Ketone body kinetics in normal,diabetic, and obese humans

We have developed a model for the kinetics of acetoacetate (A) and β-OH-butyrate (B) in normal subjects. The model contains separate compartments for blood A, B, and acetone, as well as three exchange compartments. By using the model, the synthesis, utilization, and clearance rates of A and B were determined separately. We have compared the model with others that have been proposed for ketone body metabolism and have used the model to analyse studies undertaken in newly diagnosed diabetic patients and obese subjects (before and after a 2 week period of starvation). We found that in diabetic and obese individuals the synthesis of ketone bodies was higher than normal and that the fractional losses of A and B were reduced. The results suggest that ketosis develops as a result of high synthesis rates coupled with decreased fractional loss of ketone bodies. In each group the metabolism of B was altered more than A.     

A generalized estimating equations approach to quantitative trait locus detection of non-normal traits

To date, most statistical developments in QTL detection methodology have been directed at continuous traits with an underlying normal distribution. This paper presents a method for QTL analysis of non-normal traits using a generalized linear mixed model approach. Development of this method has been motivated by a backcross experiment involving two inbred lines of mice that was conducted in order to locate a QTL for litter size. A Poisson regression form is used to model litter size, with allowances made for under- as well as over-dispersion, as suggested by the experimental data. In addition to fixed parity effects, random animal effects have also been included in the model. However, the method is not fully parametric as the model is specified only in terms of means, variances and covariances, and not as a full probability model. Consequently, a generalized estimating equations (GEE) approach is used to fit the model. For statistical inferences, permutation tests and bootstrap procedures are used. This method is illustrated with simulated as well as experimental mouse data. Overall, the method is found to be quite reliable, and with modification, can be used for QTL detection for a range of other non-normally distributed traits.     

Modelling of phytoplankton allelopathy with Monod–Haldane-type functional response—A mathematical study

In this paper, a three-tier model of phytoplankton, zooplankton and nutrient is considered and stability of different equilibrium points is analyzed along with Hopf-bifurcation around coexisting equilibrium point. Here, we have assumed toxication process as the guiding factor for bloom formation as well as its termination and this process is incorporated into our model by choosing the zooplankton grazing function as a Monod–Haldane function due to the phytoplankton toxicity. Extensive numerical simulations have been performed to validate the analytical findings and these simulation work reveal the chaotic oscillation exhibited by the model system for certain choice of the parameter values.     

Some state space models of HIV pathogenesis under treatment by anti-viral drugs in HIV-infected individuals

In this paper we have extended the model of HIV pathogenesis under treatment by anti-viral drugs given by Perelson et al. [A.S. Perelson et al., Science 271 (1999) 1582] to a stochastic model. By using this stochastic model as the stochastic system model, we have developed a state space model for the HIV pathogenesis under treatment by anti-viral drugs. In this state space model, the observation model is a statistical model based on the observed numbers of RNA virus copies over different times. For this model we have developed procedures for estimating and predicting the numbers of infectious free HIV and non-infectious free HIV as well as the numbers of different types of T cells through extended Kalman filter method. As an illustration, we have applied the method of this paper to the data of patient Nos. 104, 105 and 107 given by Perelson et al. [A.S. Perelson et al., Science 271 (1999) 1582] under treatment by Ritonavir. For these individuals, it is shown that within two weeks since treatment, most of the free HIV are non-infectious, indicating the usefulness of the treatment. Furthermore, the Kalman filter method revealed a much stronger effect of the treatment within the first 10 to 20 h than that predicted by the deterministic model.     

An enteroendocrine cell-based model for a quiescent intestinal stem cell niche

We have shown that the kinetics of conversion of intestinal crypt cell populations to a partially or wholly mutant phenotype are consistent with a model in which each crypt contains an infrequently dividing 'deep' stem cell that is the progenitor of several more frequently dividing 'proximate' stem cells. An assumption of our model is that each deep stem cell exists in a growth inhibitory niche. We have used information from the literature to develop a model for a quiescent intestinal stem cell niche. This niche is postulated to be primarily defined by an enteroendocrine cell type that maintains stem cell quiescence by secretion of growth inhibitory peptides such as somatostatin and guanylin/uroguanylin. Consistent with this model, there is evidence that the proteins postulated as defining a growth-inhibitory stem cell niche can act as intestinal tumour suppressors. Confirmation that a growth-inhibitory niche does exist would have important implications for our understanding of intestinal homeostasis and tumorigenesis.     

A simulation support system for solving large physiological models on microcomputers

Although physiological modeling and computer simulation have become useful research tools to test new scientific theories and to design and analyze laboratory experiments, developing a new model can be a tedious process because the investigator must often write very complex and specific routines for data input and output. To facilitate the design of new models (as well as the use of existing models), we have developed MODSIM, a FORTRAN-based simulation support system for the IBM PC computer than can accommodate very large dynamic models having up to several thousand equations. It provides the investigator with utilities for continuous on-line graphical and/or tubular output, as well as facilities for dynamic interaction with the model. The user must only supply a model as a list of mathematical equations written in FORTRAN, along with the initial values of the model variables and parameters. The model is precompiled, compiled, and then linked to the MODSIM utilities. Without further programming, the user can then solve the model, select variables for graphical output, and stop the model at any time to analyze the data or to change a parameter before resuming the simulation. This simulation system makes it very easy to develop new models that actively interact with the experimental research of the investigator.     

Consensus structure of Pf1 filamentous bacteriophage from X-ray fibre diffraction and solid-state NMR

Filamentous bacteriophages (filamentous bacterial viruses or Inovirus) are simple and well-characterised macromolecular assemblies that are widely used in molecular biology and biophysics, both as paradigms for studying basic biological questions and as practical tools in areas as diverse as immunology and solid-state physics. The strains fd, M13 and f1 are virtually identical filamentous phages that infect bacteria expressing F-pili, and are sometimes grouped as the Ff phages. For historical reasons fd has often been used for structural studies, but M13 and f1 are more often used for biological experiments. Many other strains have been identified that are genetically quite distinct from Ff and yet have a similar molecular structure and life cycle. One of these, Pf1, gives the highest resolution X-ray fibre diffraction patterns known for filamentous bacteriophage. These diffraction patterns have been used in the past to derive a molecular model for the structure of the phage. Solid-state NMR experiments have been used in separate studies to derive a significantly different model of Pf1. Here we combine previously published X-ray fibre diffraction data and solid-state NMR data to give a consensus structure model for Pf1 filamentous bacteriophage, and we discuss the implications of this model for assembly of the phage at the bacterial membrane.     

A Mathematical Model towards Understanding the Mechanism of Neuronal Regulation of Wake-NREMS-REMS States

In this study we have constructed a mathematical model of a recently proposed functional model known to be responsible for inducing waking, NREMS and REMS. Simulation studies using this model reproduced sleep-wake patterns as reported in normal animals. The model helps to explain neural mechanism(s) that underlie the transitions between wake, NREMS and REMS as well as how both the homeostatic sleep-drive and the circadian rhythm shape the duration of each of these episodes. In particular, this mathematical model demonstrates and confirms that an underlying mechanism for REMS generation is pre-synaptic inhibition from substantia nigra onto the REM-off terminals that project on REM-on neurons, as has been recently proposed. The importance of orexinergic neurons in stabilizing the wake-sleep cycle is demonstrated by showing how even small changes in inputs to or from those neurons can have a large impact on the ensuing dynamics. The results from this model allow us to make predictions of the neural mechanisms of regulation and patho-physiology of REMS.     

Glucose Kinetics in the Collagen-Induced Arthritis Model: An All-in-One Model to Assess Both Efficacy and Metabolic Side Effects of Glucocorticoids

Prednisolone and other glucocorticoids (GCs) are potent anti-inflammatory drugs, but chronic use is hampered by metabolic side effects. Therefore, there is an urgent medical need for improved GCs that are as effective as classical GCs but have a better safety profile. A well-established model to assess anti-inflammatory efficacy is the chronic collagen-induced arthritis (CIA) model in mice, a model with features resembling rheumatoid arthritis. Models to quantify undesired effects of glucocorticoids on glucose kinetics are less well-established. Recently, we have described a model to quantify basal blood glucose kinetics using stably-labeled glucose. In the present study, we have integrated this blood glucose kinetic model in the CIA model to enable quantification of both efficacy and adverse effects in one animal model. Arthritis scores were decreased after treatment with prednisolone, confirming the anti-inflammatory properties of GCs. Both inflammation and prednisolone induced insulin resistance as insulin secretion was strongly increased whereas blood glucose concentrations and hepatic glucose production were only slightly decreased. This insulin resistance did not directly resulted in hyperglycemia, indicating a highly adaptive compensatory mechanism in these mice. In conclusion, this ‘all-in-one’ model allows for studying effects of (novel) GC compounds on the development of arthritis and glucose kinetics in a single animal. This integrative model provides a valuable tool for investigating (drug-induced) metabolic dysregulation in an inflammatory setting.     

One-Dimensional Mathematical Model of the Atrioventricular Node Including Atrio-Nodal, Nodal, and Nodal-His Cells

Mathematical models are a repository of knowledge as well as research and teaching tools. Although action potential models have been developed for most regions of the heart, there is no model for the atrioventricular node (AVN). We have developed action potential models for single atrio-nodal, nodal, and nodal-His cells. The models have the same action potential shapes and refractoriness as observed in experiments. Using these models, together with models for the sinoatrial node (SAN) and atrial muscle, we have developed a one-dimensional (1D) multicellular model including the SAN and AVN. The multicellular model has slow and fast pathways into the AVN and using it we have analyzed the rich behavior of the AVN. Under normal conditions, action potentials were initiated in the SAN center and then propagated through the atrium and AVN. The relationship between the AVN conduction time and the timing of a premature stimulus (conduction curve) is consistent with experimental data. After premature stimulation, atrioventricular nodal reentry could occur. After slow pathway ablation or block of the L-type Ca²⁺ current, atrioventricular nodal reentry was abolished. During atrial fibrillation, the AVN limited the number of action potentials transmitted to the ventricle. In the absence of SAN pacemaking, the inferior nodal extension acted as the pacemaker. In conclusion, we have developed what we believe is the first detailed mathematical model of the AVN and it shows the typical physiological and pathophysiological characteristics of the tissue. The model can be used as a tool to analyze the complex structure and behavior of the AVN.     

Invertebrates as model organisms for research on aging biology

Invertebrate model systems, such as nematodes and fruit flies, have provided valuable information about the genetics and cellular biology involved in aging. However, limitations of these simple, genetically tractable organisms suggest the need for other model systems, some of them invertebrate, to facilitate further advances in the understanding of mechanisms of aging and longevity in mammals, including humans. This paper introduces 10 review articles about the use of invertebrate model systems for the study of aging by authors who participated in an ‘NIA-NIH symposium on aging in invertebrate model systems’ at the 2013 International Congress for Invertebrate Reproduction and Development. In contrast to the highly derived characteristics of nematodes and fruit flies as members of the superphylum Ecdysozoa, cnidarians, such as Hydra, are more ‘basal’ organisms that have a greater number of genetic orthologs in common with humans. Moreover, some other new model systems, such as the urochordate Botryllus schlosseri, the tunicate Ciona, and the sea urchins (Echinodermata) are members of the Deuterostomia, the same superphylum that includes all vertebrates, and thus have mechanisms that are likely to be more closely related to those occurring in humans. Additional characteristics of these new model systems, such as the recent development of new molecular and genetic tools and a more similar pattern to humans of regeneration and stem cell function suggest that these new model systems may have unique advantages for the study of mechanisms of aging and longevity.     

A fuzzy-genetic model for estimating forces from electromyographical activity of antagonistic muscles due to planar lower arm movements: the effect of nonlinear muscle properties

The aim of this paper is to create a model for mapping the surface electromyogram (EMG) signals to the force that generated by human arm muscles. Because the parameters of each person's muscle are individual, the model of the muscle must have two characteristics: (1) The model must be adjustable for each subject. (2) The relationship between the input and output of model must be affected by the force-length and the force-velocity behaviors are proven through Hill's experiments. Hill's model is a kinematic mechanistic model with three elements, i.e. one contractile component and two nonlinear spring elements.In this research, fuzzy systems are applied to improve the muscle model. The advantages of using fuzzy system are as follows: they are robust to noise, they prove an adjustable nonlinear mapping, and are able to model the uncertainties of the muscle.Three fuzzy coefficients have been added to the relationships of force-length (active and passive) and force-velocity existing in Hill's model. Then, a genetic algorithm (GA) has been used as a biological search method that can adjust the parameters of the model in order to achieve the optimal possible fit.Finally, the accuracy of the fuzzy genetic implementation Hill-based muscle model (FGIHM) is invested as following: the FGIHM results have 12.4% RMS error (in worse case) in comparison to the experimental data recorded from three healthy male subjects. Moreover, the FGIHM active force-length relationship which is the key characteristics of muscles has been compared to virtual muscle (VM) and Zajac muscle model. The sensitivity of the FGIHM has been evaluated by adding a white noise with zero mean to the input and FGIHM has proved to have lower sensitivity to input noise than the traditional Hill's muscle model.     

Apparent trends of amino Acid gain and loss in protein evolution due to nearly neutral variation

It has recently been claimed that certain amino acids have been increasing in frequency in all living organisms for most of the history of life on earth, while other amino acids have been decreasing in frequency. Three lines of evidence have been offered for this assertion, but each has a more plausible alternative interpretation. Here I show that unequal patterns of gains and losses for particular pairs of amino acids (such as more leucine --> phenylalanine than phenylalanine --> leucine substitutions in humans and chimpanzees since they split from a common ancestor) are consistent with a simple neutral model at equilibrium amino acid frequencies. Unequal numbers of gains and losses for particular amino acids (such as more gains than losses of cysteine) are shown by simulations to be consistent with a model of nearly neutral evolution. Unequal numbers of gains and losses for particular amino acids in human polymorphism data are shown by simulations to be explainable by the nearly neutral model as well. In a comparison of protein sequences from four strains of Escherichia coli, polarized by one outgroup strain of Salmonella, the disparity in number of gains and losses for particular amino acids is strong in terminal branches but weaker or nonexistent in internal branches, which is inconsistent with the universal trend model but as expected under the nearly neutral model.     

Pacemaker activity of the rabbit sinoatrial node. A comparison of mathematical models.

In the past decade, three mathematical models describing the pacemaker activity of the rabbit sinoatrial node have been developed: the Bristow-Clark model, the Irisawa-Noma model, and the Noble-Noble model. In a comparative study it is demonstrated that these models, as well as subsequent modifications, all have several drawbacks. A more accurate model, describing the pacemaker activity of a single pacemaker cell isolated from the rabbit sinoatrial node, was constructed. Model equations, including equations for the T-type calcium current, are based on experimental data from voltage clamp experiments on single cells that were published during the last few years. In contrast to the other models, only a small amount of background current contributes to the overall electrical charge flow. The action potential parameters of the model cell, its responses to voltage clamp steps and its current-voltage relationships have been computed. The model is used to discuss the relative contribution of membrane current components to the slow diastolic depolarization phase of the action potential.     

Parameterization for In-Silico Modeling of Ion Channel Interactions with Drugs

Since the first Hodgkin and Huxley ion channel model was described in the 1950s, there has been an explosion in mathematical models to describe ion channel function. As experimental data has become richer, models have concomitantly been improved to better represent ion channel kinetic processes, although these improvements have generally resulted in more model complexity and an increase in the number of parameters necessary to populate the models. Models have also been developed to explicitly model drug interactions with ion channels. Recent models of drug-channel interactions account for the discrete kinetics of drug interaction with distinct ion channel state conformations, as it has become clear that such interactions underlie complex emergent kinetics such as use-dependent block. Here, we describe an approach for developing a model for ion channel drug interactions. The method describes the process of extracting rate constants from experimental electrophysiological function data to use as initial conditions for the model parameters. We then describe implementation of a parameter optimization method to refine the model rate constants describing ion channel drug kinetics. The algorithm takes advantage of readily available parallel computing tools to speed up the optimization. Finally, we describe some potential applications of the platform including the potential for gaining fundamental mechanistic insights into ion channel function and applications to in silico drug screening and development.     

A model for habitat selection and species distribution derived from central place foraging theory

We have developed a habitat selection model based on central place foraging theory. An individual’s decision to include a patch in its habitat depends on the marginal fitness contribution of that patch, which is characterized by its quality and distance to the central place. The essence of the model we have developed is a fitness isocline which is a function of patch quality and travel time to the patch. It has two parameters: the maximum travel distance to a patch of infinite quality and a coefficient that appropriately scales quality by travel time. Patches falling below the isocline will have positive marginal fitness values and should be included in the habitat. The maximum travel distance depends on the availability and quality of patches, as well as on the forager’s life history, whereas the scaling parameter mostly depends on life history properties. Using the model, we derived a landscape quality metric (which can be thought of as a connectivity measure) that sums the values of available habitat in the landscape around a central place. We then fitted the two parameters to foraging data on breeding white storks (Ciconia ciconia) and estimated landscape quality, which correlated strongly with reproductive success. Landscape quality was then calculated for a larger region where re-introduction of the species is currently going on in order to demonstrate how this model can also be regarded as a species distribution model. In conclusion, we have built a general habitat selection model for central place foragers and a novel way of estimating landscape quality based on a behaviorally scaled connectivity metric.     

Genetic manipulations and examination of differentiation properties of rat induced pluripotent cells

Induced pluripotent cells have offered new exciting options in fundamental and applied studies, such as gene knockout and human disease modeling. They are also very promising for regenerative medicine. However, in order to develop this technology, it is necessary to have a proper animal model. An appropriate model is the rat, which has physiological characteristics that are closer to human ones than do mice. In this paper, we present methods of genetic modifications with rat iPS cells and their directed differentiation. These data will help for studies using the rat as an experimental model for human replacement therapy.     

Performance of reclassification statistics in comparing risk prediction models

Concerns have been raised about the use of traditional measures of model fit in evaluating risk prediction models for clinical use, and reclassification tables have been suggested as an alternative means of assessing the clinical utility of a model. Several measures based on the table have been proposed, including the reclassification calibration (RC) statistic, the net reclassification improvement (NRI), and the integrated discrimination improvement (IDI), but the performance of these in practical settings has not been fully examined. We used simulations to estimate the type I error and power for these statistics in a number of scenarios, as well as the impact of the number and type of categories, when adding a new marker to an established or reference model. The type I error was found to be reasonable in most settings, and power was highest for the IDI, which was similar to the test of association. The relative power of the RC statistic, a test of calibration, and the NRI, a test of discrimination, varied depending on the model assumptions. These tools provide unique but complementary information.