulting large and complex data sets. Rationally designed perturbations (e.g., gene knock-outs) can be used to iteratively refine hypothetical models, suggesting an approach for high-throughput biological system analysis. We introduce an approach to gene network modeling based on a scalable linear variant of fuzzy logic: a framework with greater resolution than Boolean logic models, but which, while still semi-quantitative, does not require the precise parameter measurement needed for chemical kinetics-based modeling.     

Energy-barrier models for membrane transport.

Energy-barrier models are analyzed to find hidden assumptions and establish ranges of validity. The analysis proceeds by comparison with integrated results for model continuum membranes. The main conclusions are that a simple energy-barrier model has a wide range of validity, is remarkably accurate even when its conditions of validity are not strictly met, and is almost always superior to the analogous equations of irreversible thermodynamics. Its major limitations are a possible nonphysical divergence at high electric fields or volume flows caused by breakdown of the transition-state approximation, and the inability to treat multicomponent mixtures except in a pseudobinary (Nernst-Planck) approximation.     

Multievent: an extension of multistate capture-recapture models to uncertain states

Capture-recapture models were originally developed to account for encounter probabilities that are less than 1 in free-ranging animal populations. Nowadays, these models can deal with the movement of animals between different locations and are also used to study transitions between different states. However, their use to estimate transitions between states does not account for uncertainty in state assignment. I present the extension of multievent models, which does incorporate this uncertainty. Multievent models belong to the family of hidden Markov models. I also show in this article that the memory model, in which the next state or location is influenced by the previous state occupied, can be fully treated within the framework of multievent models.     

Application of multistate models in hospital epidemiology: advances and challenges

Survival analysis has established itself as a major statistical technique in medical research. Applications in hospital epidemiology, however, are only beginning to emerge. One reason for this delay is that usually complete follow-up of patients in hospital is feasible. This overview discusses where survival techniques provide additional insight into hospital epidemiology, and where they are, in fact, needed even in the absence of right-censoring.     

Connectionistic models of boolean category representation

Several distinct connectionistic/neural representations capable of computing arbitrary Boolean functions are described and discussed in terms of possible tradeoffs between time, space, and expressive clarity. It is suggested that the ability of a threshold logic unit (TLU) to represent prototypical groupings has significant advantages for representing real world categories. Upper and lower bounds on the number of nodes needed for Boolean completeness are demonstrated. The necessary number of nodes is shown to increase exponentially with the number of input features, the exact rate of increase depending on the representation scheme. In addition, in non-recurrent networks, connection weights are shown to increase exponentially with a linear reduction in the number of nodes below approximately 2^d. This result suggests that optimum memory efficiency may require unacceptable learning time. Finally, two possible extensions to deal with non-Boolean values are considered.     

Single-particle tracking: models of directed transport.

Single-particle tracking techniques make it possible to measure motion of individual particles on the cell surface. In these experiments, individual trajectories are observed, so the data analysis must take into account the randomness of individual random walks. Methods of data analysis are discussed for models combining diffusion and directed motion. In the uniform flow model, a tracer simultaneously diffuses and undergoes directed motion. In the conveyor belt model, a tracer binds and unbinds to a uniform conveyor belt moving with constant velocity. If a tracer is bound, it moves at the velocity of the conveyor belt; if it is unbound, it diffuses freely. Trajectories are analyzed using parameters that measure the extent and asymmetry of the trajectory. A method of assessing the usefulness of such parameters is presented, and pitfalls in data analysis are discussed. Joint probability distributions of pairs of extent and asymmetry parameters are obtained for a pure random walk. These distributions can be used to show that a trajectory is not likely to have resulted from a pure random walk.     

Two-carrier models for mediated transport. I. Theoretical analysis of several two-carrier models.

Several possible models of two sequential and two simultaneous carriers of different affinities are theoretically analysed. Following the analysis we suggest for each model an experimental procedure capable of testing and rejecting the model.     

Application of multilevel models to morphometric data. Part 1. Linear models and hypothesis testing.

Morphometric data usually have a hierarchical structure (i.e., cells are nested within patients), which should be taken into consideration in the analysis. In the recent years, special methods of handling hierarchical data, called multilevel models (MM), as well as corresponding software have received considerable development. However, there has been no application of these methods to morphometric data yet. In this paper we report our first experience of analyzing karyometric data by means of MLwiN - a dedicated program for multilevel modeling. Our data were obtained from 34 follicular adenomas and 44 follicular carcinomas of the thyroid. We show examples of fitting and interpreting MM of different complexity, and draw a number of interesting conclusions about the differences in nuclear morphology between follicular thyroid adenomas and carcinomas. We also demonstrate substantial advantages of multilevel models over conventional, single-level statistics, which have been adopted previously to analyze karyometric data. In addition, some theoretical issues related to MM as well as major statistical software for MM are briefly reviewed.     

Assessment of costs of reproduction in a pelagic seabird using multistate mark-recapture models

We used a long‐term population band‐resight survey database, a parallel reproduction database, and multistate mark–recapture analysis to assess the costs of reproduction, a keystone concept of life‐history evolution, in Nazca boobies (Sula granti) from Punta Cevallos, Isla Española, Galápagos, Ecuador. We used eight years of resight and breeding data to compare models that included sex‐ and state‐specific survival probabilities and probabilities of transition between reproductive states using multistate mark–recapture models. Models that included state‐specific effects were compared with models lacking such effects to evaluate costs of reproduction. The top model, optimizing the trade‐off of model simplicity and fit to the data using the Akaike Information Criterion (AIC), showed evidence of a temporally varying survival cost of reproduction: nonbreeders showed higher annual survival than breeders did in some years. Because increasing investment among breeders showed no negative association with survival and subsequent breeding success, this evidence indicates a cost to both males and females of initiating, but not of continuing, a reproductive attempt. In some cases, breeders reaching the highest reproductive state (fledging an offspring) showed higher survival or subsequent breeding success than did failed breeders, consistent with differences in overall quality that promote both survival and reproduction. Although a male‐biased adult sex ratio was observed in this population of Nazca boobies, models of state‐ and sex‐specific survival and transition probabilities were not supported, indicating that males and females do not incur different costs of reproduction, and that the observed sex ratio bias is not due to sex‐specific adult mortality.     

Alternative time representation in dopamine models

Dopaminergic neuron activity has been modeled during learning and appetitive behavior, most commonly using the temporal-difference (TD) algorithm. However, a proper representation of elapsed time and of the exact task is usually required for the model to work. Most models use timing elements such as delay-line representations of time that are not biologically realistic for intervals in the range of seconds. The interval-timing literature provides several alternatives. One of them is that timing could emerge from general network dynamics, instead of coming from a dedicated circuit. Here, we present a general rate-based learning model based on long short-term memory (LSTM) networks that learns a time representation when needed. Using a naïve network learning its environment in conjunction with TD, we reproduce dopamine activity in appetitive trace conditioning with a constant CS-US interval, including probe trials with unexpected delays. The proposed model learns a representation of the environment dynamics in an adaptive biologically plausible framework, without recourse to delay lines or other special-purpose circuits. Instead, the model predicts that the task-dependent representation of time is learned by experience, is encoded in ramp-like changes in single-neuron activity distributed across small neural networks, and reflects a temporal integration mechanism resulting from the inherent dynamics of recurrent loops within the network. The model also reproduces the known finding that trace conditioning is more difficult than delay conditioning and that the learned representation of the task can be highly dependent on the types of trials experienced during training. Finally, it suggests that the phasic dopaminergic signal could facilitate learning in the cortex.     

Discrimination criteria for apparent two-site transport models.

The medical beliefs of a people have in the past been studied principally by cultural anthropologists. The focus of these studies is usually on intrasocietal dynamics and cultural relativism—a striking orientation. However, beliefs about disease are integral to the way groups have and continue to adapt, and are thus important to both social and biological scientists. In order to study the role of medical beliefs in the adaptation of the group, a comparative approach is needed. This requires viewing these beliefs more generically, comparing their symbolic properties, and analyzing how they are used in explaining and dealing with actual occurrences of disease. The concept of a taxonomy of disease is introduced, as well as the notion of different semantic regions in the taxonomy. In the attempt to clarify the biological significance of a group's taxonomy of disease, and of its mode of operation, the ideas of uncertainty and information are employed. The significance and fruitfulness of this approach is discussed.     

Testing transport models and transport data by means of kinetic rejection criteria.

The proenzyme form of C1r catalytic domains was generated by limited proteolysis of native C1r with thermolysin in the presence of 4-nitrophenyl-4'-guanidinobenzoate. The final preparation, isolated by high-pressure gel permeation in the presence of 2 M-NaCl, was 70-75% proenzyme and consisted of a dimeric association of two gamma B domains, each resulting from cleavage of peptide bonds at positions 285 and 286 of C1r. Like native C1r, the isolated domains autoactivated upon incubation at 37 degrees C. Activation was inhibited by 4-nitrophenyl-4'-guanidinobenzoate but was nearly insensitive to di-isopropyl phosphorofluoridate; likewise, compared to pH 7.4, the rate of activation was decreased at pH 5.0, but was not modified at pH 10.0. In contrast, activation of the (gamma B)2 domains was totally insensitive to Ca2+. Activation of the catalytic domains, which was correlated with an irreversible increase of intrinsic fluorescence, comparable with that previously observed with native C1r [Villiers, Arlaud & Colomb (1983) Biochem. J. 215, 369-375], was reversibly inhibited at high ionic strength (2 M-NaCl), presumably through stabilization of a non-activatable conformational state. Detailed comparison of the properties of native C1r and its catalytic domains indicates that the latter contain all the structural elements that are necessary for intramolecular activation, but probably lack a regulatory mechanism associated with the N-terminal alpha beta region of C1r.     

Electrolyte absorption by gallbladders: models of transport.

A model of electrolyte absorption by gallbladder epithelium has been presented previously on the basis of studies on gallbladders of 12 species, including fishes, frogs, toad, turtle, guinea pig, rabbit, cat and dog. This model incorporates several physiologic and morphologic characteristics common to other transporting epithelia (e.g., intestine) such as energy-dependent solute pumps, osmotically-induced water flow into the lateral intercellular space and bulk flow of fluid driven by hydrostatic pressure along the lateral space toward the basement membrane. Because the transepithelial PD across the gallbladders of each of these species was near zero under most experimental conditions, the active transport mechanism (or, “pump”) at the basolateral membrane was considered to move Na and Cl in a coupled, one-for-one manner. The carrier mechanism was postulated to have a binding site for Na and one for Cl; it would function only if both sites were filled.Gallbladders from six other species investigated more recently (including man, monkeys, goose and Necturus) have serosa-positive transepithelial PDs of 2–8 mV. The possibility was suggested that rheogenic Na transport from mucosa to serosa might account for the PD in this group of tissues and the original model of transport would be inappropriate. This review will explore the possibility that a single model of electrolyte transport accounts for the data collected on gallbladders with PDs near zero and those having significant transepithelial PDs.An important finding which helps to reconcile the experimental observations on the two groups of gallbladders was the demonstration of coupled flux of Na and Cl from the mucosal solution into the epithelial cells. It appears that this rigid coupling of Na and Cl influx accounts for the lack of a significant PD in gallbladders of those species investigated in the earlier studies, and that rheogenic Na transport may be a property common to gallbladders of all species.     

Two-carrier models for mediated transport I. Theoretical analysis of several two-carrier models

Several possible models of two sequential and two simultaneous carriers of different affinities are theoretically analysed. Following the analysis we suggest for each model an experimental procedure capable of testing and rejecting the model.