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Mathematical models of the dynamics of HIV and hepatitis C virus infection have proven to be of great utility in understanding pathogenesis and designing better treatments. Here, we review the state of the art in modeling and interpreting data obtained from hepatitis B virus infected patients treated with antiviral agents.
Antiviral immune effector mechanisms can be divided broadly into lytic and nonlytic components. We use mathematical models to investigate the fundamental question of which type of response is required to combat different types of viral infection. According to our model, the relative roles of the two types of component depend on the cytopathicity of the virus relative to its rate of replication. If the viral cytopathicity is low relative to the rate of viral replication, the model predicts that a combination of lytic and nonlytic effector mechanisms is likely to be required to resolve the disease, particularly if the virus replicates at a fast rate. By contrast, if viral cytopathicity is high relative to the replication rate of the virus, then lytic and nonlytic mechanisms can, in principle, resolve the infection independently. We discuss our findings in the context of specific viral infections and use our model to interpret empirical data.
Proline racemase catalyzes the interconversion of D- and L-proline. Previous studies in this laboratory have established that the reaction proceeds by means of a two-base mechanism in which one base on the enzyme removes the substrate alpha-hydrogen as a proton and the conjugate acid of another base donates a proton to the opposite side of the alpha-carbon (Cardinale, G.J., and Abeles, R.H., (1968), Biochemistry 7, 3970. An assumption of the proposed mechanism was that no proton exchange occurs from the enzyme-substrate complex. In the present study, we have shown that the rate of 3H release from DL-[alpha-3H]proline, in the presence of proline racemase, decreases with increasing proline concentrations. These results establish that release of the substrate derived proton from the enzyme occurs largely, possibly exclusively, after release of the product. Under initial velocity conditions, the rate of 3H release from L-[alpha-3H]proline is not reduced with increasing L-proline concentrations. Thus, the enzyme-bound proton derived from one isomer can only be "captured" by the other isomer. We conclude that there are two forms of the enzyme; one binds L-proline and the other D-proline. Release of the substrate derived proton from enzyme is more rapid than the interconversion of these two forms. These results are consistent with the previously proposed mechanism. Proline racemase is composed of similar subunits of mol wt 38,000 as determined by gel electrophoresis in the presence of sodium dodecyl sulfate. Equilibrium dialysis experiments detect only one substrate binding site for every two subunits. When the oxidized form of the enzyme, which is inactive and cannot bind substrate, is reduced by thiol to yield active enzyme, two cysteine sulfhydryl groups per dimer become available to react with iodoacetate. Inactivation of the enzyme occurs upon modification of one of these cysteines. All iodoacetate incorporation occurs at the same point in the primary sequence of the enzyme, and can be prevented by the presence of proline or pyrrole-2-carboxylate, a substrate analog. A model is proposed in which a single active site is formed by elements of two identical subunits. Although the data are consistent with this model, another interpretation, in which half of the subunits are nonfunctional, cannot be ruled out.
A bivariate Markov chain approach that includes both enduring (long-term) and ephemeral (short-term) behavioral effects in models for capture-recapture experiments is proposed. The capture history of each animal is modeled as a Markov chain with a bivariate state space with states determined by the capture status (capture/noncapture) and marking status (marked/unmarked). In this framework, a conditional-likelihood method is used to estimate the population size and the transition probabilities. The classical behavioral model that assumes only an enduring behavioral effect is included as a special case of the bivariate Markovian model. Another special case that assumes only an ephemeral behavioral effect reduces to a univariate Markov chain based on capture/noncapture status. The model with the ephemeral behavioral effect is extended to incorporate time effects; in this model, in contrast to extensions of the classical behavioral model, all parameters are identifiable. A data set is analyzed to illustrate the use of the Markovian models in interpreting animals' behavioral response. Simulation results are reported to examine the performance of the estimators.
In a temporal bisection task with humans, the observer is required to decide whether a probe duration (t) is more similar to the short referent (S), an R(S) response, or to the long referent (L), an RL response. Temporal bisection yields a psychometric function relating the proportion of long responses, P(R(L)), to probe duration t. The value of t at which R(S) and R(L) occur with equal frequency, P(R(L)) = .5, is referred to as the bisection point, T1/2. Bisection models usually interpret T1/2 as identifying the value of t that is equally confusable with S and L, but they differ in their predictions for the location of T1/2. The present paper presents new data relevant to the location and interpretation of T1/2. The data indicate that the empirical values usually are biased, the biases being influenced by duration range, L:S ratio, and probe spacing. Moreover, the biases often are not consistent across observers. It is concluded that empirical values of T1/2 should not be interpreted as indicating the value of t that is equally confusable with S and L.
Because of limitations of the univariate frailty model in analysis of multivariate survival data, a bivariate frailty model is introduced for the analysis of bivariate survival data. This provides tremendous flexibility especially in allowing negative associations between subjects within the same cluster. The approach involves incorporating into the model two possibly correlated frailties for each cluster. The bivariate lognormal distribution is used as the frailty distribution. The model is then generalized to multivariate survival data with two distinguished groups and also to alternating process data. A modified EM algorithm is developed with no requirement of specification of the baseline hazards. The estimators are generalized maximum likelihood estimators with subject-specific interpretation. The model is applied to a mental health study on evaluation of health policy effects for inpatient psychiatric care.
Pulmonary uptake of basic amine xenobiotics such as lidocaine may influence the onset of drug effect and ameliorate toxicity. To date, pharmacokinetic analysis of pulmonary drug uptake has been only semiquantitative and ill-suited for relating pharmacodynamics to pharmacokinetics or for estimating the time course of the fraction of drug dose residing in the lung during a single pass. We have developed recirculatory models in an experiment in which lidocaine was injected into the right atrium simultaneously with markers of intravascular space (indocyanine green) and total body water (antipyrine); this was followed by rapid arterial and mixed venous blood sampling. Such models are interpretable physiologically and are capable of characterizing the kinetics of the pulmonary uptake of lidocaine in addition to peripheral tissue distribution and elimination. The apparent pulmonary tissue volume of lidocaine (39 ml/kg) was nearly ninefold greater than that of antipyrine (4.5 ml/kg). The recirculatory model characterized both arterial and mixed venous data, but the latter data were not essential for estimating lidocaine's pulmonary disposition either before or after recirculation of drug was evident.
MOTIVATION: The microarray technology allows for the simultaneous monitoring of thousands of genes for each sample. The high-dimensional gene expression data can be used to study similarities of gene expression profiles across different samples to form a gene clustering. The clusters may be indicative of genetic pathways. Parallel to gene clustering is the important application of sample classification based on all or selected gene expressions. The gene clustering and sample classification are often undertaken separately, or in a directional manner (one as an aid for the other). However, such separation of these two tasks may occlude informative structure in the data. Here we present an algorithm for the simultaneous clustering of genes and subset selection of gene clusters for sample classification. We develop a new model selection criterion based on Rissanen's MDL (minimum description length) principle. For the first time, an MDL code length is given for both explanatory variables (genes) and response variables (sample class labels). The final output of the proposed algorithm is a sparse and interpretable classification rule based on cluster centroids or the closest genes to the centroids. RESULTS: Our algorithm for simultaneous gene clustering and subset selection for classification is applied to three publicly available data sets. For all three data sets, we obtain sparse and interpretable classification models based on centroids of clusters. At the same time, these models give competitive test error rates as the best reported methods. Compared with classification models based on single gene selections, our rules are stable in the sense that the number of clusters has a small variability and the centroids of the clusters are well correlated (or consistent) across different cross validation samples. We also discuss models where the centroids of clusters are replaced with the genes closest to the centroids. These models show comparable test error rates to models based on single gene selection, but are more sparse as well as more stable. Moreover, we comment on how the inclusion of a classification criterion affects the gene clustering, bringing out class informative structure in the data. AVAILABILITY: The methods presented in this paper have been implemented in the R language. The source code is available from the first author.
In connection with the function of a newly constructed absorption model the problem of interpretation of values obtained by models in regard of bioavailability is discussed. Wrong interpretations can be obtained if nonanalogous values are compared. An interpretation is proposed to calculate a value which is analogous to the relative bioavailability (calculated bioavailability). The efficiency of the absorption model and of the interpretation method is demonstrated by three examples of preparations of phenytoin, digoxin and chloramphenicol. We compared these results with the bioavailability of these preparations and we found a good correspondence.
Our current understanding of Mg(2+) binding to RNA, in both thermodynamic and structural terms, is largely based on classical studies of transfer RNAs. Based on these studies, it is clear that magnesium ions are crucial for stabilizing the folded structure of tRNA. We present here a rigorous theoretical model based on the nonlinear Poisson-Boltzmann (NLPB) equation for understanding Mg(2+) binding to yeast tRNA(Phe). We use this model to interpret a variety of experimental Mg(2+) binding data. In particular, we find that the NLPB equation provides a remarkably accurate description of both the overall stoichiometry and the free energy of Mg(2+) binding to yeast tRNA(Phe) without any fitted parameters. In addition, the model accurately describes the interaction of Mg(2+) with localized regions of the RNA as determined by the pK(a) shift of differently bound fluorophores. In each case, we find that the model also reproduces the univalent salt-dependence and the anticooperativity of Mg(2+) binding. Our results lead us to a thermodynamic description of Mg(2+) binding to yeast tRNA(Phe) based on the NLPB equation. In this model, Mg(2+) binding is simply explained by an ensemble of ions distributed according to a Boltzmann weighted average of the mean electrostatic potential around the RNA. It appears that the entire ensemble of electrostatically bound ions superficially mimics a few strongly coordinated ions. In this regard, we find that Mg(2+) stabilizes the tertiary structure of yeast tRNA(Phe) in part by accumulating in regions of high negative electrostatic potential. These regions of Mg(2+) localization correspond to bound ions that are observed in the X-ray crystallographic structures of yeast tRNA(Phe). Based on our results and the available thermodynamic data, there is no evidence that specifically coordinated Mg ions have a significant role in stabilizing the native tertiary structure of yeast tRNA(Phe) in solution.
The divalent binding of a bis(adamantyl)-functionalized calix[4]arene (1) to an EDTA-tethered beta-cyclodextrin (CD) dimer (2) in solution (1.2 x 10(7) M(-)(1)) was 3 orders of magnitude weaker than the binding constant ( approximately 10(10) M(-)(1)) for the interaction of 1 at CD self-assembled monolayers (SAMs) on gold. This difference in binding is rationalized using a theoretical model, which interprets the divalent binding as two consecutive monovalent binding events, i.e., an intermolecular interaction followed by an intramolecular binding event, the latter of which is associated with an effective concentration term accounting for the close proximity of the two interacting species. The methodology presented in the model is applicable to divalent binding both in solution and at SAMs and indicates that the difference in observed binding constants mainly stems from a difference in effective concentration.
Although understanding cells' responses to mechanical stimuli is seen as increasingly important for understanding cell biology, how to best measure, interpret, and model cells' mechanical properties remains unclear. We determine the frequency-dependent shear modulus of cultured mammalian cells by using four different methods, both unique and well established. This approach clarifies the effects of cytoskeletal heterogeneity, ATP-dependent processes, and cell regional variations on the interpretation of such measurements. Our results clearly indicate two qualitatively similar, but distinct, mechanical responses, corresponding to the cortical and intracellular networks, each having an unusual, weak power-law form at low frequency. The two frequency-dependent responses we observe are remarkably similar to those reported for a variety of cultured mammalian cells measured with different techniques, suggesting it is a useful consensus description. Finally, we discuss possible physical explanations for the observed mechanical response.
Information on nasal particle deposition is used in risk assessments for exposure to airborne particulate pollutants and for optimizing the delivery of therapeutic aerosols. Monkeys are commonly used to assess the therapeutic potential of inhaled substances and to a lesser extent the toxicity of inhaled xenobiotics. Yet no reliable measurements of the deposition efficiency of monkey nasal airways for particles >1 microm have been reported to date. The goals of this study were to measure the deposition efficiency (>1 microm) of a replica of monkey nasal airways and to investigate potential differences in nasal deposition between humans and monkeys by comparing results with similar measurements recently reported for human nasal replicas. The monkey nasal replica was an acrylic mold made from a postmortem cast of the nasal airways of a 12-kg, male rhesus monkey. Particle deposition in the monkey nasal mold was measured for monodisperse aerosols between 1 and 10 microm and constant inspiratory flow rates between 2 and 7 lpm. Total deposition efficiency increased from nearly 0 to 100% with increasing particle inertia and was uniquely determined by values of an inertial impaction parameter. The deposition efficiencies of the monkey replica agreed well with those of human nasal replicas when compared according to equivalent Stokes numbers based on minimum cross-sectional area. Results from this study could improve monkey-to-human extrapolation models and interpretations of data from particle toxicity and therapeutic aerosol studies using monkeys.
The classic diffusion model-based interpretation of percutaneous absorption is compared to a simple kinetic analysis. The physicochemical significance and the major deductions of the two approaches are shown to be in general agreement. In particular, the effect of penetrant oil/water partition coefficient on transdermal flux is consistently predicted by the two models. Diffusional and kinetic assessments of skin penetration enhancement are then shown to reveal similar dependencies upon penetrant physical chemistry. It is demonstrated that the requirements for successful promotion of a lipophilic drug's transdermal flux are quite different from those necessary for a hydrophilic penetrant. Finally, in light of published transport data and our increased comprehension of the stratum corneum barrier function, the evidence for (and significance of) different absorption paths across the stratum corneum is considered. In addition, the impact of penetrant "size" on transport is addressed. It is argued that currently held beliefs concerning (i) a putative "polar" route through the stratum corneum and (ii) the dependence of flux on molecular weight warrant considerable further attention before their unequivocal acceptance is appropriate.
The Q7K/L331/L631 HIV-1 protease mutant was expressed in Escherichia coli and the effect of binding a substrate-analog inhibitor, acetyl-pepstatin, was investigated by fluorescence spectroscopy and molecular dynamics. The dimeric enzyme has four intrinsic tryptophans, located at positions 6 and 42 in each monomer. Fluorescence spectra and acrylamide quenching experiments show two differently accessible Trp populations in the apoenzyme with k(q1) = 6.85 x 10(9) M(-1) s(-1) and k(q2) = 1.88 x 10(9) M(-1) s(-1), that merge into one in the complex with k(q) = 1.78 x 10(9) M(-1) s(-1). 500 ps trajectory analysis of Trp X1/X2 rotameric interconversions suggest a model to account for the observed Trp fluorescence. In the simulations, Trp6/Trp6B rotameric interconversions do not occur on this timescale for both HIV forms. In the apoenzyme simulations, however, both Trp42s and Trp42Bs are flipping between X1/X2 states; in the complexed form, no such interconverions occur. A detailed investigation of the local Trp environments sampled during the molecular dynamics simulation suggests that one of the apoenzyme Trp42B rotameric interconversions would allow indole-quencher contact, such as with nearby Tyr59. This could account for the short lifetime component. The model thus interprets the experimental data on the basis of the conformational fluctuations of Trp42s alone. It suggests that the rotameric interconversions of these Trps, located relatively far from the active site and at the very start of the flap region, becomes restrained when the apoenzyme binds the inhibitor. The model is thus consistent with associating components of the fluorescence decay in HIV-1 protease to ground state conformational heterogeneity.
A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from approximately 1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed approximately 10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0. 3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).
Human DNA can be damaged by natural metabolism through free radical production. It has been suggested that the equilibrium between innate damage and cellular DNA repair results in an oxidative DNA damage background that potentially contributes to disease and aging. Efforts to quantitatively characterize the human oxidative DNA damage background level, based on measuring 8-oxoguanine lesions as a biomarker, have led to estimates that vary over three to four orders of magnitude, depending on the method of measurement. We applied a previously developed and validated quantitative pathway model of human DNA base excision repair, integrating experimentally determined endogenous damage rates and model parameters from multiple sources. Our estimates of at most 100 8-oxoguanine lesions per cell are consistent with the low end of data from biochemical and cell biology experiments, a result robust to model limitations and parameter variation. Our findings show the power of quantitative system modeling to interpret composite experimental data and make biologically and physiologically relevant predictions for complex human DNA repair pathway mechanisms and capacity.
The proportional odds model is illustrated in the analysis of two efficacy scales used in a phase II clinical trial involving 81 schizophrenic patients. The proportional odds model preserves the discrete, ordinal nature of one of the scales. The analysis of this data suggested that the relationship between the two scales is not captured by a linear proportional odds model. A linear model and a piecewise linear model for the explanatory variable were therefore compared using likelihood-based analyses. Residuals from both models were compared. Predicted probabilities for the ordinal categories were constructed from the estimated model. Extensions and limitations of the model for interpretation of other trials and for the planning of future trials are discussed.