A stochastic model for a progressive chronic disease

For many progressive chronic diseases, there exist useful prognostic indicators for the course of the disease and the survival of the patient. The evolution of such an indicator is modelled as a monotone transformation of a pure birth process with killing. Explicit formulas are derived for the probability distribution of this process at an arbitrary time, the distribution of the first-passage times, the joint distribution of the survival time and the maximum of the process, and the marginals of this joint distribution. In two examples, the general formulas are evaluated in closed form.     

A stochastic model for then-compartment irreversible system

This paper deals with a stochasticn-compartment irreversible system with a non-homogeneous Poisson input and arbitrary residence time for each of the compartments. Results relating to the number of particles present in each of the compartments as well as the total number of particles present in the system at any time are derived. Further, explicit expressions for the auto covariance function for each compartment and the cross-covariance function between any two compartments with a given time lag are obtained. As a particular case, then-compartment irreversible system is analyzed with homogeneous Poisson input and exponential residence time distribution for each of the compartments. The possible applications of the model are discussed.     

A steady state model of sequential irreversible enzyme reactions

Summary One of the questions which arises in the study of certain inborn errors of metabolism as well as in the field of enzyme kinetics is: what are the quantitative relationships between parameters of enzyme activity and substrate pool sizes in a metabolic pathway? A steady state model has been devised to answer this question for a homogeneous system of non-branched sequential irreversible enzyme reactions which follow Michaelis-Menten kinetics. The concentration of a substrate in such a pathway, [S_i], is a function of 5 variables: (a) the K_M of the enzyme which forms the substrate (K_{M (i–1)}), (b) the K_M of the enzyme which utilizes the substrate (K_{M i}), (c) the V_max of the enzyme which forms the substrate (V_{m (i–1)}), (d) the V_max of the enzyme which utilizes the substrate (V_{m i}) and (e) the immediate precursor concentration [S_(i–1)] where [S_i] = K_{M i} V_{m (i–1)} [S_(i–1)]/[S_(i–1)] (V_mi -V_{m (i–1)}) + K_{M (i–1)}) V_mi The model introduces and defines the concept of and conditions for amplification. An input in the form of a steady state concentration of precursor [S_(i–1)] may be amplified as an output in the form of an increased steady state concentration of product [S_i]. The model also defines the values of the above 5 parameters which do not allow attainment of a steady state for the type of pathway considered.From the Metabolism Branch, National Cancer Institute, National Institutes of Health, Bethesda, Maryland 20014.     

Disseminated trichosporonosis in a murine model of chronic granulomatous disease

Over a period of ten months, five mice submitted to our service (the Pathology Section of the Veterinary Resources Program, Office of Research Services at the National Institutes of Health, Bethesda, Md.) were diagnosed with disseminated trichosporonosis. These mice had pyogranulomatous inflammation in multiple organs, including lung, liver, lymph nodes, salivary gland, and skin. Fungal elements in many of the lesions were identified, using special histochemical stains, and Trichosporon beigelii was obtained by use of culture of specimens at affected sites. This saprophytic fungus has caused disseminated disease in immunosuppressed humans. However, despite widespread use of immunosuppressed rodents in research, to the authors' knowledge, this organism had not previously been reported to cause spontaneous disseminated disease in laboratory mice. All affected mice had a genetically engineered defect in p47(phox), a critical component of the nicotinamide dinucleotide phosphate (NADPH) oxidase, the enzyme responsible for generating the phagocyte oxidative burst. These animals are used as a murine model of human chronic granulomatous disease. We discuss the lesions, differential diagnosis, identification of the organism, and the role of NADPH oxidase in protecting against disseminated trichosporonosis.     

A model of the statistical power of comparative genome sequence analysis

Comparative genome sequence analysis is powerful, but sequencing genomes is expensive. It is desirable to be able to predict how many genomes are needed for comparative genomics, and at what evolutionary distances. Here I describe a simple mathematical model for the common problem of identifying conserved sequences. The model leads to some useful rules of thumb. For a given evolutionary distance, the number of comparative genomes needed for a constant level of statistical stringency in identifying conserved regions scales inversely with the size of the conserved feature to be detected. At short evolutionary distances, the number of comparative genomes required also scales inversely with distance. These scaling behaviors provide some intuition for future comparative genome sequencing needs, such as the proposed use of “phylogenetic shadowing” methods using closely related comparative genomes, and the feasibility of high-resolution detection of small conserved features.     

Probabilistic Gompertz model of irreversible growth

Characterizing organism growth within populations requires the application of well-studied individual size-at-age models, such as the deterministic Gompertz model, to populations of individuals whose characteristics, corresponding to model parameters, may be highly variable. A natural approach is to assign probability distributions to one or more model parameters. In some contexts, size-at-age data may be absent due to difficulties in ageing individuals, but size-increment data may instead be available (e.g., from tag-recapture experiments). A preliminary transformation to a size-increment model is then required. Gompertz models developed along the above lines have recently been applied to strongly heterogeneous abalone tag-recapture data. Although useful in modelling the early growth stages, these models yield size-increment distributions that allow negative growth, which is inappropriate in the case of mollusc shells and other accumulated biological structures (e.g., vertebrae) where growth is irreversible. Here we develop probabilistic Gompertz models where this difficulty is resolved by conditioning parameter distributions on size, allowing application to irreversible growth data. In the case of abalone growth, introduction of a growth-limiting biological length scale is then shown to yield realistic length-increment distributions.     

A simple model for determining affinity from irreversible thermal shifts

Thermal denaturation (Tm) data are easy to obtain; it is a technique that is used by both small labs and large‐scale industrial organizations. The link between ligand affinity (K _D) and ΔTm is understood for reversible denaturation; however, there is a gap in our understanding of how to quantitatively interpret ΔTm for the many proteins that irreversibly denature. To better understand the origin, and extent of applicability, of a K _D to ΔTm correlate, we define equations relating K _D and ΔTm for irreversible protein unfolding, which we test with computational models and experimental data. These results suggest a general relationship exists between K _D and ΔTm for irreversible denaturation.     

Spatial analysis of vector-borne disease: A four-species model

Summary Disease can influence a host population's dynamics directly or indirectly through effects on the host's interactions with competitors and exploiters. We present a stochastic, spatially explicit model for the epidemiological landscape of a vector-borne disease. Two host species, of unequal competitive strength, are attacked by a selective parasite; the parasite serves as a vector for a pathogen. We emphasize the importance of the ecological stencil, i.e. the local area where ecological interactions govern a site's species composition. We demonstrate analytically that varying the size of the ecological stencil critically affects the dynamics of the host densities and the potential equilibrium configuration of the system. We point out how parallel computing can efficiently employ the geometry of the stencil's local transitions to predict large-scale spatio-temporal patterns of the model community.     

Structural analysis of the inhibition of thermolysin by an active-site-directed irreversible inhibitor

The mode of binding of the irreversible thermolysin inhibitor ClCH2CO-DL-(N-OH)Leu-OCH3 [Rasnick, D., & Powers, J.C. (1978) Biochemistry 17, 4363-4369] has been determined by X-ray crystallography at a resolution of 2.3 A and the structure of the covalent complex refined to give a crystallographic residual of 17.0%. This is the first such structural study of an active-site-directed covalent complex of a zinc protease. As anticipated by Rasnick and Powers, the inhibitor alkylates Glu-143 in the thermolysin active site, and the hydroxamic acid moiety coordinates the zinc ion. The formation of the covalent complex is associated with a significant shift in a segment of the polypeptide backbone in the vicinity of the active site. This conformational adjustment appears to be necessary to relieve steric hindrance which would otherwise prevent alkylation of Glu-143. It is suggested that this steric hindrance, which occurs for thermolysin but would not be expected for carboxypeptidase A, accounts for the previously inexplicable difference in reactivity of these two metalloproteases toward N-haloacetyl amino acids. The relevance of this steric hindrance to the mechanism of catalysis is discussed. In agreement with previous results [Kester, W. R., & Matthews, B. W. (1977) Biochemistry 16, 2506-2516], it appears that steric hindrance prevents the direct attack of Glu-143 on the carbonyl carbon of an extended substrate, therefore ruling out the anhydride pathway in thermolysin-catalyzed hydrolysis of polypeptide substrates and their ester analogues.     

Plasmodium berghei: development of an irreversible experimental malaria model in Wistar rats

A protocol to infect five-week-old Wistar rats by Plasmodium berghei which resulted in 100% mortality was developed in this work. In order to accomplish this goal, the effect of the administration of 10(7) and 10(8) parasitized erythrocytes by i.v. and i.p. route was investigated. The animals inoculated with 10(7) parasitized red blood cells by i.p. and i.v. routes showed 25 and 50% mortality, respectively. Inoculation with 10(8) parasitized erythrocytes by both routes resulted in a 100% lethal infection. The i.v. inoculation showed less scattered results and it was preferred over the i.p. route. The suitability of the protocol developed was evaluated by treating infected Wistar rats with chloroquine (30 mg/kg/day). A decreased parasitemia after the treatment was observed until the complete eradication of the parasite, around 10 days post-inoculation. Parasitemia depression after chloroquine treatment demonstrates the utility of the model developed to test new antimalarial drugs.     

Reversing disability of irreversible lung disease.

Pulmonary rehabilitation is a comprehensive multifaceted team approach for integrating medical management, coping skills, self-management techniques, and exercise reconditioning. It provides patients with chronic lung disease the ability to adapt and live full and nearly normal lives. These changes are possible because the overall disability includes significant reversible components: Patients have bronchospasm, infection, and cor pulmonale; they respond to progressively impaired lungs by progressive inactivity, leading to physical deconditioning. Both factors contribute to dyspnea. Because patients naturally fear dyspnea, they panic easily. During panic, their work of breathing may increase and respiratory failure may result. Pulmonary rehabilitation provides good medical management; provides exercises to increase strength, endurance, and tolerance to dyspnea; and trains patients in panic control. These programs have not been shown to lengthen life span or improve static lung function. They increase exercise performance and render patients functional, independent, and subject to fewer hospital admissions. Pulmonary rehabilitation is the only approach to chronic lung disease short of lung transplantation that improves the long-term outlook for these patients.     

Progression from acute to chronic disease in a murine parent-into-F1 model of graft-versus-host disease

The parent-into-immunocompetent-F(1) model of graft-vs-host disease (GVHD) induces immune dysregulation, resulting in acute or chronic GVHD. The disease outcome is thought to be determined by the number of parental anti-F(1) CTL precursor cells present in the inoculum. Injection of C57BL/6 (B6) splenocytes into (B6 x DBA/2)F(1) (B6D2F(1)) mice (acute model) leads to extensive parental cell engraftment and early death, whereas injection of DBA/2 cells (chronic model) results in little parental cell engraftment and a lupus-like disease. This study demonstrated that injection of BALB/c splenocytes into (BALB/c x B6)F(1) (CB6F(1)) mice resulted in little engraftment of parental lymphocytes and the development of lupus as expected. Injection of B6 splenocytes into CB6F(1) initiated an initial burst of parental cell engraftment similar to that of B6 into B6D2F(1). However, the acute disease resolved, and the CB6F(1) mice went on to develop chronic GVHD with detectable Abs to ssDNA, dsDNA, and extractable nuclear Ags. Limiting dilution CTL assays determined that B6 splenocytes have CTL precursor frequencies of 1/1000 against both CB6F(1) and B6D2F(1), whereas DBA/2 and BALB/c splenocytes have a CTL precursor frequency of 1/20,000 for their respective F(1)s. The Th cell precursor frequency for B6 anti-DBA/2 was 3-fold higher than that for B6 anti-BALB/c determined by limiting dilution proliferation assays. These results indicate the importance of adequate allospecific helper as well as effector T cells for the induction and maintenance of acute GVHD in this model, and presents an unexpected model in which initial acute GVHD is replaced by the chronic form of disease.     

A statistical model for multidimensional irreversible electroporation cell death in tissue

Background  

Irreversible electroporation (IRE) is a minimally invasive tissue ablation technique which utilizes electric pulses delivered by electrodes to a targeted area of tissue to produce high amplitude electric fields, thus inducing irreversible damage to the cell membrane lipid bilayer. An important application of this technique is for cancer tissue ablation. Mathematical modelling is considered important in IRE treatment planning. In the past, IRE mathematical modelling used a deterministic single value for the amplitude of the electric field required for causing cell death. However, tissue, particularly cancerous tissue, is comprised of a population of different cells of different sizes and orientations, which in conventional IRE are exposed to complex electric fields; therefore, using a deterministic single value is overly simplistic.     

Differential serum proteomic analysis in a model of metabolic disease

Protein profiling would aid in better understanding the pathophysiology of metabolic disease. Here, we report on differential proteomic analysis using an animal model of diabetes mellitus and associated metabolic disorders (Otsuka Long-Evans Tokushima Fatty rat). Serum was analyzed by a new two-dimensional liquid chromatography system which separated proteins by chromatofocusing and subsequent reversed-phase chromatography. This is the first application of this approach to differential serum proteomics. Differentially expressed proteins, identified with MALDI-TOF mass spectrometry, included apolipoproteins and alpha2-HS-glycoprotein. These findings add to our understanding of the underlying pathophysiology. This new proteomic analysis is a promising tool to elucidate disease mechanisms.     

Half-time analysis of the kinetics of irreversible enzyme inhibition by an unstable site-specific reagent

The half-time method for the determination of Michaelis parameters from enzyme progress-curve data (Wharton, C.W. and Szawelski, R.J. (1982) Biochem. J. 203, 351-360) has been adapted for analysis of the kinetics of irreversible enzyme inhibition by an unstable site-specific inhibitor. The method is applicable to a model in which a product (R) of the decomposition of the site-specific reagent, retaining the chemical moiety responsible for inhibitor specificity, binds reversibly to the enzyme with dissociation constant Kr: (formula; see text). Half-time plots of simulated enzyme inactivation time-course data are shown to be unbiased, and excellent estimates of the apparent second-order rate constant for inactivation (k +2/Ki) and Kr can be obtained from a series of experiments with varying initial concentrations of inhibitor. Reliable estimates of k +2 and Ki individually are dependent upon the relative magnitudes of the kinetic parameters describing inactivation. The special case, Kr = Ki, is considered in some detail, and the integrated rate equation describing enzyme inactivation shown to be analogous to that for a simple bimolecular reaction between enzyme and an unstable irreversible inhibitor without the formation of a reversible enzyme-inhibitor complex. The half-time method can be directly extended to the kinetics of enzyme inactivation by an unstable mechanism-based (suicide) inhibitor, provided that the inhibitor is not also a substrate for the enzyme.     

Lyme disease: a unique human model for an infectious etiology of rheumatic disease

Lyme disease is a complex immune-mediated multi-system disorder that is infectious in origin and inflammatory or "rheumatic" in expression. Through its epidemiologic characteristics, large numbers of a seasonally synchronized patient population are readily available for prospective study. Lyme disease has a known clinical onset ("zero time"), marked by the characteristic expanding skin lesion, erythema chronicum migrans, and a clearly defined pre-articular phase. At least some manifestations of the disorder are responsive to antibiotics, and the causative agent--a spirochete--is now known. These advantages make Lyme disease unique as a human model for an infectious etiology of rheumatic disease.     

A bromoacetylated analogue of cyanopindolol: an irreversible antagonist at rat beta-adrenoceptors

A high affinity, chemically reactive cyanopindolol derivative. N8-bromoacetyl-N1-3'-(2-cyano-4-indolyloxy)-2'-hydroxypropyl-[Z]-1 ,8-diamino-p-menthane (Br-CYP) was synthesized and its interaction with beta-adrenoceptors characterized. Studies with rat heart, lung, brain, and red blood cell membranes indicated that the compound displaced 3H-dihydroalprenolol (3H-DHA) from beta-adrenoceptors with IC50 values in the nanomolar range. The concentration of functional beta-adrenoceptors in membranes was markedly reduced when membranes were preincubated with Br-CYP and then extensively washed prior to assay. (+/-)Alprenolol and (-)isoproterenol, but not (+)isoproterenol, when included in the preincubation prevented this reduction in binding sites by Br-CYP. Br-CYP was active in vivo when injected intraperitoneally into rats. A dose of 10 micrograms/kg reduced the concentration of binding sites in membranes from heart by 30%, lung by 36%, and RBC by 70%, but did not affect sites on brain membranes 16 hours after injection. Higher doses blocked virtually all the 3H-DHA binding sites in the peripheral organs studied. Br-CYP reduced the concentration of beta-adrenoceptors in membranes from these same tissues (but not brain tissue) as long as two weeks after injection with recovery of binding occurring more rapidly in heart tissue than lung and red blood cells. These results suggest that Br-CYP may be a useful compound for in vivo studies of the biochemistry and pharmacology of beta-adrenergic systems.