Cross reactions in radioimmunoassay: a mathematical model for correcting assay results, as exemplified by eliminating the interference of intact thyrotropin in an assay of its beta subunit.

1987 ◽  
Vol 33 (5) ◽  
pp. 658-660 ◽  
Author(s):  
C Dotti ◽  
G P Ceda ◽  
L Denti ◽  
S Cavalieri ◽  
G Borasi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Conservation Laws ◽  
Regression Line ◽  
Beta Subunit ◽  
Mass Action ◽  
Constant Concentration ◽  
Actual Concentration ◽  
Cross Reactions

Abstract To correct the results of a radioimmunoassay for beta-thyrotropin (TSH) subunit by eliminating the proportion ascribable to intact TSH, we have devised a method that experimentally reproduces the conditions under which the interference develops. Beta-TSH subunit was assayed in several preparations containing known concentrations of both beta-TSH and TSH. The TSH-induced overestimation of beta-TSH was linearly related to the concentration of antigen in the sample. At a constant concentration of TSH, therefore, the following equation is applicable: F = aE + b, where F is the measured (but overestimated) concentration of beta-TSH, E is the actual concentration of beta-TSH, and a and b are the slope and the intercept of the regression line, respectively. a and b, once expressed as a function of TSH, allow the correction of the overestimation. The analysis of the results according to the mass action and conservation laws shows that the antiserum is more avid for the interferent (intact TSH) than for the antigen (beta-TSH).

Simulation of cancer treatment using the MATLAB SimBiology application

2021 ◽  
Vol 14 (3) ◽  
pp. 90-96
Author(s):  
Anastasia Goncharova ◽  
Maria Vil'
Keyword(s):  
Mathematical Model ◽  
Cancer Treatment ◽  
Interference Competition ◽  
The Body ◽  
Continuous Treatment ◽  
Constant Concentration ◽  
Application Package ◽  
The Mathematical Model ◽  
Cancerous Cells

The paper presents the implementation of the mathematical model of cancer taking into account interference competition and the model of continuous treatment with a constant concentration of the drug in the patient's blood. The implementation was carried out using the MATLAB SimBiology application package. The principle of implementation of different stages of the course of the disease within the framework of one model is described. On the basis of the constructed models and SimBiology tools, a modification was carried out that implements the discrete administration of doses of the drug in courses and takes into account its dynamics in the body, taking into account the assumption that the drug is consumed only to suppress cancerous cells.

scholarly journals A MATHEMATICAL MODEL FOR EBOLA EPIDEMIC WITH SELF-PROTECTION MEASURES

2018 ◽  
Vol 26 (01) ◽  
pp. 107-131 ◽  
Author(s):  
T. BERGE ◽  
M. CHAPWANYA ◽  
J. M.-S. LUBUMA ◽  
Y. A. TEREFE
Keyword(s):  
Mathematical Model ◽  
Ebola Virus ◽  
Virus Disease ◽  
Mass Action ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Protection Measures ◽  
Globally Asymptotically Stable ◽  
New Formulation ◽  
Self Protection

A mathematical model presented in Berge T, Lubuma JM-S, Moremedi GM, Morris N Shava RK, A simple mathematical model for Ebola in Africa, J Biol Dyn 11(1): 42–74 (2016) for the transmission dynamics of Ebola virus is extended to incorporate vaccination and change of behavior for self-protection of susceptible individuals. In the new setting, it is shown that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number [Formula: see text] is less than or equal to unity and unstable when [Formula: see text]. In the latter case, the model system admits at least one endemic equilibrium point, which is locally asymptotically stable. Using the parameters relevant to the transmission dynamics of the Ebola virus disease, we give sensitivity analysis of the model. We show that the number of infectious individuals is much smaller than that obtained in the absence of any intervention. In the case of the mass action formulation with vaccination and education, we establish that the number of infectious individuals decreases as the intervention efforts increase. In the new formulation, apart from supporting the theory, numerical simulations of a nonstandard finite difference scheme that we have constructed suggests that the results on the decrease of the number of infectious individuals is valid.

Reversal of Dabigatran's Anticoagulant Activity in the Monkey by a Specific Antidote and Pharmacokinetic and Pharmacodynamic Modeling

Blood ◽  
2012 ◽  
Vol 120 (21) ◽  
pp. 22-22 ◽  
Author(s):  
Joshuaine Toth ◽  
Guanfa Gan ◽  
Joanne van Ryn ◽  
Holly Dursema ◽  
Jennifer Isler ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Anticoagulant Activity ◽  
Plasma Concentrations ◽  
Mass Action ◽  
Pharmacodynamic Modeling ◽  
Dependent Manner ◽  
Thrombin Time ◽  
Binding Interaction ◽  
Mass Action Kinetics ◽  
Dose Dependent

Abstract Abstract 22 Background: The objective of this study is to determine the pharmacokinetics (PK) and pharmacodynamics (PD) of dabigatran (a small molecule thrombin inhibitor) and its antidote (a humanized Fab against dabigatran) in the monkey and to develop a combined mechanistic mathematical model to describe the data. Methods: There were three groups: control, antidote alone and dabigatran etexilate (DE) + antidote. Rhesus monkeys (n = 2/group) received either 12 mg/kg/day of DE or vehicle orally on Days 1–4, 15–18 and 29–32 with a single IV dose of the antidote administered 90 minutes after DE on Days 4, 18 and 32. Doses of the antidote were 30, 90 or 175 mg/kg, respectively. PK parameters of the antidote and sum dabigatran (dabigatran plus its glucuronides) were determined after measurements of plasma concentrations. Coagulation activity was measured using a diluted thrombin time assay to determine the activity of the unbound sum dabigatran. Results: The PK of the antidote were not affected by dabigatran. Clearance of the antidote was low (0.87 mL/min/kg) and steady-state volume of distribution was small (0.06 L/kg), indicating that the antidote was mostly restricted to plasma. The plasma profile of the antidote was bi-phasic with a short initial phase t1/2 of 0.4 hour (h) and a terminal phase t1/2 of 4.3 h. Immediately after antidote dosing, plasma concentrations of sum dabigatran increased, a consequence of the rapid redistribution of dabigatran and its glucuronides from tissue to plasma due to binding to the antidote. Complete reversal of dabigatran's anticoagulant activity was observed immediately after antidote dosing at all three dose levels, as measured by the diluted thrombin time assay, which indicates that all dabigatran was bound to the antidote. The degree to which this reversal effect was maintained over an extended period (24 h) was dose-dependent. A mechanistic ordinary differential equation model, based on the mass action kinetics for describing the distribution, binding and elimination of dabigatran and its antidote, was developed by combining the PK models for dabigatran and the antidote and adding the binding interaction (1:1 stoichiometry) between the two compounds. The distribution and elimination parameters of the dabigatran-antidote complex were assumed to be the same as those of the antidote, based on similar measured PK parameters of the antidote with and without dabigatran in the monkey. The combined PK/PD model of dabigatran and antidote was able to describe the in vivo PK/PD data observed in monkeys. Conclusion: The dabigatran-specific antidote successfully reversed the anticoagulant activity of dabigatran in the monkey in a dose-dependent manner, and our combined mathematical model accurately describes monkey PK/PD data of sum dabigatran and its antidote. Insights gained from this model will be used to guide model development for clinical trials. Disclosures: Toth: Boehringer Ingelheim: Employment. Gan:Boehringer Ingelheim: Employment. van Ryn:Boehringer Ingelheim: Employment. Dursema:Boehringer Ingelheim: Employment. Isler:Boehringer Ingelheim: Employment. Coble:Boehringer Ingelheim: Employment. Burke:Boehringer Ingelheim: Employment. Lalovic:Boehringer Ingelheim: Employment. Olson:Boehringer Ingelheim: Employment.

scholarly journals Mathematical modeling quantifies ERK-activity in response to inhibition of the BRAFV600E-MEK-ERK cascade

2021 ◽  
Author(s):  
Sara Hamis ◽  
Yury Kapelyukh ◽  
Aileen McLaren ◽  
Colin J. Henderson ◽  
C. Roland Wolf ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Drug Resistance ◽  
Chemical Reactions ◽  
Molecular Mechanisms ◽  
Braf Inhibitor ◽  
Mass Action ◽  
Model Parameters ◽  
Mass Action Kinetics ◽  
Erk Activity

AbstractSimultaneous inhibition of multiple components of the BRAF-MEK-ERK cascade (vertical inhibition) has become a standard of care for treating BRAF-mutant melanoma. However, the molecular mechanisms of how vertical inhibition synergistically suppress intracellular ERK activity, and as a consequence cell proliferation, are yet to be fully elucidated.In this study, we develop a mechanistic mathematical model that describes how the mutant BRAF-inhibitor, dabrafenib, and the MEK-inhibitor, trametinib, affect signaling through the BRAFV600E-MEK-ERK cascade. We formulate a system of chemical reactions that describes cascade signaling dynamics and, using mass action kinetics, the chemical reactions are re-expressed as ordinary differential equations. Using model parameters obtained from in vitro data available in the literature, these equations are solved numerically to obtain the temporal evolution of the concentrations of the components in the signaling cascade.Our mathematical model provides a quantitative method to compute how dabrafenib and trametinib can be used in combination to synergistically inhibit ERK activity in BRAFV600E mutant melanoma cells. This work elucidates molecular mechanisms of vertical inhibition of the BRAFV600E-MEK-ERK cascade and delineates how elevated cellular BRAF concentrations generate drug resistance to dabrafenib and trametinib. In addition, the computational simulations suggest that elevated ATP levels could be a factor in drug resistance to dabrafenib. The mathematical model that is developed in this study will have generic application in the improved design of anticancer combination therapies that target BRAF-MEK-ERK pathways.

scholarly journals MATHEMATICAL MODELS AND RECOGNITION METHODS FOR MOBILE SUBSCRIBERS MUTUAL PLACEMENT

T-Comm ◽  
2021 ◽  
Vol 15 (4) ◽  
pp. 49-56
Author(s):  
Vadim V. Ziyadinov ◽  
◽  
Maxim V. Tereshonok ◽  
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Mobile Networks ◽  
Convolution Neural Network ◽  
Mass Action ◽  
Validation Dataset ◽  
Neural Network Training ◽  
Processing Application ◽  
Network Training ◽  
Placement Types

The challenge of mobile subscribers’ groups and crowd’s behavior prediction during the mass events is now increasingly important. Operative methods application of this task solution is difficult; accordingly, development and application of technical methods is necessary. The method of this problem solution consists of subscribers’ telephone conversations recording in a zone of mass action, and the following speech recognition, the semantic analysis and statistical processing application. However, there is a tendency demand decrease for mobile systems voice services with simultaneous demand growth for data traffic nowadays. The purpose of this paper is to create a mathematical model of mobile networks subscribers’ mutual placement types, applicable for automatization of the subscribers’ activities nature prediction systems. The research method consists of mathematical simulation model development for pseudo-random examples generation of subscribers’ mutual placement types set, creation of training dataset, convolution neural network training and usage of training results to recognize the new examples. The results obtained. A mathematical model is proposed allowing to create a representative training and validation dataset of mobile networks subscribers’ mutual placement types for neural network training and testing. The convolution neural network trained using these samples has shown high classification accuracy results with a wide class of subscribers’ mutual placement types.

scholarly journals A general technique for the detection of switch-like bistability in chemical reaction networks governed by mass action kinetics with conservation laws

2020 ◽  
Author(s):  
Brandon C Reyes ◽  
Irene Otero-Muras ◽  
Vladislav A Petyuk
Keyword(s):  
Conservation Laws ◽  
Signaling Pathways ◽  
Chemical Reaction ◽  
Reaction Network ◽  
Mass Action ◽  
Numerical Continuation ◽  
Reaction Networks ◽  
General Technique ◽  
Bistable Switch ◽  
Mass Action Kinetics

AbstractBackgroundTheoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws.ResultsIn this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves 1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, 2) minimization of the objective function to search for conditions resulting in a zero eigenvalue 3) computation of a confidence level that describes if the global minimum has been found and 4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability.ConclusionsWe have developed a variation of an optimization-based method for discovery of bistability, which is not limited to the structure of the chemical reaction network. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

scholarly journals Data-driven dynamical model indicates that the heat shock response in Chlamydomonas reinhardtii is tailored to handle natural temperature variation

2018 ◽  
Vol 15 (142) ◽  
pp. 20170965 ◽  
Author(s):  
Stefano Magni ◽  
Antonella Succurro ◽  
Alexander Skupin ◽  
Oliver Ebenhöh
Keyword(s):  
Mathematical Model ◽  
Heat Shock ◽  
Chlamydomonas Reinhardtii ◽  
Heat Shock Response ◽  
Mass Action ◽  
Data Driven ◽  
Dynamical Model ◽  
Misfolded Proteins ◽  
Mass Action Kinetics ◽  
Shock Response

Global warming exposes plants to severe heat stress, with consequent crop yield reduction. Organisms exposed to high temperature stresses typically protect themselves with a heat shock response (HSR), where accumulation of unfolded proteins initiates the synthesis of heat shock proteins through the heat shock transcription factor HSF1. While the molecular mechanisms are qualitatively well characterized, our quantitative understanding of the underlying dynamics is still very limited. Here, we study the dynamics of HSR in the photosynthetic model organism Chlamydomonas reinhardtii with a data-driven mathematical model of HSR. We based our dynamical model mostly on mass action kinetics, with a few nonlinear terms. The model was parametrized and validated by several independent datasets obtained from the literature. We demonstrate that HSR quantitatively and significantly differs if an increase in temperature of the same magnitude occurs abruptly, as often applied under laboratory conditions, or gradually, which would rather be expected under natural conditions. In contrast to rapid temperature increases, under gradual changes only negligible amounts of misfolded proteins accumulate, indicating that the HSR of C. reinhardtii efficiently avoids the accumulation of misfolded proteins under conditions most likely to prevail in nature. The mathematical model we developed is a flexible tool to simulate the HSR to different conditions and complements the current experimental approaches.

The Main Provisions of the Methodology for Assessing the Convergence of the Results of Mathematical Modeling of Continuous Processes of Avionics Devices and Field Experiments

2018 ◽  
Vol 19 (10) ◽  
pp. 680-688
Author(s):  
V. V. Slatin ◽  
M. A. Demkin ◽  
A. V. Golubkina
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Measurement Errors ◽  
Field Experiments ◽  
Least Squares Method ◽  
Regression Line ◽  
Flight Tests ◽  
Continuous Processes ◽  
Statistical Hypotheses ◽  
The Mathematical Model

The questions of estimation of convergence of the processes received in single flight tests of an aviation complex and at mathematical modeling are considered. This evaluation is performed based on the methods of analysis of variance and means of verification of statistical hypotheses in decision-making on the convergence of the compared processes. For each of the compared processes, the least squares method determines the regression lines. By methods of mathematical statistics the permissible proximity of regression lines of the compared processes is established and the average regression line equivalent to the mathematical expectation of the analyzed statistical processes is determined. With respect to this line, the variance of deviations of the compared statistical processes is determined and their belonging to the General sample of processes is estimated. This suggests that under normal laws of the distribution of measurement errors there is an adequacy of the processes of the mathematical model of the stages of operation of the aviation complex and the observed processes of these stages during flight tests of the aviation complex under study.

Sign in / Sign up

Export Citation Format

Share Document