Necmettin Yildirim

Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data

A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of beta-galactosidase activity versus time data, as well as a set of data on beta-galactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steady-state behavior, and that this corresponds to a cusp bifurcation in the model dynamics.

Β2-Adrenergic Receptor Signaling and Desensitization Elucidated by Quantitative Modeling of Real Time cAMP Dynamics

G protein-coupled receptor signaling is dynamically regulated by multiple feedback mechanisms, which rapidly attenuate signals elicited by ligand stimulation, causing desensitization. The individual contributions of these mechanisms, however, are poorly understood. Here, we use an improved fluorescent biosensor for cAMP to measure second messenger dynamics stimulated by endogenous β2-adrenergic receptor (β2AR) in living cells. β2AR stimulation with isoproterenol results in a transient pulse of cAMP, reaching a maximal concentration of ∼10 μm and persisting for less than 5 min. We investigated the contributions of cAMP-dependent kinase, G protein-coupled receptor kinases, and β-arrestin to the regulation of β2AR signal kinetics by using small molecule inhibitors, small interfering RNAs, and mouse embryonic fibroblasts. We found that the cAMP response is restricted in duration by two distinct mechanisms in HEK-293 cells: G protein-coupled receptor kinase (GRK6)-mediated receptor phosphorylation leading to β-arrestin mediated receptor inactivation and cAMP-dependent kinase-mediated induction of cAMP metabolism by phosphodiesterases. A mathematical model of β2AR signal kinetics, fit to these data, revealed that direct receptor inactivation by cAMP-dependent kinase is insignificant but that GRK6/β-arrestin-mediated inactivation is rapid and profound, occurring with a half-time of 70 s. This quantitative system analysis represents an important advance toward quantifying mechanisms contributing to the physiological regulation of receptor signaling.

Dynamics and bistability in a reduced model of the lac operon

It is known that the lac operon regulatory pathway is capable of showing bistable behavior. This is an important complex feature, arising from the nonlinearity of the involved mechanisms, which is essential to understand the dynamic behavior of this molecular regulatory system. To find which of the mechanisms involved in the regulation of the lac operon is the origin of bistability, we take a previously published model which accounts for the dynamics of mRNA, lactose, allolactose, permease and beta-galactosidase involvement and simplify it by ignoring permease dynamics (assuming a constant permease concentration). To test the behavior of the reduced model, three existing sets of data on beta-galactosidase levels as a function of time are simulated and we obtain a reasonable agreement between the data and the model predictions. The steady states of the reduced model were numerically and analytically analyzed and it was shown that it may indeed display bistability, depending on the extracellular lactose concentration and growth rate.

Parameter estimation of nonlinear models in biochemistry: a comparative study on optimization methods

The most commonly used numerical optimization techniques include the Simplex method, Brents algorithm, Levenberg-Marquardt algorithm, direct search complex algorithm and a quasi-Newton method. In the present study, to compare these methods for a nonlinear model from enzyme kinetic theory known as Michaelis Menten equation, we have developed FORTRAN programs for all of these methods and also numerical solution of an initial value problem to compare optimization methods in terms of number of function evaluations, convergences and computation times. According to these factors, we have found that the Simplex method is the best followed by the Direct search algorithm.

Combined computational and experimental analysis reveals mitogen-activated protein kinase-mediated feedback phosphorylation as a mechanism for signaling specificity.

A series of mathematical models was used to quantitatively characterize pheromone-stimulated kinase activation and determine how mitogen-activated protein (MAP) kinase specificity is achieved. The findings reveal how feedback phosphorylation of a common pathway component can limit the activity of a competing MAP kinase through feedback phosphorylation of a common activator, and thereby promote signal fidelity.

Mathematical modeling of RGS and G-protein regulation in yeast.

G-protein-activated signaling pathways are capable of adapting to a persistent external stimulus. Desensitization is thought to occur at the receptor level as well as through negative feedback by a family of proteins called regulators of G-protein signaling (RGS). The pheromone response pathway in yeast is a typical example of such a system, and the relative simplicity of this pathway makes it an attractive system in investigating the regulatory role of RGS proteins. Two studies have used computational modeling to gain insight into how this pathway is regulated (Hao et al., 2003; Yi et al., 2003). This article provides an introduction to computational analysis of signaling pathways by developing a mathematical model of the pheromone response pathway that synthesizes the results of these two investigations. Our model qualitatively captures many features of the pathway and suggests an additional mechanism for pathway inactivation. It also illustrates that a complete understanding of signaling pathways requires an investigation of their time-dependent behavior.

An improvement on Fibonacci search method in optimization theory

Among the other elimination methods, Fibonacci search method is regarded as the best one to find the optimal point for single valued functions. In the present study, employing Lucas numbers instead of Fibonacci numbers, we have made partial improvements on location of the intervals that contain optimal point in the Fibonacci search algorithm. For that purpose, using two well known test functions in optimization theory, a computer program was developed in MAPLE to examine this idea. It was seen that the improved method is giving better results than the previous method in the sense that converging the optimal point more rapidly.

Combined computational and experimental analysis reveals MAP kinase-mediated feedback phosphorylation as a mechanism for signaling specificity

A series of mathematical models was used to quantitatively characterize pheromone-stimulated kinase activation and determine how mitogen-activated protein (MAP) kinase specificity is achieved. The findings reveal how feedback phosphorylation of a common pathway component can limit the activity of a competing MAP kinase through feedback phosphorylation of a common activator, and thereby promote signal fidelity.

Kinetic Analysis of Multi Enzyme Systems: A Case Study of the Closed System of Creatine Kinase, Hexokinase and Glucose 6-Phosphate Dehydrogenase

This paper describes a general methodology to handle closed multi enzyme systems using mixture of symbolic (which depends on the Gröbner Basis technique) and numerical computation methods. The applicability of the proposed method has been examined for the closed three-enzyme system of rabbit heart creatine kinase (EC 2.7.3.2), yeast hexokinase (EC 2.7.1.1) and human erythrocyte glucose 6-phosphate dehydrogenase (EC 1.1.1.49) using experimental data.

An analysis of the kinetics of unstable enzymatic systems using MAPLE

In this paper, we presented a general kinetic analysis of the reversible enzymatic system for the case in which the substrate, the enzyme-substrate complex and the product are all unstable. Using computer algebra technique, we solve the system of ordinary differential equations symbolically under the assumption [E]@?[S]. Since this condition satisfied inside the cells, it can be more relevant to physiological problems. Then using numerical values, simulation progress curves for the concentration of all species are obtained.