Differential roles of transcriptional and translational negative autoregulations in protein dynamics.

Cells continuously respond to stimuli to function properly by employing a wide variety of regulatory mechanisms that often involve protein up or down regulations. This study focuses on dynamics of a protein with negative autoregulations in E. coli, and assumes that the input signal up-regulates the protein, and then the protein down-regulates its own production via 2 distinct types of mechanisms. The mathematical models describe the dynamics of mRNA and protein for 3 scenarios: (i) a simplistic model with no regulation, (ii) a model with transcriptional negative autoregulation, and (iii) a model with translational negative autoregulation. Our analysis shows that the negative autoregulation models produce faster responses and quicker return times to the input signals compared to the model with no regulation, while the transcriptional autoregulation model is the only model capable of producing oscillatory dynamics. The stochastic simulations predict that the transcriptional autoregulation model is the noisiest followed by the simplistic model, and the translational autoregulation model has the least noise. The noise level depends on the strength of inhibition. Furthermore, the transcriptional autoregulation model filters out the noise in the input signal for longer periods of time, and this time increases as the strength of the feedback gets stronger.

Mathematical modeling reveals differential regulation of MAPK activity by phosphatase proteins in the yeast pheromone response pathway.

To prevent indefinite cellular responses to external signals, cells utilize various adaptation mechanisms. The yeast mating-response pathway is a model cellular system that exhibits adaptation to persistent external signals. This pathway employs a mitogen-activated protein kinase (MAPK) cascade which is composed of two well-known negative feedback inhibitions that involve the yeast phosphatase proteins Ptp3 and Msg5. The phosphorylated form of the yeast MAPK protein Fus3 (pFus3) triggers the phosphorylation of both phosphatases, but transcriptionally upregulates only Msg5. To study the biological rationale for the existence of two distinct negative feedback inhibitions acting on pFus3, we used published experimental data to develop a mathematical model which quantifies the inhibitory roles of these phosphatase proteins on pFus3. Our analyses show that the inhibition of pFus3 due to Ptp3 is largely independent of the signal profile, and is most impactful at early time points after pheromone induction. Conversely, the feedback inhibition due to Msg5 is highly dependent on the signal profile, and is most influential after pFus3 attains its maximum cellular abundance. Similarly, Ptp3 reduces the variation in the pFus3 dynamics at early time points while the noise-reduction effects of Msg5 become stronger as time passes.

Differential transcriptional regulation by alternatively designed mechanisms: A mathematical modeling approach.

Cells maintain cellular homeostasis employing different regulatory mechanisms to respond external stimuli. We study two groups of signal-dependent transcriptional regulatory mechanisms. In the first group, we assume that repressor and activator proteins compete for binding to the same regulatory site on DNA (competitive mechanisms). In the second group, they can bind to different regulatory regions in a noncompetitive fashion (noncompetitive mechanisms). For both competitive and noncompetitive mechanisms, we studied the gene expression dynamics by increasing the repressor or decreasing the activator abundance (inhibition mechanisms), or by decreasing the repressor or increasing the activator abundance (activation mechanisms). We employed delay differential equation models. Our simulation results show that the competitive and noncompetitive inhibition mechanisms exhibit comparable repression effectiveness. However, response time is fastest in the noncompetitive inhibition mechanism due to increased repressor abundance, and slowest in the competitive inhibition mechanism by increased repressor level. The competitive and noncompetitive inhibition mechanisms through decreased activator abundance show comparable and moderate response times, while the competitive and noncompetitive activation mechanisms by increased activator protein level display more effective and faster response. Our study exemplifies the importance of mathematical modeling and computer simulation in the analysis of gene expression dynamics.

Mathematical modeling deciphers the benefits of alternatively-designed conserved activatory and inhibitory gene circuits.

Cells employ a variety of mechanisms as a response to external signals to maintain cellular homeostasis. In this study, we examine four activatory and four inhibitory protein synthesis mechanisms at both population and single cell level that can be triggered by a transient external signal. Activation mechanisms result from the assumption that cells can employ four different modes to temporarily increase the levels of a protein: decreased mRNA degradation, increased mRNA synthesis, decreased protein degradation and increased protein synthesis. For the inhibition mechanisms it is assumed that a cell can reduce a protein's level through four ways: increased mRNA degradation, reduced mRNA synthesis, increased protein degradation and reduced protein synthesis. Deterministic and stochastic models were developed to analyze the dynamic responses of these eight mechanisms to a transient signal. Three different response metrics were used to measure different aspects of the response. These metrics are (i) mid-protein abundance (mP), (ii) time required for the protein to reach the mid-protein level (mT), and (iii) duration of response (D), which is defined as the total time for which the protein (P) abundance are above or below of mid-protein level. Our simulations show that of the activation mechanisms, the signal-dependent increase in mRNA synthesis and protein synthesis are more effective and faster, than the signal dependent decrease in mRNA and protein degradation. On the other hand, the mechanism involving signal dependent increase in protein synthesis is noisier than the signal dependent increase in mRNA synthesis in regard to all metrics used. Of the four inhibition mechanisms, the signal-dependent increase in the protein degradation is the most effective and fastest of the four inhibition mechanisms. It is also noisiest of the four inhibition mechanisms before the protein levels reach a steady state around 100 minutes.

Dynamics matter: differences and similarities between alternatively designed mechanisms.

Cells selectively respond to external stimuli to maintain cellular homeostasis by making use of different regulatory mechanisms. We studied two classes of signal-dependent regulatory inhibition and activation mechanisms in this study. Inhibition mechanisms assume that inhibition can occur in two different ways: either by increasing the degradation rate or decreasing the production rate. Similarly, it is assumed that signal-triggered activation can occur either through increasing production rate or decreasing degradation rate. We devised mathematical models (deterministic and stochastic) to compare and contrast responses of these activation and inhibition mechanisms to a time dependent discrete signal. Our simulation results show that the signal-dependent increased degradation mechanism is a more effective, noisier and quicker way to inhibit the protein abundance compared to the signal-dependent decreased activation mechanism. On the other hand, the signal-dependent increased production mechanism can produce a much stronger and faster response than the signal-dependent decreased degradation mechanism. However, our simulations predict that both of the activation mechanisms have roughly similar noise structures. Our analysis exemplifies the importance of mathematical modeling in the analysis of biological regulatory networks.

The characteristics of patients with chronic hepatitis B in Turkey.

AIM: To evaluate the characteristics of patients with hepatitis B virus (HBV) infection and summarize the treatment modalities. METHODS: By September 30, 2011 the data of 7871 HBsAg (+) patients were complied and analysed according to demographic and medical records (age, sex, laboratory tests, treatment with antiviral agents) in thirty centres of Turkey. RESULTS: Of the 7871 patients 3078 (39.1%) were females; mean (standard deviation) age was 35 (14) years, 3180 (40.4%) were HBsAg positive (+) after admission to a hospital, 1488 (18.9%) after blood donation and 967 (11.9%) were found during routine screening. The HBV prevalence among relatives of HBsAg (+) patients was 1764 (22.4%), and most frequently infected family members were siblings and mothers, 4961 (63.0%) and 2149 (27.3%), respectively). Anti-HDV was negative in 7407 94.1% of patients. Three-fourths of the patients 6383 (81.1%) were HBeAg negative (-). Mean (SD) ALT was 85.8 (266.4) U/L. Majority of patients, 5588 (71.0%) were chronic hepatitis-B patients under treatment, while 2283 (29.0%) were asymptomatic carriers without treatment and only 165 (2.1%) of patients were cirrhotic and 6612 (84.0%) of those were compensated. One-third of the patients 2983 (37.9%) were under a combined treatment, while others were under monotherapy. Lamivudine, entecavir and adefovir were the most frequently used oral therapies, used for 2583 (32.8%), 11.6% and 787 (10.0%) of patients, respectively), while 2975 (37.8%) of patients were under interferon treatment. CONCLUSION: Hepatitis B is still a problem in our country. First task of the physicians and our state should be to prevent the development and spread of the disease with education and vaccination programs, safe blood transfusions, and control of barbers.

Efficacy and safety of tenofovir disoproxil fumarate in pregnancy for the prevention of vertical transmission of HBV infection.

AIM: To evaluate the effects of tenofovir disoproxil fumarate (TDF) use during late pregnancy to reduce hepatitis B virus (HBV) transmission in highly viremic mothers. METHODS: This retrospective study included 45 pregnant patients with hepatitis B e antigen (+) chronic hepatitis B and HBV DNA levels > 107 copies/mL who received TDF 300 mg/d from week 18 to 27 of gestation (n = 21). Untreated pregnant patients served as controls (n = 24). All infants received 200 IU of hepatitis B immune globulin (HBIG) within 24 h postpartum and 20 µg of recombinant HBV vaccine at 4, 8, and 24 wk. Perinatal transmission rate was determined by hepatitis B surface antigen and HBV DNA results in infants at week 28. RESULTS: At week 28, none of the infants of TDF-treated mothers had immunoprophylaxis failure, whereas 2 (8.3 %) of the infants of control mothers had immunoprophylaxis failure (P = 0.022). There were no differences between the groups in terms of adverse events in mothers or congenital deformities, gestational age, height, or weight in infants. At postpartum week 28, significantly more TDF-treated mothers had levels of HBV DNA < 250 copies/mL and normalized alanine aminotransferase compared with controls (62% vs none, P < 0.001; 82% vs 61%, P = 0.012, respectively). CONCLUSION: TDF therapy during the second or third trimester reduced perinatal transmission rates of HBV and no adverse events were observed in mothers or infants.

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

Different environmental stimuli often use the same set of signaling proteins to achieve very different physiological outcomes. The mating and invasive growth pathways in yeast each employ a mitogen-activated protein (MAP) kinase cascade that includes Ste20, Ste11, and Ste7. Whereas proper mating requires Ste7 activation of the MAP kinase Fus3, invasive growth requires activation of the alternate MAP kinase Kss1. To determine how MAP kinase specificity is achieved, we used a series of mathematical models to quantitatively characterize pheromone-stimulated kinase activation. In accordance with the computational analysis, MAP kinase feedback phosphorylation of Ste7 results in diminished activation of Kss1, but not Fus3. These 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 the low and high affinity arabinose transport systems in Escherichia coli.

A mathematical model was developed for the low and high affinity arabinose transport systems in E. coli. The model is a system of three ordinary differential equations and takes the dynamics of mRNAs for the araE and araFGH proteins and the internal arabinose into account. Special attention was paid to estimate the model parameters from the literature. Our analysis and simulations suggest that the high affinity transport system helps the low affinity transport system to respond to high concentration of extracellular arabinose faster, whereas the high affinity transport system responds to a small amount of extracellular arabinose. Steady state analysis of the model also predicts that there is a regime for the extracellular concentration of arabinose where the arabinose system can show bistable behavior.

Deterministic and stochastic simulation and analysis of biochemical reaction networks the lactose operon example.

A brief introduction to mathematical modeling of biochemical regulatory reaction networks is presented. Both deterministic and stochastic modeling techniques are covered with examples from enzyme kinetics, coupled reaction networks with oscillatory dynamics and bistability. The Yildirim-Mackey model for lactose operon is used as an example to discuss and show how deterministic and stochastic methods can be used to investigate various aspects of this bacterial circuit.

beta2-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 beta(2)-adrenergic receptor (beta(2)AR) in living cells. beta(2)AR stimulation with isoproterenol results in a transient pulse of cAMP, reaching a maximal concentration of approximately 10 microm and persisting for less than 5 min. We investigated the contributions of cAMP-dependent kinase, G protein-coupled receptor kinases, and beta-arrestin to the regulation of beta(2)AR 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 beta-arrestin mediated receptor inactivation and cAMP-dependent kinase-mediated induction of cAMP metabolism by phosphodiesterases. A mathematical model of beta(2)AR signal kinetics, fit to these data, revealed that direct receptor inactivation by cAMP-dependent kinase is insignificant but that GRK6/beta-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.

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.

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.

Modeling operon dynamics: the tryptophan and lactose operons as paradigms.

Understanding the regulation of gene control networks and their ensuing dynamics will be a critical component in the understanding of the mountain of genomic data being currently collected. This paper reviews recent mathematical modeling work on the tryptophan and lactose operons which are, respectively, the classical paradigms for repressible and inducible operons.

Regulators of G protein signaling and transient activation of signaling: experimental and computational analysis reveals negative and positive feedback controls on G protein activity.

Cellular responses to hormones and neurotransmitters are necessarily transient. The mating pheromone signal in yeast is typical. Signal initiation requires cell surface receptors, a G protein heterotrimer, and down-stream effectors. Signal inactivation requires Sst2, a regulator of G protein signaling (RGS) protein that accelerates GTPase activity. We conducted a quantitative analysis of RGS and G protein expression and devised computational models that describe their activity in vivo. These results indicated that pheromone-dependent transcriptional induction of the RGS protein constitutes a negative feedback loop that leads to desensitization. Modeling also suggested the presence of a positive feedback loop leading to resensitization of the pathway. In confirmation of the model, we found that the RGS protein is ubiquitinated and degraded in response to pheromone stimulation. We identified and quantitated these positive and negative feedback loops, which account for the transient response to external signals observed in vivo.

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.