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PubMed2006

Mathematical modeling of subgenomic hepatitis C virus replication in Huh-7 cells.

Cell-based hepatitis C virus (HCV) replicon systems have provided a means for understanding HCV replication mechanisms and for testing new antiviral agents. We describe here a mathematical model of HCV replication that assumes that the translation of the HCV polyprotein occurs in the cytoplasm, that HCV RNA synthesis occurs in vesicular-membrane structures, and that the strategy of replication involves a double-stranded RNA intermediate. Our results shed light on the intracellular dynamics of subgenomic HCV RNA replication from transfection to steady state within Huh-7 cells. We predict the following: (i) about 6 x 10(3) ribosomes are involved in generating millions of HCV NS5B-polymerase molecules in a Huh-7 cell, (ii) the observed 10:1 asymmetry of plus- to minus-strand RNA levels can be explained by a higher-affinity (200-fold) interaction of HCV NS5B polymerase-containing replication complexes with HCV minus-strand RNA over HCV plus-strand RNA in order to initiate synthesis, (iii) the latter higher affinity can also account for the observed approximately 6:1 plus-strand/minus-strand ratio in vesicular-membrane structures, and (iv) the introduction of higher numbers of HCV plus-strand RNA by transfection leads to faster attainment of steady-state but does not change the steady-state HCV RNA level. Fully permissive HCV replication systems have been developed, and the model presented here is a first step toward building a comprehensive model for complete HCV replication. Moreover, the model can serve as an important tool in understanding HCV replication mechanisms and should prove useful in designing and evaluating new antivirals against HCV.

Cell Line, Tumor↗

PubMed2003

Study of a mathematical model of metal ion complexes in solvent sublation.

Separation of metal ion complex, [(C(12)H(8)N(2))(3)Fe(2+)], with surfactant sodium dodecylphrate (DLS) complex from aqueous phase was carried out by solvent sublation, which obeys first-order kinetics. On the base of the complete transport mechanisms, the Langmuir adsorption, and the ion complex equilibrium in the aqueous phase, a mathematical model for the [(C(12)H(8)N(2))(3)Fe(2+)]-surfactant ion complex is obtained with the aid of the Mathematic 4.0 program, 4th Runge-Kutta method, and the Matlab programs. The effects of many parameters, such as K(a), K(l), K(ow), d(i), V(o), V(w), and Q(a), on solvent sublation are investigated. Furthermore, the simulation showed that the model is substantiated for experiments on the solvent sublation of the complex.

Journal Article↗

PubMed2002

Mathematical modeling of myoglobin facilitated transport of oxygen in devices containing myoglobin-expressing cells.

Low pO(2) is perhaps the most significant factor in artificial pancreas failure. In these environments, not only is the beta cell production of insulin reduced, but the cell death rate is also significantly higher. Mathematical models are developed to test the feasibility of facilitated oxygen transport in enhancing O(2) flux to genetically engineered cells in a bioartificial device such as a pancreas. For this device, it is proposed that beta cells be genetically engineered to express myoglobin throughout the cell. In addition, the significance of including myoglobin throughout the alginate matrix present to provide immuno-protection for the transplanted cells is considered. The mathematical analysis predicts that myoglobin facilitated oxygen transport has the potential of increasing the oxygen concentration at the centre of a cluster of cells (islet) with an effective radius of 100 microm by 50%. These theoretical models for myoglobin facilitated oxygen transport with homogeneous Michaelis-Menten consumption also indicate that including myoglobin in the alginate gel would beneficially improve the flux of oxygen to the transplanted cells.

Alginates↗

PubMed1979

Mathematical model of cell growth and phosphatase biosynthesis in Saccharomyces carlsbergensis under phosphate limitation.

The rate kinetics of growth and acid phosphate formation in the batch culture of Saccharomyces carlsbergensis LAM 1068 was studied under varying degrees of phosphate limitation. The mathematical model that was developed is concerned with the time lag for exponential growth, the biphasic growth on a substrate (glucose) and its product (ethanol), sustained growth on conservative phosphate, and the derepression of acid phosphatase. The numerical calculations using appropriate parametric constants successfully described the variation in the cell mass, glucose, ethanol, and inorganic phosphate concentrations, and the enzyme activity of acid phosphatase during aerobic growth of S. carlsbergensis under five different conditions of phosphate starvation. A simulation study revealed that the optimum initial phosphate concentration in the medium giving a high productivity of acid phosphatase was 2.0 mg phosphorus/g glucose liter.

Acid Phosphatase↗

PubMed1998

Mathematical modelling of juxtacrine cell signalling.

Juxtacrine signalling is emerging as an important means of cellular communication, in which signalling molecules anchored in the cell membrane bind to and activate receptors on the surface of immediately neighbouring cells. We develop a mathematical model to describe this process, consisting of a coupled system of ordinary differential equations, with one identical set of equations for each cell. We use a generic representation of ligand-receptor binding, and assume that binding exerts a positive feedback on the secretion of new receptors and ligand. By linearising the model equations about a homogeneous equilibrium, we categorize the range and extent of signal patterns as a function of parameters. We show in particular that the signal decay rate depends crucially on the form of the feedback functions, and can be made arbitrarily small by appropriate choice of feedback, for any set of kinetic parameters. As a specific example, we consider the application of our model to juxtacrine signalling by TGF alpha in response to epidermal wounding. We demonstrate that all the predictions of our linear analysis are confirmed in numerical simulations of the non-linear system, and discuss the implications for the healing response.

Cell Communication↗

PubMed2001

Determination of contact hip stress from nomograms based on mathematical model.

Nomograms are presented that enable determination of maximal stress on the hip joint weight bearing area if certain geometrical parameters of the hip and pelvis and the body weight are known. The nomograms are calculated by using previously developed mathematical models. It is demonstrated how the maximal stress on the hip joint weight bearing area is determined from the presented nomograms for a hip for which the geometrical parameters were obtained from a standard anteroposterior rentgenograph. This simple and noninvasive method may give insight into the biomechanical status of the hip which should be considered in routine surgical planning and as a part of the routine examination of the patient without the use of any additional tools.

Biomechanical Phenomena↗

PubMedDate not supplied

A mathematical model for cisplatin cellular pharmacodynamics.

A simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls) on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (approximately 100 hours). The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy.

Antineoplastic Agents↗

PubMed2005

Mathematical modeling of the nitric oxide/cGMP pathway in the vascular smooth muscle cell.

The nitric oxide (NO)/cGMP pathway in the vascular smooth muscle cell (VSMC) is an important cellular signaling system for the regulation of VSMC relaxation. We present a mathematical model to investigate the underlying mechanisms of this pathway. The model describes the flow of NO-driven signal transduction: NO activation of soluble guanylate cyclase (sGC), sGC- and phosphodiesterase-catalyzed cGMP production and degradation, cGMP-mediated regulation of protein targets including the Ca2+-activated K+ (KCa) channel, and the myosin contractile system. Model simulations reproduce major NO/cGMP-induced VSMC relaxation effects, including intracellular Ca2+ concentration reduction and Ca2+ desensitization of myosin phosphorylation and force generation. Using the model, we examine several testable principles. 1) Rapid sGC desensitization is caused by end-product cGMP feedback inhibition; a large fraction of the steady-state sGC population is in an inactivated intermediate state, and cGMP production is limited well below maximum. 2) NO activates the K(Ca) channel with both cGMP-dependent and -independent mechanisms; moderate NO concentration affects the K(Ca) via the cGMP-dependent pathway, whereas higher NO concentration is accommodated by a cGMP-independent mechanism. 3) Chronic NO synthase inhibition may cause underexpressions of K+ channels including inward rectifier and K(Ca) channels. 4) Ca2+ desensitization of the contractile system is distinguished from Ca2+ sensitivity of myosin phosphorylation. The model integrates these interactions among the heterogeneous components of the NO signaling system and can serve as a general modeling framework for studying NO-mediated VSMC relaxation under various physiological and pathological conditions. New data can be readily incorporated into this framework for interpretation and possible modification and improvement of the model.

Animals↗

PubMed1994

A physiologically based mathematical model of dermal absorption in man.

A sound understanding of the mechanisms determining percutaneous absorption is necessary for toxicological risk assessment of chemicals contacting the skin. As part of a programme investigating these mechanisms we have developed a physiologically based mathematical model. The structure of the model parallels the multi-layer structure of the skin, with separate surface, stratum corneum and viable tissue layers. It simulates the effects of partitioning and diffusive transport between the sub-layers, and metabolism in the viable epidermis. In addition the model describes removal processes on the surface of the skin, including the effects of washing and desquamation, and rubbing off onto clothing. This model is applied to data on the penetration of the herbicide fluazifop-butyl through human skin in vivo and in vitro. Part of this dataset is used to estimate unknown model parameter values and the remainder is used to provide a partial validation of the model. Only a small fraction of the applied dose was absorbed through the skin; most of it was removed by washing or onto clothing. The model provides a quantitative description of these loss processes on the skin surface.

Administration, Cutaneous↗

PubMed2001

Improving the sensitivity of stereotactic core biopsy to diagnose ductal carcinoma in situ of the breast: a mathematical model.

Stereotactic core biopsy (SCB) is performed on mammographically suspicious, non-palpable lesions of the breast. Reported sensitivities of SCB for the detection of ductal carcinoma in situ (DCIS) vary from 41% to 93%. We have developed a simple mathematical model to predict the probability of retrieving at least one diagnostic core from a focus of DCIS. We make recommendations of the number of samples needed for different sized areas of microcalcification. The sensitivity of SCB is affected by needle placement accuracy, diameter of the area of microcalcification (d), histological density of DCIS (x) (calculated as 7.5% by previous studies) and number of core samples (n) removed. The probability of achieving at least one representative core sufficient for diagnosis (P(core)) is defined as: P(core) = 1-(1 + p ([1- (x/100)]d - 1 ))n, where rho is the probability of a SCB accurately targeting the area of microcalcification. At least seven core samples should be removed in small foci (<5 mm) of DCIS to achieve a 0.75 probability of an accurate diagnosis. The probability of a diagnostic biopsy of larger areas of DCIS (>10 mm) is 0.95 when five cores are removed. This formula serves as an explanation to patients why SCB may fail to diagnose DCIS, and justifies the retrieval of more core samples to increase the probability of an accurate diagnosis and to reduce the chance of a non-representative core. In the absence of sufficient samples, a wire-guided open biopsy is necessary to exclude DCIS.

Biopsy↗

PubMedDate not supplied

[A mathematical model of pre-epidemic circulation: an analysis of the mechanisms of oriented transformation].

The probable mechanisms of the regulation of the clonal composition of the infective agent in the course of its pre-epidemic circulation are studied. The mathematical model (in the form of two subsystems) describes asymptomatic circulation and the dynamics of the clonal composition: the beginning of the active circulation of faintly virulent variants, the oriented selection of virulent variants and the fixation of the epidemic variant.

Cloning, Molecular↗

PubMed1997

Release of nitric oxide from donors with known half-life: a mathematical model for calculating nitric oxide concentrations in aerobic solutions.

The NO concentrations released from donor compounds are difficult to predict as they are determined by formation and inactivation reactions. To calculate the concentrations of NO over time, we have developed a mathematical model which is based on a system of two differential equations describing the first order decomposition of the NO donor in association with the third order reaction of NO with oxygen. Although there is no closed formula for the solution, it can be easily computed by any standard numerical differential solver or simulation software with the following input parameters: initial concentration and decomposition rate constant of the NO donor, O2 concentration, and rate constant for NO autoxidation. The model was validated by monitoring NO release from 2,2-diethyl-1-nitroso-oxyhydrazine (DEA/NO) with a Clark-type NO-sensitive electrode at two different temperatures (25 and 37 degrees C) and DEA/NO concentrations ranging from 1 to 10 microM. Under all conditions, there was an excellent agreement between experimental and calculated data. In addition to the computer modeling, we present graphical plots which allow a rough but very easy estimation of the actual NO concentrations if appropriate computer software should not be available.

Kinetics↗

PubMed1988

Mechanical capabilities of the human jaw muscles studied with a mathematical model.

The human muscles of mastication have complex shapes with large attachment areas. This suggests a variety of bite force directions and magnitudes. The possible range of these and the concomitant joint force of each individual muscle were determined by a mathematical model describing static equilibrium conditions in the sagittal plane. The range of force directions for each muscle was defined by the action lines of the most anterior and most posterior (for the lateral pterygoid, most superior and most inferior) muscle fibre bundles. Calculations from the various directions of the reaction force in the temporomandibular joint demonstrated that each muscle can produce a unique variety of bite force directions. Except for the lateral pterygoid and posterior temporalis, the range and orientation of possible bite forces was closely related to the orientation of the joint force. In general, at the canine tooth the bite forces were directed more posteriorly than at the second molar. Within a muscle, distinct portions may produce considerably different bite force magnitudes; the largest bite forces are produced at horizontal and vertical joint force directions. The posterior portions of the deep masseter and temporalis muscles and the lateral pterygoid muscle have the largest mechanical advantage. In the majority of muscles the magnitude of the joint reaction force is smallest at an oblique joint force direction.

Aged↗

PubMed2005

Mathematical modeling of planar polarity.

Although it is well established that the Frizzled receptor is involved in the transmission of polarity information from cell to cell in the Drosophila cuticle, its precise role is still unclear. A recent paper by presents a mathematical model of a feedback loop-based mechanism for propagation of polarity between cells that can account for the known functions of Frizzled.

Adaptor Proteins, Signal Transducing↗

PubMed1985

Creatinine clearance estimation from serum creatinine values: an analysis of three mathematical models of glomerular function.

The logarithmic relationship of serum creatinine and creatinine clearance was analyzed in 100 adult patient studies using a geometric regression technique. Each sex was independently analyzed, and the subsequently derived regression formulae were age corrected resulting in mathematical models useful in estimating creatinine clearance from serum creatinine concentrations. These formulae were tested prospectively in another group of 100 patient studies in which creatinine clearance had been determined, and the results compared to values derived by use of two other published formulae. This newer method resulted in a closer distribution of data around a line of identity compared to other formulae and allowed for a good "bedside" estimation of creatinine clearance from serum creatinine concentration.

Adolescent↗

PubMed2005

Mathematical modeling of primary hepatitis C infection: noncytolytic clearance and early blockage of virion production.

BACKGROUND & AIMS: Although hepatitis C virus kinetics and immune determinants during primary infection have been described, the virus-host interplay is not fully understood. We used mathematical modeling to elucidate and quantify virus-host dynamics. METHODS: Ten chimpanzees were infected intrahepatically with H77-RNA (n = 3) or intravenously with infected serum. Blood samples were taken 1-3 times per week for 6 months. A new model was fitted to the observed HCV RNA and alanine aminotransferase (ALT) kinetics. RESULTS: After infection, viral levels increased in a biphasic manner with a transient decline in between. This can be explained by a partial block (mean, 91%) of virion production, possibly due to an endogenous type I interferon response. After reaching maximum levels, a long viral plateau (mean, 6.1 log cp/mL) can be explained by blind homeostasis and lack of susceptible cells. Modest elevations in ALT levels (21-93 IU/L) were concurrently observed, indicating a shorter half-life of infected versus noninfected hepatocytes (mean ratio, 2.6). Following the ALT flare, viral titers rapidly declined to a lower (mean, 4.5 log cp/mL; n = 6) or undetectable level (n = 4). This decline is compatible with increased cell death (mean minimal estimate half-life, 28.7 days) and noncytolytic clearance (mean maximal estimate half-life, 24.1 days) of infected cells. CONCLUSIONS: Our results quantify virus-host dynamics during primary HCV infection and suggest that endogenous type I interferon slows virus production in the early acute phase. Partial or effective virus control correlates with the half-life of infected cells regulated by both cytolytic and noncytolytic mechanisms.

Alanine Transaminase↗

PubMed2006

Bone remodeling in health and disease: lessons from mathematical modeling.

Parathyroid hormone is the single anabolic treatment for osteoporosis currently approved by U.S. Food and Drug Administration. The physiology underlying anabolic actions of parathyroid hormone remains mysterious, since only when applied intermittently, does it increase bone mass. This study employs mathematical modeling to consider multiple concomitant effects of parathyroid hormone and local regulators on bone turnover. Remarkably, due to coupling between osteoclasts and osteoblasts, anabolic effects of parathyroid hormone emerged from a single action-stimulation of osteoclastic bone resorption. This study provides a novel conceptual framework for the development of highly desirable anabolic treatments for bone diseases.

Bone Diseases↗

PubMed1975

[Intracranial pressure. II. Experimental verification of a mathematical model].

The authors report the results of experiments (performed on the dog in vitro and in vivo) which were designed to verify hypotheses made concerning vascular elasticity and characteristics of CSF resorption, as well as to test the validity of a mathematical model that was described in a previous paper. The authors concluded that the equations of the model account for most of the phenomena satisfactorily, but fail to predict a rebound phenomena which occurs after sudden injections in the cisterna magna. The elasticity coefficient S appears to be constant over a range of 200 mm Hg. On the other hand, the filtration coefficient K depends upon pressure, probably due to morphological changes in the size and shape of the CSF valves. These discrepancies are taken into account in a more general model that is presented in the following paper.

Animals↗