Dynamics of granzyme B-induced apoptosis: Mathematical modeling

Evdokia N. Golovchenko, Leonid G. Hanin, Scott H Kaufmann, Kirill V. Tyurin, Mikhail A. Khanin

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Apoptosis is mediated by an intracellular biochemical system that mainly includes proteins (procaspases, caspases, inhibitors, Bcl-2 protein family as well as substances released from mitochondrial intermembrane space). The dynamics of caspase activation and target cleavage in apoptosis induced by granzyme B in a single K562 cell was studied using a mathematical model of the dynamics of granzyme B-induced apoptosis developed in this work. Also the first application of optimization approach to determination of unknown kinetic constants of biochemical apoptotic reactions was presented. The optimization approach involves solving of two problems: direct and inverse. Solving the direct optimization problem, we obtain the initial (baseline) concentrations of procaspases for known kinetic constants through conditional minimization of a cost function based on the principle of minimum protein consumption by the apoptosis system. The inverse optimization problem is aimed at determination of unknown kinetic constants of apoptotic biochemical reactions proceeding from the condition that the optimal concentrations of procaspases resulting from the solution of the direct optimization problem coincide with the observed ones, that is, those determined by biochemical methods. The Multidimensional Index Method was used to perform numerical solution of the inverse optimization problem.

Original languageEnglish (US)
Pages (from-to)54-68
Number of pages15
JournalMathematical Biosciences
Volume212
Issue number1
DOIs
StatePublished - Mar 2008

Fingerprint

Granzymes
Apoptosis
system optimization
apoptosis
Cell death
Mathematical Modeling
mathematical models
Inverse Optimization
Optimization Problem
Kinetics
caspases
Protein
kinetics
modeling
Inverse Problem
Bcl-2
Unknown
Proteins
Caspase Inhibitors
protein

Keywords

  • Apoptosis
  • Caspase activation
  • Granzyme B
  • Mathematical modeling

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Dynamics of granzyme B-induced apoptosis : Mathematical modeling. / Golovchenko, Evdokia N.; Hanin, Leonid G.; Kaufmann, Scott H; Tyurin, Kirill V.; Khanin, Mikhail A.

In: Mathematical Biosciences, Vol. 212, No. 1, 03.2008, p. 54-68.

Research output: Contribution to journalArticle

Golovchenko, Evdokia N. ; Hanin, Leonid G. ; Kaufmann, Scott H ; Tyurin, Kirill V. ; Khanin, Mikhail A. / Dynamics of granzyme B-induced apoptosis : Mathematical modeling. In: Mathematical Biosciences. 2008 ; Vol. 212, No. 1. pp. 54-68.
@article{3c02fa567e9049769ac28b81382ca0cb,
title = "Dynamics of granzyme B-induced apoptosis: Mathematical modeling",
abstract = "Apoptosis is mediated by an intracellular biochemical system that mainly includes proteins (procaspases, caspases, inhibitors, Bcl-2 protein family as well as substances released from mitochondrial intermembrane space). The dynamics of caspase activation and target cleavage in apoptosis induced by granzyme B in a single K562 cell was studied using a mathematical model of the dynamics of granzyme B-induced apoptosis developed in this work. Also the first application of optimization approach to determination of unknown kinetic constants of biochemical apoptotic reactions was presented. The optimization approach involves solving of two problems: direct and inverse. Solving the direct optimization problem, we obtain the initial (baseline) concentrations of procaspases for known kinetic constants through conditional minimization of a cost function based on the principle of minimum protein consumption by the apoptosis system. The inverse optimization problem is aimed at determination of unknown kinetic constants of apoptotic biochemical reactions proceeding from the condition that the optimal concentrations of procaspases resulting from the solution of the direct optimization problem coincide with the observed ones, that is, those determined by biochemical methods. The Multidimensional Index Method was used to perform numerical solution of the inverse optimization problem.",
keywords = "Apoptosis, Caspase activation, Granzyme B, Mathematical modeling",
author = "Golovchenko, {Evdokia N.} and Hanin, {Leonid G.} and Kaufmann, {Scott H} and Tyurin, {Kirill V.} and Khanin, {Mikhail A.}",
year = "2008",
month = "3",
doi = "10.1016/j.mbs.2007.12.002",
language = "English (US)",
volume = "212",
pages = "54--68",
journal = "Mathematical Biosciences",
issn = "0025-5564",
publisher = "Elsevier Inc.",
number = "1",

}

TY - JOUR

T1 - Dynamics of granzyme B-induced apoptosis

T2 - Mathematical modeling

AU - Golovchenko, Evdokia N.

AU - Hanin, Leonid G.

AU - Kaufmann, Scott H

AU - Tyurin, Kirill V.

AU - Khanin, Mikhail A.

PY - 2008/3

Y1 - 2008/3

N2 - Apoptosis is mediated by an intracellular biochemical system that mainly includes proteins (procaspases, caspases, inhibitors, Bcl-2 protein family as well as substances released from mitochondrial intermembrane space). The dynamics of caspase activation and target cleavage in apoptosis induced by granzyme B in a single K562 cell was studied using a mathematical model of the dynamics of granzyme B-induced apoptosis developed in this work. Also the first application of optimization approach to determination of unknown kinetic constants of biochemical apoptotic reactions was presented. The optimization approach involves solving of two problems: direct and inverse. Solving the direct optimization problem, we obtain the initial (baseline) concentrations of procaspases for known kinetic constants through conditional minimization of a cost function based on the principle of minimum protein consumption by the apoptosis system. The inverse optimization problem is aimed at determination of unknown kinetic constants of apoptotic biochemical reactions proceeding from the condition that the optimal concentrations of procaspases resulting from the solution of the direct optimization problem coincide with the observed ones, that is, those determined by biochemical methods. The Multidimensional Index Method was used to perform numerical solution of the inverse optimization problem.

AB - Apoptosis is mediated by an intracellular biochemical system that mainly includes proteins (procaspases, caspases, inhibitors, Bcl-2 protein family as well as substances released from mitochondrial intermembrane space). The dynamics of caspase activation and target cleavage in apoptosis induced by granzyme B in a single K562 cell was studied using a mathematical model of the dynamics of granzyme B-induced apoptosis developed in this work. Also the first application of optimization approach to determination of unknown kinetic constants of biochemical apoptotic reactions was presented. The optimization approach involves solving of two problems: direct and inverse. Solving the direct optimization problem, we obtain the initial (baseline) concentrations of procaspases for known kinetic constants through conditional minimization of a cost function based on the principle of minimum protein consumption by the apoptosis system. The inverse optimization problem is aimed at determination of unknown kinetic constants of apoptotic biochemical reactions proceeding from the condition that the optimal concentrations of procaspases resulting from the solution of the direct optimization problem coincide with the observed ones, that is, those determined by biochemical methods. The Multidimensional Index Method was used to perform numerical solution of the inverse optimization problem.

KW - Apoptosis

KW - Caspase activation

KW - Granzyme B

KW - Mathematical modeling

UR - http://www.scopus.com/inward/record.url?scp=39649105002&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39649105002&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2007.12.002

DO - 10.1016/j.mbs.2007.12.002

M3 - Article

C2 - 18249416

AN - SCOPUS:39649105002

VL - 212

SP - 54

EP - 68

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -