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PubMed2004

Why the lysogenic state of phage lambda is so stable: a mathematical modeling approach.

We develop a mathematical model of the phage lambda lysis/lysogeny switch, taking into account recent experimental evidence demonstrating enhanced cooperativity between the left and right operator regions. Model parameters are estimated from available experimental data. The model is shown to have a single stable steady state for these estimated parameter values, and this steady state corresponds to the lysogenic state. When the CI degradation rate (gammacI) is slightly increased from its normal value (gammacI approximately 0.0 min(-1)), two additional steady states appear (through a saddle-node bifurcation) in addition to the lysogenic state. One of these new steady states is stable and corresponds to the lytic state. The other steady state is an (unstable) saddle node. The coexistence these two globally stable steady states (the lytic and lysogenic states) is maintained with further increases of gammacI until gammacI approximately 0.35 min(-1), when the lysogenic steady state and the saddle node collide and vanish (through a reverse saddle node bifurcation) leaving only the lytic state surviving. These results allow us to understand the high degree of stability of the lysogenic state because, normally, it is the only steady state. Further implications of these results for the stability of the phage lambda switch are discussed, as well as possible experimental tests of the model.

Bacteriophage lambda↗

PubMed1998

Evaluation of bovine viral diarrhea virus control using a mathematical model of infection dynamics.

A mathematical model for infection with bovine viral diarrhea virus (BVDV) was created comprising a series of coupled differential equations. The model architecture is a development of the traditional model framework using susceptible, infectious and removed animals (the SIR model). The model predicts 1.2% persistent infection (within the range of field estimates) and is fairly insensitive to alterations of structure or parameter values. This model allows us to draw important conclusions regarding the control of BVD, particularly with respect to the importance of persistently infected (PI) animals in maintaining BVD as an endemic entity in the herd. Herds without PI animals are likely to experience episodic reproductive losses at intervals of two to three years, unlike herds with PI animals which will not see such marked episodic manifestations of infection. Instead, these herds will experience an initial peak of disease which will settle to low-level chronic reproductive losses. The model indicates that vaccine coverage for herd immunity (to avoid episodic manifestations of disease) need be only 57% without PI animals, although 97% coverage is required when PI animals are present. Analysis of model behavior suggests a program of detection and removal of PI animals may enhance the effectiveness of a vaccine program provided these animals are in the herd for 10 days or less. The best results would be seen with PI animals in the herd for 5 or fewer days.

Animals↗

PubMed1998

Plant growth influenced by photosynthetic irradiance and temperature. Part I: Mathematical model for standard conditions.

The mathematical model of plant growth based on the analysis of photosynthesis has been developed. In the analysis, the leaf was treated as a control system, where the photosynthetically active radiation is an input value of the system and the leaf or plant dry mass is an output one. Environmental factors which influence plant growth are treated as disturbances. Part I presents the theory for standard plant growth conditions. Theoretical and experimental results were compared for lettuce cultivated in a greenhouse and phytotron. Part II develops the model for nonstandard conditions.

Lactuca↗

PubMed1989

The simulation of continuous arteriovenous hemodialysis with a mathematical model.

We have developed a mathematical model that predicts the performance of continuous arteriovenous hemodialysis. Given patient (plasma protein concentration, hematocrit, mean arterial pressure, central venous pressure) and circuit (flow resistance, membrane hydraulic permeability, dialyzer mass transfer coefficient, ultrafiltrate column height, dialysate flow rate) characteristics as inputs, predictions of hydraulic and oncotic pressure distribution, filtration rate, blood flow, total, diffusive, and convective urea clearances are provided. The model was tested by perfusing a circuit with bovine blood under conditions of pure ultrafiltration, zero net ultrafiltration and dialysis, or combined ultrafiltration and dialysis (countercurrent dialysate flow at rates of 10, 20, and 30 ml/min). In order to permit computation, membrane hydraulic permeability and flow resistances were measured. Dialyzer mass transfer coefficient for urea could not be measured directly and so was determined by fitting model predictions to measured urea clearances. For all conditions of operation, a urea mass transfer coefficient of 0.014 cm/min successfully simulated the data. Predictions of blood flow, filtrate generation rate, and circuit pressure distribution were accurate. At lower dialysate flow rates, urea clearance approximated the sum of dialysate flow and filtration rate. At higher dialysate flows, however, departure from this ideal blood-dialysate equilibrium was observed. Model predictions regarding the relative contributions of diffusion and convection to urea clearance were explored. Under conditions of nearly perfect equilibration of urea between blood and dialysate at the blood inlet, the model predicts that the diffusive clearance of urea will increase with increasing rate of filtration and may exceed the rate of dialysate inflow.

Hemofiltration↗

PubMed1989

Optimal insulin infusion resulting from a mathematical model of blood glucose dynamics.

Mathematical optimization techniques are applied to a simplified mathematical model of blood glucose dynamics to derive insulin infusion programs for the control of blood glucose levels in diabetic individuals. Two particular cases are discussed. First, the insulin infusion program which results in an initially high blood glucose level being reduced to acceptable levels. Second, the control of blood glucose levels following a meal, prior to which blood glucose and net blood-glycemic hormone were at their fasting levels.

Blood Glucose↗

PubMed1983

Electrophoresis: mathematical modeling and computer simulation.

A mathematical model of electrophoretic separation processes has been developed and adapted for computer simulations. The model is used to predict the characteristic behavior of a variety of electrophoretic techniques from a knowledge of chemical equilibria and physical transport phenomena. The model provides a unifying basis for a rational classification of all electrophoretic processes.

Computers↗

PubMed1977

Dialysis continuous process for ammonium-lactate fermentation of whey: mathematical model and computer simulation.

A mathematical model was developed to describe a dialysis process for the continuous fermentation of whey lactose to lactic acid, with neutralization to a constant pH by ammonia. In the process, whey of a relatively high concentration is fed into the fermentor circuit at a relatively low rate so that the residual concentration of lactose is low. The fermentor effluent contains ammonium lactate, bacterial cells, and residual whey solids and could be used as a nitrogen-enriched feedstuff for ruminant animals. Only water is fed into the dialysate circuit at a relatively high rate. The dialysate effluent contains purified ammonium lactate and could be converted to lactic acid and ammonium sulfate for industry. The fermentation was specifically modeled as a set of equations representing material balances and rate relationships in the two circuits. Dialysis continuous fermentations, in general, were modeled by combining these equations and by using dimensionless parameters. The generalized model was then solved for the steady state and used to simulate the specific fermentation on a digital computer. The results showed the effects of various material and operational and kinetic parameters on the process and predicted that it could be operated efficiently.

Journal Article↗

PubMed2004

Genetic manipulation of calcium-handling proteins in cardiac myocytes. II. Mathematical modeling studies.

We developed a mathematical model specific to rat ventricular myocytes that includes electrophysiological representation, ionic homeostasis, force production, and sarcomere movement. We used this model to interpret, analyze, and compare two genetic manipulations that have been shown to increase myocyte relaxation rates, parvalbumin (Parv) de novo expression, and sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA2a) overexpression. The model was used to seek mechanistic insights into 1) the relative contribution of two mechanisms by which SERCA2a overexpression modifies Ca2+ sequestration, i.e., more pumps and an increase in the SERCA2a-to-phospholamban ratio, 2) the mechanisms behind postrest potentiation and how Parv and SERCA2a influence this response, and 3) why Parv myocytes retain their fast kinetics when endogenous SERCA2a is partially impaired by thapsigargin (a condition used to mimic diastolic dysfunction). The model was also utilized to predict whether Parv metal-binding characteristics might be modified to improve diastolic and systolic functions and whether Parv or SERCA2a might affect diastolic Ca2+ levels and myocyte energetics. One outcome of the model was to demonstrate a higher peak and total ATP consumption in SERCA2a myocytes and more even distribution of ATP throughout the cardiac cycle in Parv myocytes. This may have implications for failing hearts that are energetically compromised.

Animals↗

PubMed1984

Homeostatic capability of rate-sensitive feedback system: mathematical model.

We have predicted the mathematical model of rate-sensitive feedback control system and have investigated its homeostatic capability by using computer simulations. The results are summarized as follows. By installing a cyclic enzyme system as feedback control element, we could assume the rate-sensitive feedback system at molecular level. This type of feedback had realistic constant-value control capability for external perturbations. This feedback system was more effective for the exclusion of perturbation than was the concentration-sensitive feedback. A large-loop feedback was more stable for perturbation than was short-loop feedback. In sequential feedback system, every key enzyme sensitive to feedback control had to vary the activity at same time for the system to keep homeostasis.

Animals↗

PubMed1998

The pressure-volume curve is greatly modified by recruitment. A mathematical model of ARDS lungs.

A mathematical model of the ARDS lung, with simulated gravitational superimposed pressure, evaluated the effect of varying alveolar threshold opening pressures (TOP), PEEP and peak inspiratory pressure (PIP) on the static pressure-volume (PV) curve. The lower inflection point (Pflex) was affected by SP and TOP, and did not accurately indicate PEEP required to prevent end-expiratory collapse. Reinflation of collapsed lung units (recruitment) continued on the linear portion of the PV curve, which had a slope at any volume greater than the total compliance of aerated alveoli. As recruitment diminished, the reduced PV slope could produce an upper Pflex at 20 to 30 cm H2O pressure. An upper Pflex caused by alveolar overdistension could be modified or eliminated by recruitment with high TOP. With constant PIP as PEEP increased, and TOP range of 5 to 60 cm H2O, PEEP to prevent end-expiratory collapse was indicated by minimum PV slope above 20 cm H2O, minimum hysteresis, and maximum volume at a pressure of 20 cm H2O. With constant inflation volume as PEEP increased, the effect on PV slope was unpredictable. Although increased PV slope indicated recruitment, maximum PV slope usually underestimated PEEP required to prevent end-expiratory collapse. Therefore, with this model the PV curve did not reliably predict optimal ventilator settings.

Humans↗

PubMed2000

[A study on the trend of tuberculosis in an area of Shanghai City using mathematical model].

A widely-used mathematical model (compartmental model) in epidemiological studies was utilized to analyze the tuberculosis situation in area Y of Shanghai from 1971 till 1994. In this model, the whole population was divided into 5 groups, (susceptible, latent, prevalent, healed and immune). Six parameters (effective BCG coverage, immune loss rate, infection rate, disease risk, cure rate and heal loss rate) were introduced and discussed to describe the transmission of tuberculosis. The computed tuberculosis data from this model agree quite well with the observed data. The results show that the susceptible group is the largest among all groups. In 1994, the annual risk of infection was estimated to be 0.26%. It is predicted that elderly people will comprise an increasing percentage of tuberculosis patients in the future. It is also found that it will still take a long time to eliminate tuberculosis under current medical situations.

China↗

PubMedDate not supplied

Catalytic wet oxidation: mathematical modeling of multicompound destruction.

A mathematical model of a three-phase catalytic reactor, CatReac, was developed for analysis and optimization of a catalytic oxidation reactor that is used in the International Space Station potable water processor. The packed-bed catalytic reactor, known as the volatile reactor assembly (VRA), is operated as a three-phase reactor and contains a proprietary catalyst, a pure-oxygen gas phase, and the contaminated water. The contaminated water being fed to the VRA primarily consists of acetic acid, acetone, ethanol, 1-propanol, 2-propanol, and propionic acid ranging in concentration from 1 to 10 mg/L. The Langmuir-Hinshelwood Hougen-Watson (L-H) (Hougen, 1943) expression was used to describe the surface reaction rate for these compounds. Single and multicompound short-column experiments were used to determine the L-H rate parameters and calibrate the model. The model was able to predict steady-state multicomponent effluent profiles for short and full-scale reactor experiments.

Catalysis↗

PubMedDate not supplied

[Mathematical models in hemostasis physiology].

A mathematical model of spatial propagation of blood coagulation is proposed. The control mechanism of advancement of the activation zone is established. The intrinsic and extrinsic pathways of blood coagulation are considered. Blood flow transfer of the activated factors is shown to play a significant role in stopping advancement of the activation zone. This effect is amplified by the coagulation cascade. Propagation of the concentration wave is related to the model indices.

Animals↗

PubMedDate not supplied

[Mathematical model of histamine bronchospasm].

A mathematical model of changes in histamine concentration in the wall of human bronchiole was constructed. The parameters of the model adequately characterize the state of patients with bronchial asthma.

Asthma↗

PubMed2001

Delayed fluorescence induction transients: mathematical modelling based on the chosen kinetic models.

The paper deals with mathematical modelling of the transients obtained by fitting of delayed fluorescence (DF) induction trace. The transients are in certain, doubtless connection with electrochemical gradient (ECG) formed across thylakoid membranes upon illumination. The fitting of the C and D transients by using consecutive model for first-order reactions (A --> B --> C) showed that they might play a role of the intermediate (B), according to scheme down bellow: ("A1 state")ECG (k1(C transient))--> C transient (k2(C transient))--> products, ("A2 state")ECG (k1(D transient))--> D transient (k2(D transient))--> products. The two ECG controlled "states" (A1 & A2) are not the same, which does not exclude some sort of proportionality. On the other hand, the E band, contributing mainly to the stationary level of DF induction trace, may be fitted by parallel model of at least two first-order reactions.

Electrochemistry↗

PubMedDate not supplied

[Mathematical model of children mortality].

A mathematical model of infantile mortality is proposed. The model is based on the probability principle of organism-environment interactions assuming that the organism is able to remember the diseases encountered previously and resist them. The adequacy of the model was assessed using the demographic database for two countries. The dynamics of the model parameters during the last century is presented.

Algorithms↗

PubMed1976

Computer simulation of local anesthetic effects using a mathematical model of myelinated nerve.

A mathematical model of myelinated axon was programmed for digital computer solution of the consequences of the conduction characteristics when the model membrane was affected by local anesthetics simulated by alteration of the ionic conductance parameter. The effects of tetrodotoxin on impulse conduction were studied in detail by means of a systematic reduction in sodium conductance in 1 to 10 nodes of Ranvier. Rhis technique simulates the method used experimentally and clinically to achieve a conduction block with the circumscribed application of local anesthetics to segments of nerve axons or nerve trunks. The analysis of the tetrodotoxin "dose-response" relationships revealed the fact that the model myelinated axon could support three types of conduction when depressed by this drug. One type of conduction of a subnormal impulse at the nodes of Ranvier; a second is characterized by a form of decremental conduction in which the rate of decrement of the nodal impulse is linear with distance. The third type is a second form of decremental conduction which is exponential in configuration and is seen when the g(Na) at the nodes of Ranvier is reduced to less than 27% of normal. Parallel experiments were performed to simulate the effects of lidocaine and some significant differences were observed. Analysis of the action potentials within the internodel region suggests that, although immune to drug action in the model, the internodal segment affects the generation of action potentials at the nodes. A commentary is presented on the limitations of the model as it reflects known pharmacologic relationships in real myelinated axons.

Anesthetics, Local↗

PubMed1998

Kinetics of T cell proliferation: a mathematical model and data analysis.

A mathematical model of in vitro T cell proliferation controlled by IL-2 internalization is presented. The model describes the T cell transition from G1 to S+G2+M stages of the cell cycle and introduces "molecular" equations for the G1-S phase control. These equations consider current knowledge of the biochemical mechanisms of receptor synthesis, ligand-receptor binding, and internalization of ligand-receptor complexes. The model describes the kinetic data for in vitro T cell proliferation at various IL-2 concentrations (50-500 pM) for various exposure time (6-26 h). The kinetic parameters were calculated based on the model. The results obtained suggest that increase in the IL-2 concentration and exposures decrease the critical ligand-receptor concentration in the cells which control proliferation. The time tau, which characterizes the delay in the G1-S transition, was constant at various IL-2 concentrations.

Animals↗