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  1. Article ; Online: An autonomous mathematical model for the mammalian cell cycle.

    Williams, Katherine S / Secomb, Timothy W / El-Kareh, Ardith W

    Journal of theoretical biology

    2023  Volume 569, Page(s) 111533

    Abstract: A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. A ...

    Abstract A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. A novel feature of the model is inclusion of cycle tasks such as origin licensing and initiation, nuclear envelope breakdown and kinetochore attachment, and their interactions with controllers (molecular complexes involved in cycle control). Other key features are that the model is autonomous, except for a dependence on external growth factors; the variables are continuous in time, without instantaneous resets at phase boundaries; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: the Cyclin D1-Cdk4/6 complex, APC
    MeSH term(s) Animals ; Separase ; Cell Cycle/physiology ; Cell Cycle Proteins/metabolism ; Cell Division ; Mammals ; Models, Theoretical
    Chemical Substances Separase (EC 3.4.22.49) ; Cell Cycle Proteins
    Language English
    Publishing date 2023-05-15
    Publishing country England
    Document type Journal Article ; Research Support, N.I.H., Extramural
    ZDB-ID 2972-5
    ISSN 1095-8541 ; 0022-5193
    ISSN (online) 1095-8541
    ISSN 0022-5193
    DOI 10.1016/j.jtbi.2023.111533
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article ; Online: Additive Damage Models for Cellular Pharmacodynamics of Radiation-Chemotherapy Combinations.

    Williams, Katherine S / Secomb, Timothy W / El-Kareh, Ardith W

    Bulletin of mathematical biology

    2017  Volume 80, Issue 5, Page(s) 1236–1258

    Abstract: Many cancer patients receive combination treatments with radiation and chemotherapy. Available mathematical models for cellular pharmacodynamics have limited ability to represent observed in vitro responses to radiochemotherapy. Here, a family of ... ...

    Abstract Many cancer patients receive combination treatments with radiation and chemotherapy. Available mathematical models for cellular pharmacodynamics have limited ability to represent observed in vitro responses to radiochemotherapy. Here, a family of additive damage models is proposed to describe cell kill resulting from radiochemotherapy with fixed schedule and variable doses. The pathways by which the agents produce cellular damage are assumed to converge in a single cell death process, so that survival depends on total damage, which can be represented as a sum of contributions from the various damage pathways. Heterogeneity in response across the cell population is ascribed to variations in the damage threshold for cell kill. The family of proposed models includes effects of one or two pathways of damage for each agent, saturation in drug responses, and cooperative or antagonistic interactions between agents. Models from this family with 4-7 unknown parameters are tested for their ability to fit 218 in vitro literature data sets for a range of drugs and cell lines. Overall, the additive damage models are found to outperform models based on the existing concept of independent cell kill, according to the corrected Akaike Information Criterion. The results are used to assess the importance of the various effects included in the models. These additive damage models have potential applications to the optimization of treatment and to the analysis and interpretation of in vitro screening data for new drug-radiation combinations.
    MeSH term(s) Cell Death/drug effects ; Cell Death/radiation effects ; Chemoradiotherapy/methods ; Chemoradiotherapy/statistics & numerical data ; Databases, Factual ; Dose-Response Relationship, Drug ; Dose-Response Relationship, Radiation ; Humans ; Mathematical Concepts ; Models, Biological ; Neoplasms/pathology ; Neoplasms/therapy
    Language English
    Publishing date 2017-08-28
    Publishing country United States
    Document type Journal Article ; Research Support, N.I.H., Extramural
    ZDB-ID 184905-0
    ISSN 1522-9602 ; 0007-4985 ; 0092-8240
    ISSN (online) 1522-9602
    ISSN 0007-4985 ; 0092-8240
    DOI 10.1007/s11538-017-0316-z
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  3. Article ; Online: The additive damage model: a mathematical model for cellular responses to drug combinations.

    Jones, Leslie Braziel / Secomb, Timothy W / Dewhirst, Mark W / El-Kareh, Ardith W

    Journal of theoretical biology

    2014  Volume 357, Page(s) 10–20

    Abstract: Mathematical models to describe dose-dependent cellular responses to drug combinations are an essential component of computational simulations for predicting therapeutic responses. Here, a new model, the additive damage model, is introduced and tested in ...

    Abstract Mathematical models to describe dose-dependent cellular responses to drug combinations are an essential component of computational simulations for predicting therapeutic responses. Here, a new model, the additive damage model, is introduced and tested in cases where varying concentrations of two drugs are applied with a fixed exposure schedule. In the model, cell survival is determined by whether cellular damage, which depends on the concentrations of the drugs, exceeds a lethal threshold, which varies randomly in the cell population with a prescribed statistical distribution. Cellular damage is assumed to be additive, and is expressed as a sum of separate terms for each drug. Each term has a saturable dependence on drug concentration. The model has appropriate behavior over the entire range of drug concentrations, and is predictive, given single-agent dose-response data for each drug. The proposed model is compared with several other models, by testing their ability to fit 24 data sets for platinum-taxane combinations and 21 data sets for various other combinations. The Akaike Information Criterion is used to assess goodness of fit, taking into account the number of unknown parameters in each model. Overall, the additive damage model provides a better fit to the data sets than any previous model. The proposed model provides a basis for computational simulations of therapeutic responses. It predicts responses to drug combinations based on data for each drug acting as a single agent, and can be used as an improved null reference model for assessing synergy in the action of drug combinations.
    MeSH term(s) Dose-Response Relationship, Drug ; Drug Combinations ; Models, Biological
    Chemical Substances Drug Combinations
    Language English
    Publishing date 2014-05-04
    Publishing country England
    Document type Journal Article ; Research Support, N.I.H., Extramural ; Research Support, Non-U.S. Gov't
    ZDB-ID 2972-5
    ISSN 1095-8541 ; 0022-5193
    ISSN (online) 1095-8541
    ISSN 0022-5193
    DOI 10.1016/j.jtbi.2014.04.032
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  4. Article ; Online: Cell cycle checkpoint models for cellular pharmacology of paclitaxel and platinum drugs.

    El-Kareh, Ardith W / Labes, Rachel E / Secomb, Timothy W

    The AAPS journal

    2008  Volume 10, Issue 1, Page(s) 15–34

    Abstract: A pharmacokinetic-pharmacodynamic mathematical model is developed for cellular pharmacology of chemotherapeutic drugs for which the decisive step towards cell death occurs at a point in the cell cycle, presumably corresponding to a cell cycle checkpoint. ...

    Abstract A pharmacokinetic-pharmacodynamic mathematical model is developed for cellular pharmacology of chemotherapeutic drugs for which the decisive step towards cell death occurs at a point in the cell cycle, presumably corresponding to a cell cycle checkpoint. For each cell, the model assumes a threshold level of some intracellular species at that checkpoint, beyond which the cell dies. The threshold level is assumed to have a log-normal distribution in the cell population. The kinetics of formation of the lethal intracellular species depends on the drug, and on the cellular pharmacokinetics and binding kinetics of the cell. Specific models are developed for paclitaxel and for platinum drugs (cisplatin, oxaliplatin and carboplatin). In the case of paclitaxel, two separate mechanisms of cell death necessitate a model that accounts for two checkpoints, with different intracellular species. The model was tested on a number of in vitro cytotoxicity data sets for these drugs, and found overall to give significantly better fits than previously proposed cellular pharmacodynamic models. It provides an explanation for the asymptotic convergence of dose-response curves as exposure time becomes long.
    MeSH term(s) Cell Cycle/drug effects ; Cell Cycle/physiology ; Cell Line, Tumor ; Dose-Response Relationship, Drug ; Humans ; Models, Biological ; Paclitaxel/pharmacology ; Platinum Compounds/pharmacology
    Chemical Substances Platinum Compounds ; Paclitaxel (P88XT4IS4D)
    Language English
    Publishing date 2008-02-05
    Publishing country United States
    Document type Comparative Study ; Journal Article ; Research Support, N.I.H., Extramural
    ISSN 1550-7416
    ISSN (online) 1550-7416
    DOI 10.1208/s12248-007-9003-6
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  5. Article: Two-mechanism peak concentration model for cellular pharmacodynamics of Doxorubicin.

    El-Kareh, Ardith W / Secomb, Timothy W

    Neoplasia (New York, N.Y.)

    2005  Volume 7, Issue 7, Page(s) 705–713

    Abstract: A mathematical model is presented for the cellular uptake and cytotoxicity of the anticancer drug doxorubicin. The model assumes sigmoidal, Hill-type dependence of cell survival on drug-induced damage. Experimental evidence indicates distinct ... ...

    Abstract A mathematical model is presented for the cellular uptake and cytotoxicity of the anticancer drug doxorubicin. The model assumes sigmoidal, Hill-type dependence of cell survival on drug-induced damage. Experimental evidence indicates distinct intracellular and extracellular mechanisms of doxorubicin cytotoxicity. Drug-induced damage is therefore expressed as the sum of two terms, representing the peak values over time of concentrations of intracellular and extracellular drugs. Dependence of cell kill on peak values of concentration rather than on an integral over time is consistent with observations that dose-response curves for doxorubicin converge to a single curve as exposure time is increased. Drug uptake by cells is assumed to include both saturable and unsaturable components, consistent with experimental data. Overall, the model provides better fits to in vitro cytotoxicity data than previous models. It shows how saturation of cellular uptake or binding with concentration can result in plateaus in the dose-response curve at high concentrations and short exposure, as observed experimentally in some cases. The model provides a unified framework for analyzing doxorubicin cellular pharmacokinetic and pharmacodynamic data, and can be applied in mathematical models for tumor response and treatment optimization.
    MeSH term(s) Animals ; Antibiotics, Antineoplastic/pharmacokinetics ; Antibiotics, Antineoplastic/pharmacology ; Area Under Curve ; Cell Line, Tumor ; Cell Survival/drug effects ; Dose-Response Relationship, Drug ; Doxorubicin/pharmacokinetics ; Doxorubicin/pharmacology ; Humans ; Models, Biological ; Models, Theoretical ; Statistics as Topic ; Time Factors
    Chemical Substances Antibiotics, Antineoplastic ; Doxorubicin (80168379AG)
    Language English
    Publishing date 2005-07-12
    Publishing country United States
    Document type Journal Article ; Research Support, N.I.H., Extramural ; Research Support, U.S. Gov't, P.H.S.
    ZDB-ID 1483840-0
    ISSN 1522-8002
    ISSN 1522-8002
    DOI 10.1593/neo.05118
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  6. Article: A theoretical model for intraperitoneal delivery of cisplatin and the effect of hyperthermia on drug penetration distance.

    El-Kareh, Ardith W / Secomb, Timothy W

    Neoplasia (New York, N.Y.)

    2004  Volume 6, Issue 2, Page(s) 117–127

    Abstract: A theoretical model for the intraperitoneal (i.p.) delivery of cisplatin and heat to tumor metastases in tissues adjacent to the peritoneal cavity is presented. The penetration distance (the depth to which drug diffuses directly from the cavity into ... ...

    Abstract A theoretical model for the intraperitoneal (i.p.) delivery of cisplatin and heat to tumor metastases in tissues adjacent to the peritoneal cavity is presented. The penetration distance (the depth to which drug diffuses directly from the cavity into tissues) is predicted to be on the order of 0.5 mm. The model shows that exchange with the microvasculature has more effect than cellular uptake in limiting the penetration distance. Possible effects of hyperthermia are simulated, including increased cell uptake of drug, increased cell kill at a given level of intracellular drug, and decreased microvascular density. The model suggests that the experimental finding of elevated intracellular platinum levels up to a depth of 3 to 5 mm when drug is delivered i.p. by a heated infusion solution is due to penetration of heat to this distance, causing increased cell uptake of drug. Beyond a depth of about 0.5 mm, the drug is delivered mainly through the circulation. Use of sodium thiosulfate to deactivate systemic cisplatin may therefore be counterproductive when heat is delivered locally. The model suggests that i.p. delivery of heat, combined with systemic delivery of drug, may be as effective as i.p. delivery of heat and drug.
    MeSH term(s) Animals ; Antineoplastic Agents/pharmacokinetics ; Cisplatin/pharmacokinetics ; Combined Modality Therapy ; Female ; Hyperthermia, Induced ; Injections, Intraperitoneal ; Models, Theoretical ; Ovarian Neoplasms/drug therapy ; Rats
    Chemical Substances Antineoplastic Agents ; Cisplatin (Q20Q21Q62J)
    Language English
    Publishing date 2004-03
    Publishing country United States
    Document type Journal Article ; Research Support, U.S. Gov't, Non-P.H.S. ; Research Support, U.S. Gov't, P.H.S.
    ZDB-ID 1483840-0
    ISSN 1522-8002
    ISSN 1522-8002
    DOI 10.1593/neo.03205
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  7. Article: A mathematical model for cisplatin cellular pharmacodynamics.

    El-Kareh, Ardith W / Secomb, Timothy W

    Neoplasia (New York, N.Y.)

    2003  Volume 5, Issue 2, Page(s) 161–169

    Abstract: 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 ... ...

    Abstract 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.
    MeSH term(s) Antineoplastic Agents/pharmacology ; Area Under Curve ; Cell Line, Tumor ; Cisplatin/pharmacology ; Dose-Response Relationship, Drug ; Female ; Head and Neck Neoplasms/drug therapy ; Humans ; Kinetics ; Models, Chemical ; Models, Statistical ; Models, Theoretical ; Ovarian Neoplasms/drug therapy ; Time Factors
    Chemical Substances Antineoplastic Agents ; Cisplatin (Q20Q21Q62J)
    Language English
    Publishing date 2003-02-17
    Publishing country United States
    Document type Journal Article ; Research Support, U.S. Gov't, Non-P.H.S.
    ZDB-ID 1483840-0
    ISSN 1522-8002
    ISSN 1522-8002
    DOI 10.1016/s1476-5586(03)80008-8
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