Use Of Steady-state Model Research Articles

Abstract C235: An investigation of the p53 ubiquitin-proteasome system using a novel non-steady-state enzyme kinetic model.

Abstract Overzealous MDM2-mediated ubiquitination of p53 characterizes and sustains over 50% of all human cancers. Successful targeted cancer therapy hinges on a thorough understanding of the ubiquitination process. Unfortunately, current steady-state enzyme kinetic models fail to accurately describe the ubiquitin-proteasome system, due to the assumption that the enzyme (E3 ligase) is expressed at infinitesimally smaller concentrations than the substrates (ubiquitin-conjugated E2 and target protein). This limitation of the quasi-steady state assumption prohibits the use of steady-state models when analyzing the cancerous consequences of extreme ubiquitin-ligase overexpression. This paper derives a novel non-steady-state mathematical model of reversible ordered ternary complex enzyme kinetics, which can be used to simulate the behavioral response of the ubiquitin-proteasome system to specific variations in the cellular concentrations of p53, MDM2, and ubiquitin-conjugated E2D3. Computer simulations of the model were used to study the effects of E2D3-Ub and MDM2 concentrations on the rates of p53 ubiquitination at different temperatures. In each process, it was observed that the ubiquitin-ligase MDM2 accelerates the carcinogenic ubiquitination process, while ubiquitin-conjugated E2 inhibits it. It was also discovered that E2D3-Ub is more effective inhibitor of overzealous p53 ubiquitination when present at higher concentrations. However, it was also observed that high concentrations of p53 hinder the ability of E2D3-Ub to decelerate the reaction. The mathematical model successfully reproduced the experimentally observed p53-MDM2 interaction. The derived model therefore suggests MDM2 as a prospective target for cancer therapy. In addition, the findings of this project propose recombinant E2D3-Ub as a new promising protein-based anticancer drug for targeting overzealous p53 ubiquitination. The derived model can suggest new therapeutic solutions for decreasing the harmful effects of many human cancers, bacterial infections, and inflammatory diseases (such as rheumatoid arthritis) characterized by an overzealous ubiquitin-proteasome system. Finally, computational simulation of this novel model provides a safe, fast, and cost-effective preliminary alternative to expensive in vitro experimentation. Citation Information: Mol Cancer Ther 2013;12(11 Suppl):C235. Citation Format: Prem M. Talwai. An investigation of the p53 ubiquitin-proteasome system using a novel non-steady-state enzyme kinetic model. [abstract]. In: Proceedings of the AACR-NCI-EORTC International Conference: Molecular Targets and Cancer Therapeutics; 2013 Oct 19-23; Boston, MA. Philadelphia (PA): AACR; Mol Cancer Ther 2013;12(11 Suppl):Abstract nr C235.

A Novel Mathematical Model of Targeted Cancer Therapy along p53 Proteasomal Degradation Pathways

Overzealous MDM2-mediated ubiquitination of p53 characterizesand sustains over 50% of all human cancers. Successful targeted cancer therapyhinges on a thorough understanding of the ubiquitination process.Unfortunately, current steady-state enzyme kinetic models fail to accuratelydescribe the ubiquitin-proteasome system, due to the assumption that the enzyme(E3 ligase) is expressed at infinitesimally smaller concentrations than thesubstrates (E2 conjugase and target protein). This limitation of the quasi-steadystate assumption prohibits the use of steady-state models when analyzing thecancerous consequences of extreme ubiquitin-ligase overexpression. This paperderives a novel non-steady-state mathematical model of ternary complex enzymekinetics, which can be used to simulate the behavioral response of theubiquitin-proteasome system to specific variations in the cellularconcentrations of targeted the E2 conjugase, E3 ligase, and target protein.Computer simulations of the model were used to study the effects of E2D3 andMDM2 concentrations on the rates of p53 ubiquitination at differenttemperatures. At each temperature, it was observed that the ubiquitin-ligaseMDM2 accelerates the dangerous degradation process, while the ubiquitinconjugating-enzyme E2D3 inhibits it. It was also discovered that E2D3 is a moreeffective inhibitor of p53 ubiquitination at higher body temperatures, whereas MDM2 is then a less-effective catalyst. The derived model therefore suggests MDM2 as a prospective target for cancer therapy. In addition, the findings of this project propose recombinant E2D3 as a new promising protein-basedanticancer drug and a potential tumor suppressor protein. The mathematical model successfully reproduced the experimentally observed p53-MDM2 interaction. Further in vivo experimentation is necessary for additional validation of thecomputational results. The derived model can suggest new therapeutic solutions for decreasing the harmful effects of many human cancers, bacterial infections,and inflammatory diseases (such as rheumatoid arthritis) characterized by an overzealous ubiquitin-proteasome system.

Modelling and dynamic simulation of gradual performance deterioration of a crushing circuit – Including time dependence and wear

The use of steady-state models in process simulation is a well-established method in many process industries. Designing a large crushing plant by relying on steady-state simulations alone will not generally provide the full picture of possible operational performance. The dynamics and variation between equipment and stochastic events can significantly reduce predicted plant performance. In order to dynamically simulate the crushing circuit, models for process equipment need to be further developed.The purpose of this paper is to create a wear function for an existing Particle Size Distribution model (i.e., a Swebrec-function) with data obtained from a real crusher operating at gradually increasing closed side settings. This is done to create an accurate and updated model of the crusher in which the transient consequences of wear are captured. The Swebrec-function and correlation model were implemented into simulation software with simulated events; this simulation was validated with actual process readings. Improved simulations were then attained with the developed functions.

DETERMINING CRITICAL WATER QUALITY CONDITIONS FOR INORGANIC NITROGEN IN DRY, SEMI‐URBANIZED WATERSHEDS1

ABSTRACT: Traditional approaches to establishing critical water quality conditions, based on statistical analysis of low flow conditions and expressed as a recurrence interval for low flow conditions (e.g., 7Q10), may be inappropriate for drier watersheds. The use of 7Q10 as a standard design flow assumes year‐round flow, but in these watersheds, 7Q10 is zero or very small. In addition, the increasing use of multiple year dynamic water quality models at daily time steps can supercede the use of steady state approaches. Many of these watersheds are also under increasing urbanization pressure, which accentuates the flashiness of runoff and the episodic nature of critical water quality conditions. To illustrate, the conditions in the Santa Clara River, California, are considered. A statistical analysis indicates that higher inorganic nitrogen concentrations correlate strongly with low flow. However, peaks in concentrations can occur during the first storms, particularly where nonpoint source contribution is significant. Critical conditions can thus occur at different flow regimes depending on the relative magnitude of flow and pollutant contributions from various sources. The use of steady state models for these dry semi‐urbanized watersheds based on 7Q10 flows is thus unlikely to accurately simulate the potential for exceeding water quality objectives. Dynamic simulation of water quality is necessary, and as the recent intense storm event sampling data indicate, the models should be formulated to consider even smaller time steps. This places increasing demand on computational resources and datasets to accurately calibrate the models at this temporal resolution.

Ice-Sheet Erosion—A Result of Maximum Conditions?

AbstractUnderstanding the relationship between the morphology of former ice-sheet beds and glaciological processes is handicapped by the difficulty of establishing which stage of a cycle of ice-sheet growth and decay is responsible for most erosion. Discussions at this conference and in the literature display a variety of opinions, some favouring periods of ice-sheet build up, others periods of fluctuations, and still others steady-state maximum conditions. Here it is suggested that there is geomorphological evidence which points to the dominance of maximum conditions.Along the eastern margins of the Laurentide and Greenland ice sheets there is a sharp discontinuity between Alpine relief which stood above the ice-sheet surface at the maximum and plateau scenery which was covered by the ice sheet. Often the two types of relief are adjacent and yet separated by an altitudinal difference of only 100–200 m. The existence of an abrupt rather than gradual transition from one relief type to the other suggests that most glacial sculpture must have taken place while the ice sheet was at its maximum extent. In other geomorphological situations where high mountains were submerged by ice sheets, the major erosional landforms are frequently found to relate to ice sheets rather than to local mountain glaciers, again suggesting the dominance of erosion during full ice-sheet conditions. Finally, the identification of patterns of glacial erosion on an ice-sheet scale in North America and Greenland points to erosion when the ice sheets were fully expanded, rather than to the variable flow conditions associated with growth or decay.If ice-sheet erosion is accepted as being a result of maximum conditions, then it places certain constraints on glacial theory, for example the need to develop theories of glacial erosion which apply beneath ice thicknesses of several thousand metres. It also suggests that the use of steady-state models of ice sheets is likely to be a profitable way of relating glaciological processes to the morphology of former ice-sheet beds.

Ice-Sheet Erosion—A Result of Maximum Conditions?

Abstract Understanding the relationship between the morphology of former ice-sheet beds and glaciological processes is handicapped by the difficulty of establishing which stage of a cycle of ice-sheet growth and decay is responsible for most erosion. Discussions at this conference and in the literature display a variety of opinions, some favouring periods of ice-sheet build up, others periods of fluctuations, and still others steady-state maximum conditions. Here it is suggested that there is geomorphological evidence which points to the dominance of maximum conditions. Along the eastern margins of the Laurentide and Greenland ice sheets there is a sharp discontinuity between Alpine relief which stood above the ice-sheet surface at the maximum and plateau scenery which was covered by the ice sheet. Often the two types of relief are adjacent and yet separated by an altitudinal difference of only 100–200 m. The existence of an abrupt rather than gradual transition from one relief type to the other suggests that most glacial sculpture must have taken place while the ice sheet was at its maximum extent. In other geomorphological situations where high mountains were submerged by ice sheets, the major erosional landforms are frequently found to relate to ice sheets rather than to local mountain glaciers, again suggesting the dominance of erosion during full ice-sheet conditions. Finally, the identification of patterns of glacial erosion on an ice-sheet scale in North America and Greenland points to erosion when the ice sheets were fully expanded, rather than to the variable flow conditions associated with growth or decay. If ice-sheet erosion is accepted as being a result of maximum conditions, then it places certain constraints on glacial theory, for example the need to develop theories of glacial erosion which apply beneath ice thicknesses of several thousand metres. It also suggests that the use of steady-state models of ice sheets is likely to be a profitable way of relating glaciological processes to the morphology of former ice-sheet beds.