Two-compartment Mathematical Model Research Articles

Developing a computational pharmacokinetic model of systemic snakebite envenomation and antivenom treatment

Snakebite envenomation is responsible for over 100,000 deaths and 400,000 cases of disability annually, most of which are preventable through access to safe and effective antivenoms. Snake venom toxins span a wide molecular weight range, influencing their absorption, distribution, and elimination within the body. In recent years, a range of scaffolds have been applied to antivenom development. These scaffolds similarly span a wide molecular weight range and subsequently display diverse pharmacokinetic behaviours. Computational simulations represent a powerful tool to explore the interplay between these varied antivenom scaffolds and venoms, to assess whether a pharmacokinetically optimal antivenom exists. The purpose of this study was to establish a computational model of systemic snakebite envenomation and treatment, for the quantitative assessment and comparison of conventional and next-generation antivenoms. A two-compartment mathematical model of envenomation and treatment was defined and the system was parameterised using existing data from rabbits. Elimination and biodistribution parameters were regressed against molecular weight to predict the dynamics of IgG, F(ab’)2, Fab, scFv, and nanobody antivenoms, spanning a size range of 15–150 kDa. As a case study, intramuscular envenomation by Naja sumatrana (equatorial spitting cobra) and its treatment using Fab, F(ab’)2, and IgG antivenoms was simulated. Variable venom dose tests were applied to visualise effective antivenom dose levels. Comparisons to existing antivenoms and experimental rescue studies highlight the large dose reductions that could result from recombinant antivenom use. This study represents the first comparative in silico model of snakebite envenomation and treatment.

Mathematical modelling identifies conditions for maintaining and escaping feedback control in the intestinal epithelium

The intestinal epithelium is one of the fastest renewing tissues in mammals. It shows a hierarchical organisation, where intestinal stem cells at the base of crypts give rise to rapidly dividing transit amplifying cells that in turn renew the pool of short-lived differentiated cells. Upon injury and stem-cell loss, cells can also de-differentiate. Tissue homeostasis requires a tightly regulated balance of differentiation and stem cell proliferation, and failure can lead to tissue extinction or to unbounded growth and cancerous lesions. Here, we present a two-compartment mathematical model of intestinal epithelium population dynamics that includes a known feedback inhibition of stem cell differentiation by differentiated cells. The model shows that feedback regulation stabilises the number of differentiated cells as these become invariant to changes in their apoptosis rate. Stability of the system is largely independent of feedback strength and shape, but specific thresholds exist which if bypassed cause unbounded growth. When dedifferentiation is added to the model, we find that the system can recover faster after certain external perturbations. However, dedifferentiation makes the system more prone to losing homeostasis. Taken together, our mathematical model shows how a feedback-controlled hierarchical tissue can maintain homeostasis and can be robust to many external perturbations.

A simple two-compartment model for analysis of feedback control of glucose regulation

The minimal model (MM) is widely used for analyzing glucose-insulin interactions under healthy and diabetic conditions. The MM departs from a two-compartment scheme and involves three states for the concentration of glucose and insulin, and the action of insulin is the remote compartment. Although the derivation of the MM model is tacitly based on plasma and interstitial fluid compartments, the interpretation of the three variables and the underlying parameters is not straightforward. For instance, it is not clear if the glucose concentration corresponds to either the plasma or interstitial fluid compartment. The issue is important given the recent developments in the monitoring of glucose dynamics via interstitial fluid measurements. Specifically, a proper model should include glucose states in both plasma and interstitial fluid compartments to dispose of a suitable framework for, e.g., monitoring and designing feedback control strategies for dealing with diabetes disorders. The present work aims to develop a two-compartment mathematical model for glucose and insulin interactions. The approach is based on mass balances of glucose and insulin in plasma and interstitial compartments. It is shown that the model is reduced to the three-states MM via very restrictive assumptions and the four-states Padova model. Numerical simulations were used to illustrate several typical dynamics linked to glucose-insulin interaction failures. The model allows the analysis of feedback control strategies systematically. For instance, the performance of feedback control strategies involving measurements in both compartments at different sampling frequencies (e.g., cascade control) is analyzed.

The Study of Effect of Toxic Metal on Plant Growth Dynamics with Time Lag: A Two-Compartment Model

A two-compartment mathematical model is proposed for the study of individual plant growth dynamics with time lag due to the presence of toxic metals in the soil. It is assumed in the model that nutrient uptake by the roots is hindered by the presence of the toxic metals. It is further assumed that there is less transfer of nutrients from the root compartment to the shoot compartment due to the toxic metals. However, the nutrient concentration decreases in the root compartment as well as in the shoot compartment, resulting in a decrease of the structural dry weight of the roots and shoots respectively. This effect was studied by considering time lag in the utilization coefficient of the nutrient concentration in the roots in the presence of toxic metals. It is further assumed in the model that the nutrient use efficiency is also affected by the presence of toxic metals, resulting in a decrease of the structural dry weight of the shoots. The inclusion of time lag results in the disturbance of the interior equilibrium stability and Hopf bifurcation occurs for a critical value of the delay parameter. This entire phenomenon was captured by numerical simulation.

Using vaccine Immunostimulation/Immunodynamic modelling methods to inform vaccine dose decision-making

Unlike drug dose optimisation, mathematical modelling has not been applied to vaccine dose finding. We applied a novel Immunostimulation/Immunodynamic mathematical modelling framework to translate multi-dose TB vaccine immune responses from mice, to predict most immunogenic dose in humans. Data were previously collected on IFN-γ secreting CD4+ T cells over time for novel TB vaccines H56 and H1 adjuvanted with IC31 in mice (1 dose groups (0.1–1.5 and 15 μg H56 + IC31), 45 mice) and humans (1 dose (50 μg H56/H1 + IC31), 18 humans). A two-compartment mathematical model, describing the dynamics of the post-vaccination IFN-γ T cell response, was fitted to mouse and human data, separately, using nonlinear mixed effects methods. We used these fitted models and a vaccine dose allometric scaling assumption, to predict the most immunogenic human dose. Based on the changes in model parameters by mouse H56 + IC31 dose and by varying the H56 dose allometric scaling factor between mouse and humans, we established that, at a late time point (224 days) doses of 0.8–8 μg H56 + IC31 in humans may be the most immunogenic. A 0.8–8 μg of H-series TB vaccines in humans, may be as, or more, immunogenic, as larger doses. The Immunostimulation/Immunodynamic mathematical modelling framework is a novel, and potentially revolutionary tool, to predict most immunogenic vaccine doses, and accelerate vaccine development.

Alterations of Brain Energy Metabolism in Type 2 Diabetic Goto-Kakizaki Rats Measured In Vivo by 13C Magnetic Resonance Spectroscopy.

Type 2 diabetes (T2D) is associated with deterioration of brain structure and function. Here, we tested the hypothesis that T2D induces a reorganization of the brain metabolic networks that support brain function. For that, alterations of neuronal and glial energy metabolism were investigated in a T2D model, the Goto-Kakizaki (GK) rat. 13C magnetic resonance spectroscopy in vivo at 14.1T was used to detect 13C labeling incorporation into carbons of glutamate, glutamine, and aspartate in the brain of GK (n=7) and Wistar (n=13) rats during intravenous [1,6-13C]glucose administration. Labeling of brain glucose and amino acids over time was analyzed with a two-compartment mathematical model of brain energy metabolism to determine the rates of metabolic pathways in neurons and glia. Compared to controls, GK rats displayed lower rates of brain glutamine synthesis (-32%, P<0.001) and glutamate-glutamine cycle (-40%, P<0.001), and mitochondrial tricarboxylic acid (TCA) cycle rate in neurons (-7%, P=0.036). In contrast, the TCA cycle rate of astrocytes was larger in GK rats than controls (+21%, P=0.042). We conclude that T2D alters brain energy metabolism and impairs the glutamate-glutamine cycle between neurons and astrocytes, in line with diabetes-induced neurodegeneration and astrogliosis underlying brain dysfunction.

Using Data from Macaques To Predict Gamma Interferon Responses after Mycobacterium bovis BCG Vaccination in Humans: a Proof-of-Concept Study of Immunostimulation/Immunodynamic Modeling Methods.

ABSTRACTMacaques play a central role in the development of human tuberculosis (TB) vaccines. Immune and challenge responses differ across macaque and human subpopulations. We used novel immunostimulation/immunodynamic modeling methods in a proof-of-concept study to determine which macaque subpopulations best predicted immune responses in different human subpopulations. Data on gamma interferon (IFN-γ)-secreting CD4+ T cells over time after recent Mycobacterium bovis BCG vaccination were available for 55 humans and 81 macaques. Human population covariates were baseline BCG vaccination status, time since BCG vaccination, gender, and the monocyte/lymphocyte cell count ratio. The macaque population covariate was the colony of origin. A two-compartment mathematical model describing the dynamics of the IFN-γ T cell response after BCG vaccination was calibrated to these data using nonlinear mixed-effects methods. The model was calibrated to macaque and human data separately. The association between subpopulations and the BCG immune response in each species was assessed. The macaque subpopulations that best predicted immune responses in different human subpopulations were identified using Bayesian information criteria. We found that the macaque colony and the human baseline BCG status were significantly (P < 0.05) associated with the BCG-induced immune response. For humans who were BCG naïve at baseline, Indonesian cynomolgus macaques and Indian rhesus macaques best predicted the immune response. For humans who had already been BCG vaccinated at baseline, Mauritian cynomolgus macaques best predicted the immune response. This work suggests that the immune responses of different human populations may be best modeled by different macaque colonies, and it demonstrates the potential utility of immunostimulation/immunodynamic modeling to accelerate TB vaccine development.

Two-compartment model as a teaching tool for cholesterol homeostasis.

Cholesterol is a vital structural and functional molecule in the human body that is only slightly soluble in water and therefore does not easily travels by itself in the bloodstream. To enable cholesterol's targeted delivery to cells and tissues, it is encapsulated by different fractions of lipoproteins, complex particles containing both proteins and lipids. Maintaining cholesterol homeostasis is a highly regulated process with multiple factors acting at both molecular and tissue levels. Furthermore, to regulate the circulatory transport of cholesterol in lipoproteins, the amount of cholesterol present depends on and is controlled by cholesterol dietary intake, de novo synthesis, usage, and excretion; abnormal and/or unbalanced cholesterol levels have been shown to lead to severe outcomes, e.g., cardiovascular diseases. To investigate cholesterol transport in the circulatory system, we have previously developed a two-compartment mathematical model. Here, we show how this model can be used as a teaching tool for cholesterol homeostasis. Using the model and a hands-on approach, students can familiarize themselves with the basic components and mechanisms behind balanced cholesterol circulatory transport as well as investigate the consequences of and countermeasures to abnormal cholesterol levels. Among others, various treatments of high blood cholesterol levels can be simulated, e.g., with commonly prescribed de novo cholesterol synthesis inhibitors.

Mathematical analyses of two-compartment model of human cholesterol circulatory transport in application to high blood cholesterol prevention, diagnosis and treatment

Cholesterol plays a vital role in human body and thus its unbalanced homeostasis leads to health problems. Elevated blood cholesterol levels are now considered a classic coronary risk factor and are suspected to lead to coronary artery diseases, causing 2.6 millions of deaths each year. However, many of the mechanisms behind cholesterol-related processes remain unknown. Mathematical and computational models can aid investigation of complex biological phenomena, yet cholesterol-focused models remain rare. Here, we develop a two-compartment mathematical model to investigate cholesterol transport in the human circulatory system. We focus on the key aspects of cholesterol circulatory transport in the lipoproteins, its de novo synthesis and bile recycling and represent them by two simultaneous linear differential equations. The solutions yield changes over time of the cholesterol levels in the liver (compartment I) and bloodstream (compartment II). Drawing from the current clinical practice, we show the application of the model to personalized high blood cholesterol prevention, diagnosis and treatment.

Mathematical Modeling of Different Molecule Removal on On-Line Haemodiafiltration: Influence of Dialysis Duration and Infusion Flow

Background: In a previous study on a nocturnal, every-other-day online haemodiafiltration scheme, different removal patterns were observed for urea, creatinine, β₂-​microglobulin, myoglobin and prolactin. The aim of this study was to evaluate the influence of dialysis duration and infusion flow (Qi) on the removal of different molecular weight (MW) solutes, and to quantify the effect of the different treatments on the kinetics of the solutes by using a classical two-compartment model. Methods: This prospective, in-center study was carried out in 10 patients on a nocturnal, every-other-day online post-dilution haemodiafiltration program. Each patient received four dialysis sessions with different conditions, two 4-h sessions (with infusion flows of 50 or 100 ml/min) and two 8-h sessions (with infusion flows of 50 or 100 ml/min). To analyze the solute kinetics, blood samples were obtained hourly during the dialysis treatments and in the first 3 h post-dialysis. Results: Removal patterns differed in the molecules studied, which were quantified by means of the two-compartment mathematical model. The main results show the impact of dialysis duration on the removal of low molecular weight molecules (urea and creatinine), while the impact of Qi is clearly shown for high molecular weight molecules (myoglobin and prolactin). For middle molecular weight solutes, such as β₂-microglobulin, both factors (duration and Qi) enhance the removal efficiency of the dialyzer. Conclusions: Our study evaluates experimentally and mathematically how treatment time and infusion flow affect the filtration of solutes of different MW during post-dilution haemodiafiltration. The results provided by the present study should help physicians to select and individualise the most appropriate schedules to deliver an optimum diffusive and convective dialysis dose for each patient.

Mathematical Two-compartment Model of Human Cholesterol Transport in Application to High Blood Cholesterol Diagnosis and Treatment

Cholesterol plays a vital role in human body. Its unbalanced homeostasis, however, leads to health related problems. The elevated blood cholesterol levels are now considered a classic coronary risk factor and are suspected to lead to coronary artery diseases, causing 2.6 millions of deaths each year. Here, we develop a two-compartment mathematical model to investigate cholesterol transport in the circulatory system and its de novo synthesis in the liver. The model is described with a set of two simultaneous linear differential equations, which solutions yield changes over time of the cholesterol levels in the liver (compartment I) and bloodstream (compartment II). We show the applicability of the model to investigate the processes associated with the high blood cholesterol, e.g. lowering the cholesterol levels by inhibiting de novo cholesterol synthesis. Taking advantage of the analytically derived relationships for the steady state (equilibrium), we show how the model could aid diagnosis of high blood cholesterol by identifying whether the disturbances in the cholesterol homeostasis are due to impaired transport from the liver to the bloodstream, or vice versa.

Kinetics Of Chronic Lymphocytic Leukemia Cells In Tissues and Blood During Therapy With The BTK Inhibitor Ibrutinib

Bruton's tyrosine kinase (BTK), an essential component of B-cell-receptor (BCR) signaling, is blocked by ibrutinib, a BTK inhibitor that is clinically active in patients with chronic lymphocytic leukemia (CLL). Characteristically, ibrutinib causes CLL cell redistribution from tissue sites into the peripheral blood during the initial weeks of therapy, resulting in a transient surge in lymphocytosis. This activity of ibrutinib is thought to be important for the anti-leukemia activity of ibrutinib in CLL, because it removes CLL cells from the tissue microenvironment and consequently deprives the leukemia cells from growth- and survival-promoting cellular and molecular signals that are present in the tissues. However, clinically it has been noted that the magnitude of lymphocytosis during ibrutinib therapy is lesser than what would be expected from the rapid reduction in overall tissue disease burden, seen during the early weeks of ibrutinib therapy, especially in patients with bulky lymph nodes.Therefore, we aimed to quantify the relative amount of tissue CLL cells redistributed into the peripheral blood, and to better characterize the dynamics of this redistribution phenomenon. Crucial kinetic parameters were estimated by fitting a two-compartment mathematical model to clinical data that document serial blood lymphocyte counts of CLL patients as well as changes in total tissue burden, calculated from radiological measurements of lymph node and spleen volumes during ibrutinib therapy. This was done in a cohort of ten relapsed CLL patients, treated with single-agent ibrutinib, 420 mg PO daily on the Phase 1b/2 ibrutinib study at MD Anderson Cancer Center. We found that during ibrutinib therapy, on average 1.7 ± 1.1% of the cells die per day in the blood, while in tissue 2.7% ± 0.99% of the cells die per day. These death rates during treatment are approximately 5 times higher than those estimated in previous studies in the absence of treatment. The average fraction of the tissue CLL cells that was redistributed into the blood during ibrutinib therapy accounted for 23.3 ± 17% (range: 1.9% to 52.6%) of the calculated total tissue disease burden, with an average time for achieving a 50% reduction in tissue CLL cells of 20.3 ± 3.6 days. These findings indicate that generally a relatively small fraction of the total tissue CLL cell burden is re-distributed into the blood during ibrutinib therapy, and that a significant amount of drug-induced cell death occurs in tissue compartments. Disclosures:Off Label Use: Ibrutinib for CLL therapy. James:Pharmacyclics: Employment, Equity Ownership. O'Brien:Pharmacyclics: Research Funding. Burger:Pharmacyclics: Research Funding.

In vivo quantification of neuro‐glial metabolism and glial glutamate concentration using 1H‐[13C] MRS at 14.1T

Astrocytes have recently become a major center of interest in neurochemistry with the discoveries on their major role in brain energy metabolism. An interesting way to probe this glial contribution is given by in vivo (13) C NMR spectroscopy coupled with the infusion labeled glial-specific substrate, such as acetate. In this study, we infused alpha-chloralose anesthetized rats with [2-(13) C]acetate and followed the dynamics of the fractional enrichment (FE) in the positions C4 and C3 of glutamate and glutamine with high sensitivity, using (1) H-[(13) C] magnetic resonance spectroscopy (MRS) at 14.1T. Applying a two-compartment mathematical model to the measured time courses yielded a glial tricarboxylic acid (TCA) cycle rate (Vg ) of 0.27 ± 0.02 μmol/g/min and a glutamatergic neurotransmission rate (VNT ) of 0.15 ± 0.01 μmol/g/min. Glial oxidative ATP metabolism thus accounts for 38% of total oxidative metabolism measured by NMR. Pyruvate carboxylase (VPC ) was 0.09 ± 0.01 μmol/g/min, corresponding to 37% of the glial glutamine synthesis rate. The glial and neuronal transmitochondrial fluxes (Vx (g) and Vx (n) ) were of the same order of magnitude as the respective TCA cycle fluxes. In addition, we estimated a glial glutamate pool size of 0.6 ± 0.1 μmol/g. The effect of spectral data quality on the fluxes estimates was analyzed by Monte Carlo simulations. In this (13) C-acetate labeling study, we propose a refined two-compartment analysis of brain energy metabolism based on (13) C turnover curves of acetate, glutamate and glutamine measured with state of the art in vivo dynamic MRS at high magnetic field in rats, enabling a deeper understanding of the specific role of glial cells in brain oxidative metabolism. In addition, the robustness of the metabolic fluxes determination relative to MRS data quality was carefully studied.

Simulating Non-Specific Influences of Body Posture and Temperature on Thigh-Bioimpedance Spectroscopy during Continuous Monitoring Applications

Application of bioimpedance spectroscopy (BIS) for continuous monitoring of body fluid volumes is gaining considerable importance in personal health care. Unless laboratory conditions are applied, both whole-body or segmental BIS configurations are subject to nonspecific influences (e.g. temperature and change in body position) reducing the method's accuracy and reproducibility. In this work, a two-compartment mathematical model, which describes the thigh segment, has been adapted to simulate fluid and solute kinetics during change in body position or variation in skin temperature. The model is an improved version of our previous one offering a good tradeoff between accuracy and simplicity. It represents the kinetics of fluid redistribution, sodium-, potassium-, and protein-concentrations based on simple equations to predict the time course of BIS variations. Validity of the model was verified in five subjects (following a sequence of 7 min supine, 20 min standing, and 40 min supine). The output of the model may reduce possible influences on BIS by up to 80%.

Pharmacokinetic Delivery and Metabolizing Rate of Nicardipine Incorporated in Hydrophilic and Hydrophobic Cyclodextrins Using Two-Compartment Mathematical Model

The dispersion routes of cyclodextrin complexes with nicardipine (NC), such as hydrophilic hydroxypropyl-β-cyclodextrin (NC/HPβCD) and hydrophobic triacetyl-β-cyclodextrin (NC/TAβCD), through the body for controlled drug delivery and sustained release have been examined. The two-compartment pharmacokinetic model described the mechanisms of how the human body handles with ingestion of NC-cyclodextrin complexes in gastrointestinal tract (GI), distribution in plasma, and their metabolism in the liver. The model showed that drug bioavailability was significantly improved after oral administration of cyclodextrin complexes. The mathematical significance of this study to predict nicardipine delivery using pharmacokinetic two-compartment mathematical model with linear ordinary differential equations (ODE) approach represents a valuable tool to emphasize its effectiveness and metabolizing rate and diminish the side effects.

Race differences in the association of oxidative stress with insulin sensitivity in African- and European-American women.

Excessive metabolism of glucose and/or fatty acids may impair insulin signaling by increasing oxidative stress. The objective of this study was to examine the association between insulin sensitivity and protein carbonyls, a systemic marker of oxidative stress, in healthy, nondiabetic women, and to determine if the relationship differed with race. Subjects were 25 African-Americans (AA, BMI 28.4 ± 6.2 kg/m(2), range 18.8-42.6 kg/m(2); age 33.1 ± 13.5 years, range 18-58 years) and 28 European-Americans (EA, BMI 26.2 ± 5.9 kg/m(2), range 18.7-48.4 kg/m(2); age 31.6 ± 12.4 years, range 19-58 years). Insulin sensitivity was determined using an intravenous glucose tolerance test incorporating [6,6-(2)H(2)]-glucose, and a two-compartment mathematical model. Multiple linear regression results indicated that insulin sensitivity was inversely associated with protein carbonyls in AA (standardized regression coefficient -0.47, P < 0.05) but not EA (0.01, P = 0.945), after adjusting for %body fat. In contrast, %body fat was significantly and positively associated with insulin sensitivity in EA (-0.54, P < 0.01) but not AA (-0.24, P = 0.196). Protein carbonyls were associated with free fatty acids (FFA) in AA (r = 0.58, P < 0.01) but not EA (r = -0.11, P = 0.59). When subjects were divided based on median levels of fasting glucose and FFA, those with higher glucose/FFA concentrations had a significantly greater concentration of circulating protein carbonyls compared to those with lower glucose/FFA concentrations (P < 0.05). These results suggest that oxidative stress independently contributes to insulin sensitivity among AA women. Further, this association in AA may be mediated by circulating FFA and/or glucose.

A two-compartment mathematical model of endotoxin-induced inflammatory and physiologic alterations in swine*

To gain insights into individual variations in acute inflammation and physiology. Large-animal study combined with mathematical modeling. Academic large-animal and computational laboratories. Outbred juvenile swine. Four swine were instrumented and subjected to endotoxemia (100 µg/kg), followed by serial plasma sampling. Swine exhibited various degrees of inflammation and acute lung injury, including one death with severe acute lung injury (PaO(2)/FIO(2) ratio μ200 and static compliance μ10 L/cm H(2)O). Plasma interleukin-1β, interleukin-4, interleukin-6, interleukin-8, interleukin-10, tumor necrosis factor-α, high mobility group box-1, and NO(2)/NO(3) were significantly (p μ .05) elevated over the course of the experiment. Principal component analysis was used to suggest principal drivers of inflammation. Based in part on principal component analysis, an ordinary differential equation model was constructed, consisting of the lung and the blood (as a surrogate for the rest of the body), in which endotoxin induces tumor necrosis factor-α in monocytes in the blood, followed by the trafficking of these cells into the lung leading to the release of high mobility group box-1, which in turn stimulates the release of interleukin-1β from resident macrophages. The ordinary differential equation model also included blood pressure, PaO(2), and FIO(2), and a damage variable that summarizes the health of the animal. This ordinary differential equation model could be fit to both inflammatory and physiologic data in the individual swine. The predicted time course of damage could be matched to the oxygen index in three of the four swine. The approach described herein may aid in predicting inflammation and physiologic dysfunction in small cohorts of subjects with diverse phenotypes and outcomes.

A Two-Compartment Mathematical Model of Neuroglial Metabolism Using [1-11C] Acetate

The purpose of this study was to develop a two-compartment metabolic model of brain metabolism to assess oxidative metabolism from [1-(11)C] acetate radiotracer experiments, using an approach previously applied in (13)C magnetic resonance spectroscopy (MRS), and compared with an one-tissue compartment model previously used in brain [1-(11)C] acetate studies. Compared with (13)C MRS studies, (11)C radiotracer measurements provide a single uptake curve representing the sum of all labeled metabolites, without chemical differentiation, but with higher temporal resolution. The reliability of the adjusted metabolic fluxes was analyzed with Monte-Carlo simulations using synthetic (11)C uptake curves, based on a typical arterial input function and previously published values of the neuroglial fluxes V(tca)(g), V(x), V(nt), and V(tca)(n) measured in dynamic (13)C MRS experiments. Assuming V(x)(g)=10 × V(tca)(g) and V(x)(n)=V(tca)(n), it was possible to assess the composite glial tricarboxylic acid (TCA) cycle flux V(gt)(g) (V(gt)(g)=V(x)(g) × V(tca)(g)/(V(x)(g)+V(tca)(g))) and the neurotransmission flux V(nt) from (11)C tissue-activity curves obtained within 30 minutes in the rat cortex with a beta-probe after a bolus infusion of [1-(11)C] acetate (n=9), resulting in V(gt)(g)=0.136±0.042 and V(nt)=0.170±0.103 μmol/g per minute (mean±s.d. of the group), in good agreement with (13)C MRS measurements.

Modeling the host response to inhalation anthrax

Inhalation anthrax, an often fatal infection, is initiated by endospores of the bacterium Bacillus anthracis, which are introduced into the lung. To better understand the pathogenesis of an inhalation anthrax infection, we propose a two-compartment mathematical model that takes into account the documented early events of such an infection. Anthrax spores, once inhaled, are readily taken up by alveolar phagocytes, which then migrate rather quickly out of the lung and into the thoracic/mediastinal lymph nodes. En route, these spores germinate to become vegetative bacteria. In the lymph nodes, the bacteria kill the host cells and are released into the extracellular environment where they can be disseminated into the blood stream and grow to a very high level, often resulting in the death of the infected person. Using this framework as the basis of our model, we explore the probability of survival of an infected individual. This is dependent on several factors, such as the rate of migration and germination events and treatment with antibiotics.

Two types of independent bursting mechanisms in inspiratory neurons: an integrative model

The network of coupled neurons in the pre-Bötzinger complex (pBC) of the medulla generates a bursting rhythm, which underlies the inspiratory phase of respiration. In some of these neurons, bursting persists even when synaptic coupling in the network is blocked and respiratory rhythmic discharge stops. Bursting in inspiratory neurons has been extensively studied, and two classes of bursting neurons have been identified, with bursting mechanism depends on either persistent sodium current or changes in intracellular Ca(2+), respectively. Motivated by experimental evidence from these intrinsically bursting neurons, we present a two-compartment mathematical model of an isolated pBC neuron with two independent bursting mechanisms. Bursting in the somatic compartment is modeled via inactivation of a persistent sodium current, whereas bursting in the dendritic compartment relies on Ca(2+) oscillations, which are determined by the neuromodulatory tone. The model explains a number of conflicting experimental results and is able to generate a robust bursting rhythm, over a large range of parameters, with a frequency adjusted by neuromodulators.