Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove that the distance between these two descriptions, as measured by expectations of functionals of the processes, converges to zero with increasing system size. Further, we prove that the delay birth-death process converges to the thermodynamic limit as system size tends to infinity. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the spatial and temporal distributions of transition pathways in metastable systems, oscillatory behavior in negative feedback circuits, and cross-correlations between nodes in a network. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay

Synchronization of Coupled Nonidentical Genetic Oscillators

The study on the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lur'e form by exploiting the special structure of biological systems. By using control theory approach, we provide a theoretical method for analyzing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.Comment: 16 pages, 3 figure

Patients achieving sustained deep remission, deep remission or sustained remission of rheumatoid arthritis are more likely than other responders to maintain remission or low disease activity after dose reduction or withdrawal of etanercept

Background Biologic disease-modifying antirheumatic drugs (bDMARDs) are important options for managing rheumatoid arthritis (RA). Once patients achieve disease control, clinicians may consider dose reduction or withdrawal of the bDMARD. Results from published studies indicate that some patients will maintain remission; however, others will flare. We analyzed data from three etanercept down-titration studies in patients with RA to determine what extent of remission provides the greatest predictability of maintaining remission following dose reduction or discontinuation. Methods Patients with moderate to severe RA from the PRESERVE, PRIZE, and Treat-to-Target (T2T) randomized controlled trials were included. We determined the proportion of patients achieving remission with etanercept at the last time point in the induction period, and sustained remission (last two time points), according to the Disease Activity Score 28-joints (DAS28), the American College of Rheumatology (ACR)/European League Against Rheumatism (EULAR) Boolean criteria, and the clinical disease activity index (CDAI). We also calculated the proportion achieving DAS28 deep remission (DAS28 ≤ 1.98), sustained deep remission (last two time points), and low disease activity (LDA), and LDA according to the CDAI. Then, we evaluated whether they maintained remission or LDA following etanercept dose reduction or withdrawal. Results Patients achieving sustained and/or deep remission were more likely than patients achieving remission or LDA to maintain remission/LDA after etanercept dose reduction or withdrawal. In PRESERVE, the proportions of patients with DAS28 sustained deep remission, deep remission, sustained remission, remission, and LDA who maintained remission following etanercept dose reduction were 81%, 67%, 58%, 56%, and 36%, respectively, P < 0.001 for trend. In PRESERVE, this trend was significant when etanercept was discontinued and when ACR/EULAR Boolean and CDAI remission criteria were used. Although some sample sizes were small, the PRIZE and T2T studies also demonstrated response trends according to ACR/EULAR Boolean and CDAI remission criteria, and T2T demonstrated response trends according to DAS28. Conclusions These results suggest that patients achieving disease control according to a stringent definition, such as sustained ACR/EULAR Boolean or CDAI remission, or a new definition of sustained deep remission by DAS28, have a higher probability of remaining in remission or LDA following etanercept dose reduction or withdrawal

Methotrexate in rheumatoid arthritis is frequently effective, even if re-employed after a previous failure

Effectiveness of therapy with individual disease-modifying antirheumatic drugs (DMARDs) in rheumatoid arthritis (RA) is limited, and the number of available DMARDs is finite. Therefore, at some stage during the lengthy course of RA, institution of traditional DMARDs that have previously been applied may have to be reconsidered. In the present study we investigated the effectiveness of re-employed methotrexate in patients with a history of previous methotrexate failure (original course). A total of 1,490 RA patients (80% female, 59% rheumatoid factor positive) were followed from their first presentation, yielding a total of 6,470 patient-years of observation. We identified patients in whom methotrexate was re-employed after at least one intermittent course of a different DMARD. We compared reasons for discontinuation, improvement in acute phase reactants, and cumulative retention rates of methotrexate therapy between the original course of methotrexate and its re-employment. Similar analyses were peformed for other DMARDs. Methotrexate was re-employed in 86 patients. Compared with the original courses, re-employment was associated with a reduced risk for treatment termination because of ineffectiveness (P = 0.02, by McNemar test), especially if the maximum methotrexate dose of the original course had been low (<12.5 mg/week; P = 0.02, by logistic regression). In a Cox regression model, re-employed MTX was associated with a significantly reduced hazard of treatment termination compared with the original course of methotrexate, adjusting for dose and year of employment (hazard ratio 0.64, 95% confidence interval 0.42–0.97; P = 0.04). These findings were not recapitulated in analyses of re-employment of other DMARDs. Re-employment of MTX despite prior inefficacy, but not re-employment of other DMARDs, is an effective therapeutic option, especially in those patients in whom the methotrexate dose of the original course was low

Remission by composite scores in rheumatoid arthritis: are ankles and feet important?

Current treatment strategies aim to achieve clinical remission in order to prevent the long-term consequences of rheumatoid arthritis (RA). Several composite indices are available to assess remission. All of them include joint counts as the assessment of the major 'organ' involved in RA, but some employ reduced joint counts, such as the 28-joint count, which excludes ankles and feet

Temporary interruption of baricitinib: characterization of interruptions and effect on clinical outcomes in patients with rheumatoid arthritis

Background In clinical practice, temporary interruption of rheumatoid arthritis (RA) therapy is common for various reasons including side effects, non-compliance, or necessity for surgery. To characterize temporary interruptions of baricitinib and placebo-matched tablets in phase 3 studies of patients with moderate-to-severe rheumatoid arthritis (RA) and describe their impact on efficacy and safety. Methods During 4 baricitinib phase 3 studies, investigators documented timing, reason, and duration of investigator-initiated temporary interruptions of study drug. In 2 studies, patients recorded RA symptoms in daily diaries for 12 weeks. Post hoc analyses investigated changes in symptom scores during interruptions and resumption of treatment. Interruptions were evaluated for reoccurrence of adverse events or laboratory abnormalities after retreatment. Results Across the placebo-controlled studies, interruptions occurred in larger proportions of baricitinib- (2 mg, 18%; 4 mg, 18%) vs placebo-treated (9%) patients in only one study (bDMARD-inadequate responder patients, RA-BEACON). In the active comparator-controlled studies, the lowest rates of interruption were in the baricitinib monotherapy arm (9%) of RA-BEGIN (vs methotrexate monotherapy or combination therapy), and proportions were similar for baricitinib (10%) and adalimumab (9%) in RA-BEAM. Adverse events were the most common reason for interruption, but their reoccurrence after drug restart was infrequent. Most interruptions lasted ≤ 2 weeks. Daily diaries indicated modest symptom increases during interruption with return to pre-interruption levels or better after resumption. Interruptions had no impact on long-term efficacy outcomes. Conclusions Consistent with its pharmacologic properties, brief interruptions of baricitinib during phase 3 studies were associated with minor increases in RA symptoms that resolved following retreatment. This analysis provides useful information for clinicians, as temporary interruption of antirheumatic therapy is common in the care of patients with RA

Glucose metabolism and oscillatory behavior of pancreatic islets

A variety of oscillations are observed in pancreatic islets.We establish a model, incorporating two oscillatory systems of different time scales: One is the well-known bursting model in pancreatic beta-cells and the other is the glucose-insulin feedback model which considers direct and indirect feedback of secreted insulin. These two are coupled to interact with each other in the combined model, and two basic assumptions are made on the basis of biological observations: The conductance g_{K(ATP)} for the ATP-dependent potassium current is a decreasing function of the glucose concentration whereas the insulin secretion rate is given by a function of the intracellular calcium concentration. Obtained via extensive numerical simulations are complex oscillations including clusters of bursts, slow and fast calcium oscillations, and so on. We also consider how the intracellular glucose concentration depends upon the extracellular glucose concentration, and examine the inhibitory effects of insulin.Comment: 11 pages, 16 figure

Correction to: Temporary interruption of baricitinib: characterization of interruptions and effect on clinical outcomes in patients with rheumatoid arthritis

Background In clinical practice, temporary interruption of rheumatoid arthritis (RA) therapy is common for various reasons including side effects, non-compliance, or necessity for surgery. To characterize temporary interruptions of baricitinib and placebo-matched tablets in phase 3 studies of patients with moderate-to-severe rheumatoid arthritis (RA) and describe their impact on efficacy and safety. Methods During 4 baricitinib phase 3 studies, investigators documented timing, reason, and duration of investigator-initiated temporary interruptions of study drug. In 2 studies, patients recorded RA symptoms in daily diaries for 12 weeks. Post hoc analyses investigated changes in symptom scores during interruptions and resumption of treatment. Interruptions were evaluated for reoccurrence of adverse events or laboratory abnormalities after retreatment. Results Across the placebo-controlled studies, interruptions occurred in larger proportions of baricitinib- (2 mg, 18%; 4 mg, 18%) vs placebo-treated (9%) patients in only one study (bDMARD-inadequate responder patients, RA-BEACON). In the active comparator-controlled studies, the lowest rates of interruption were in the baricitinib monotherapy arm (9%) of RA-BEGIN (vs methotrexate monotherapy or combination therapy), and proportions were similar for baricitinib (10%) and adalimumab (9%) in RA-BEAM. Adverse events were the most common reason for interruption, but their reoccurrence after drug restart was infrequent. Most interruptions lasted ≤ 2 weeks. Daily diaries indicated modest symptom increases during interruption with return to pre-interruption levels or better after resumption. Interruptions had no impact on long-term efficacy outcomes. Conclusions Consistent with its pharmacologic properties, brief interruptions of baricitinib during phase 3 studies were associated with minor increases in RA symptoms that resolved following retreatment. This analysis provides useful information for clinicians, as temporary interruption of antirheumatic therapy is common in the care of patients with RA