Chemical Systems with Limit Cycles.

The dynamics of a chemical reaction network (CRN) is often modeled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of concentrations of chemical species involved. Given an arbitrarily large integer [Formula: see text], we show that there exists a CRN such that its ODE model has at least K stable limit cycles. Such a CRN can be constructed with reactions of at most second-order provided that the number of chemical species grows linearly with K. Bounds on the minimal number of chemical species and the minimal number of chemical reactions are presented for CRNs with K stable limit cycles and at most second order or seventh-order kinetics. We also show that CRNs with only two chemical species can have K stable limit cycles, when the order of chemical reactions grows linearly with K.

Structure-Controlled Carbon Hosts for Dendrite-Free Aqueous Zinc Batteries.

The surging demand for environmental-friendly and safe electrochemical energy storage systems has driven the development of aqueous zinc (Zn)-ion batteries (ZIBs). However, metallic Zn anodes suffer from severe dendrite growth and large volume change, resulting in a limited lifetime for aqueous ZIB applications. Here, it is shown that 3D mesoporous carbon (MC) with controlled carbon and defect configurations can function as a highly reversible and dendrite-free Zn host, enabling the stable operation of aqueous ZIBs. The MC host has a structure-controlled architecture that contains optimal sp2 -carbon and defect sites, which results in an improved initial nucleation energy barrier and promotes uniform Zn deposition. As a consequence, the MC host shows outstanding Zn plating/stripping performance over 1000 cycles at 2 mA cm-2 and over 250 cycles at 6 mA cm-2 in asymmetric cells. Density functional theory calculations further reveal the role of the defective sp2 -carbon surface in Zn adsorption energy. Moreover, a full cell based on Zn@MC900 anode and V2 O5 cathode exhibits remarkable rate performance and cycling stability over 3500 cycles. These results establish a structure-mechanism-performance relationship of the carbon host as a highly reversible Zn anode for the reliable operation of ZIBs.

Continuous production of lipid nanoparticles by multiple-splitting in microfluidic devices with chaotic microfibrous channels.

Polydimethylsiloxane (PDMS) microfluidic devices with chaotic microfibrous channels were fabricated for the continuous production of lipid nanoparticles (LNPs). Electrospun poly(ε-caprolactone) (PCL) microfibrous matrices with different diameters (3.6 ± 0.3, 6.3 ± 0.4, and 12.2 ± 0.8 µm) were used as a template to develop microfibrous channels. The lipid solution (in ethanol) and water phase were introduced into the microfluidic device as the discontinuous and continuous phases, respectively. The smaller diameter of microfibrous channels and the higher flow rate of the continuous phase resulted in the smaller LNPs with a narrower size distribution. The multiple-splitting of the discontinuous phase and the microscale contact between the two phases in the microfibrous channels were the key features of the LNP production in our approach. The LNPs containing doxorubicin with different average sizes (89.7 ± 35.1 and 190.4 ± 66.4 nm) were prepared using the microfluidic devices for the potential application in tumor therapy. In vitro study revealed higher cellular uptake efficiency and cytotoxicity of the smaller LNPs, especially in the HepG2 cells. The microfluidic devices with microfibrous channels can be widely used as a continuous and high-throughput platform for the production of LNPs containing various active agents.

Fabrication of Microfiber-Templated Microfluidic Chips with Microfibrous Channels for High Throughput and Continuous Production of Nanoscale Droplets.

A polydimethylsiloxane (PDMS) microfluidic chip with well-interconnected microfibrous channels was fabricated by using an electrospun poly(ε-caprolactone) (PCL) microfibrous matrix and 3D-printed pattern as templates. The microfiber-templated microfluidic chip (MTMC) was used to produce nanoscale emulsions and spheres through multiple emulsification at many small micro-orifice junctions among microfibrous channels. The emulsion formation mechanisms in the MTMC were the cross-junction dripping or Y-junction splitting at the micro-orifice junctions. We demonstrated the high throughput and continuous production of water-in-oil emulsions and polyethylene glycol-diacrylate (PEG-DA) spheres with controlled size ranges from 2.84 µm to 83.6 nm and 1.03 µm to 45.7 nm, respectively. The average size of the water droplets was tuned by changing the micro-orifice diameter of the MTMC and the flow rate of the continuous phase. The MTMC theoretically produced 58 trillion PEG-DA nanospheres per hour without high shear force. In addition, we demonstrated the higher encapsulation efficiency of the PEG-DA microspheres in the MTMC than that of the microspheres fabricated by ultrasonication. The MTMC can be used as a powerful platform for the large-scale and continuous productions of emulsions and spheres.

Prolonged sitting-induced back pain influences abdominal muscle thickness in a sitting but not a supine position.

The current study explored whether (i) abdominal muscle thickness differed between non-painful supine and painful sitting positions and (ii) the sitting position was more reliable and useful than the supine position to discriminate between people with and without prolonged sitting-induced lower back pain (LBP). Participants with and without prolonged sitting-induced LBP participated. The thickness of the transversus abdominis (TrA), internal oblique (IO), and external oblique (EO) muscles was measured using ultrasonography in supine, usual sitting, and upright sitting positions. Analysis of variance was used to compare muscle thickness among the positions. Intraclass correlation coefficients and receiver operating characteristic curves were used to determine which position reliably identified between group. The group with LBP showed significantly greater EO muscle thickness than that without LBP only in the upright sitting position. In the group without LBP, the TrA thickness was significantly greater in the usual and upright sitting positions than in the supine position, but there was no significant difference in TrA thickness among three positions in LBP group. Only EO thickness in the upright sitting position significantly predicted prolonged sitting-induced LBP. The current study suggests that clinicians should assess abdominal activation patterns in the upright sitting rather than supine position before applying abdominal muscle motor control training for patients with prolonged sitting-induced LBP, and to distinguish between those with and without prolonged sitting-induced LBP.

Incorporating age and delay into models for biophysical systems.

In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have been used widely. However, some biophysical processes such as gene transcription and translation are known to have a significant gap between the initiation and the completion of the processes, which renders the usual assumption of exponential distribution untenable. In this paper, we consider relaxing this assumption by incorporating age-dependent random time delays (distributed according to a given probability distribution) into the system dynamics. We do so by constructing a measure-valued Markov process on a more abstract state space, which allows us to keep track of the 'ages' of molecules participating in a chemical reaction. We study the large-volume limit of such age-structured systems. We show that, when appropriately scaled, the stochastic system can be approximated by a system of partial differential equations (PDEs) in the large-volume limit, as opposed to ordinary differential equations (ODEs) in the classical theory. We show how the limiting PDE system can be used for the purpose of further model reductions and for devising efficient simulation algorithms. In order to describe the ideas, we use a simple transcription process as a running example. We, however, note that the methods developed in this paper apply to a wide class of biophysical systems.

Dried blood spots: Effects of less than optimal collection, shipping time, heat, and humidity.

OBJECTIVES: This study investigates how factors related to collection, storage, transport time, and environmental conditions affect the quality and accuracy of analyses of dried blood spot (DBS) samples. METHODS: Data come from the 2016 Health and Retirement Study (HRS) DBS laboratory reports and the HRS merged with the National Climatic Data Center (NCDC) Global Historical Climate Network Daily (NCDC GHCN-Daily) and the NCDC Local Climatological Data, by zip code. We ran regression models to examine the associations between assay values based on DBS for five analytes (total cholesterol, high-density lipoprotein (HDL) cholesterol, glycosylated hemoglobin (HbA1c), C-reactive protein (CRP), and cystatin C) and the characteristics of DBS cards and drops, shipping time, and temperature, and humidity at the time of collection. RESULTS: We found cholesterol measures to be sensitive to many factors including small spots, shipping time, high temperature and humidity. Small spots in DBS cards are related to lower values across all analytes. Longer DBS transit time before freezing is associated with lower values of total and HDL cholesterol and cystatin C. Results were similar whether or not venous blood sample values were included in equations. CONCLUSIONS: Small spots, long shipping time, and exposure to high temperature and humidity need to be avoided if possible. Quality of spots and cards and information on shipping time and conditions should be coded with the data to make adjustments in values when necessary. The different results across analytes indicate that results cannot be generalized to all DBS assays.

Multiscale Stochastic Reaction-Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations.

Two multiscale algorithms for stochastic simulations of reaction-diffusion processes are analysed. They are applicable to systems which include regions with significantly different concentrations of molecules. In both methods, a domain of interest is divided into two subsets where continuous-time Markov chain models and stochastic partial differential equations (SPDEs) are used, respectively. In the first algorithm, Markov chain (compartment-based) models are coupled with reaction-diffusion SPDEs by considering a pseudo-compartment (also called an overlap or handshaking region) in the SPDE part of the computational domain right next to the interface. In the second algorithm, no overlap region is used. Further extensions of both schemes are presented, including the case of an adaptively chosen boundary between different modelling approaches.

Monitoring Glutathione Dynamics and Heterogeneity in Living Stem Cells.

Glutathione (GSH) is a major antioxidant in cells, and plays vital roles in the cellular defense against oxidants and in the regulation of redox signals. In a previous report, we demonstrated that stem cell function is critically affected by heterogeneity and dynamic changes in cellular GSH concentration. Here, we present a detailed protocol for the monitoring of GSH concentration in living stem cells using FreSHtracer, a real-time GSH probe. We describe the steps involved in monitoring GSH concentration in single living stem cells using confocal microscopy and flow cytometry. These methods are simple, rapid, and quantitative, and able to demonstrate intracellular GSH concentration changes in real time. We also describe the application of FreSHtracer to the sorting of stem cells according to their GSH content using flow cytometry. Typically, microscopic or flow cytometric analyses of FreSHtracer and MitoFreSHtracer signals in living stem cells take ~2~3 h, and the fractionation of stem cells into subpopulations on the basis of cellular GSH levels takes 3~4.5 h. This method could be applied to almost every kind of mammalian cell with minor modifications to the protocol described here.

Comparison of Deterministic and Stochastic Regime in a Model for Cdc42 Oscillations in Fission Yeast.

Oscillations occur in a wide variety of essential cellular processes, such as cell cycle progression, circadian clocks and calcium signaling in response to stimuli. It remains unclear how intrinsic stochasticity can influence these oscillatory systems. Here, we focus on oscillations of Cdc42 GTPase in fission yeast. We extend our previous deterministic model by Xu and Jilkine to construct a stochastic model, focusing on the fast diffusion case. We use SSA (Gillespie's algorithm) to numerically explore the low copy number regime in this model, and use analytical techniques to study the long-time behavior of the stochastic model and compare it to the equilibria of its deterministic counterpart. Numerical solutions suggest noisy limit cycles exist in the parameter regime in which the deterministic system converges to a stable limit cycle, and quasi-cycles exist in the parameter regime where the deterministic model has a damped oscillation. Near an infinite period bifurcation point, the deterministic model has a sustained oscillation, while stochastic trajectories start with an oscillatory mode and tend to approach deterministic steady states. In the low copy number regime, metastable transitions from oscillatory to steady behavior occur in the stochastic model. Our work contributes to the understanding of how stochastic chemical kinetics can affect a finite-dimensional dynamical system, and destabilize a deterministic steady state leading to oscillations.

Quasi-Steady-State Approximations Derived from the Stochastic Model of Enzyme Kinetics.

The paper outlines a general approach to deriving quasi-steady-state approximations (QSSAs) of the stochastic reaction networks describing the Michaelis-Menten enzyme kinetics. In particular, it explains how different sets of assumptions about chemical species abundance and reaction rates lead to the standard QSSA, the total QSSA, and the reverse QSSA. These three QSSAs have been widely studied in the literature in deterministic ordinary differential equation settings, and several sets of conditions for their validity have been proposed. With the help of the multiscaling techniques introduced in Ball et al. (Ann Appl Probab 16(4):1925-1961, 2006), Kang and Kurtz (Ann Appl Probab 23(2):529-583, 2013), it is seen that the conditions for deterministic QSSAs largely agree (with some exceptions) with the ones for stochastic QSSAs in the large-volume limits. The paper also illustrates how the stochastic QSSA approach may be extended to more complex stochastic kinetic networks like, for instance, the enzyme-substrate-inhibitor system.

A Mathematical Model for Enzyme Clustering in Glucose Metabolism.

We have recently demonstrated that the rate-limiting enzymes in human glucose metabolism organize into cytoplasmic clusters to form a multienzyme complex, the glucosome, in at least three different sizes. Quantitative high-content imaging data support a hypothesis that the glucosome clusters regulate the direction of glucose flux between energy metabolism and building block biosynthesis in a cluster size-dependent manner. However, direct measurement of their functional contributions to cellular metabolism at subcellular levels has remained challenging. In this work, we develop a mathematical model using a system of ordinary differential equations, in which the association of the rate-limiting enzymes into multienzyme complexes is included as an essential element. We then demonstrate that our mathematical model provides a quantitative principle to simulate glucose flux at both subcellular and population levels in human cancer cells. Lastly, we use the model to simulate 2-deoxyglucose-mediated alteration of glucose flux in a population level based on subcellular high-content imaging data. Collectively, we introduce a new mathematical model for human glucose metabolism, which promotes our understanding of functional roles of differently sized multienzyme complexes in both single-cell and population levels.

Robustness and period sensitivity analysis of minimal models for biochemical oscillators.

Biological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

Using a guide template with a handpiece sleeve to locate the abutment screw position of a cement-retained implant restoration.

The existing techniques for drilling a screw access hole in cement-retained restorations are limited by inaccurate drill guidance and ineffective cooling of the drilling area. An approach for fabricating a guide template to provide screw retrievability using computer-aided design and computer-aided manufacturing (CAD/CAM) is described. A handpiece sleeve was made by 3-dimensional printing and incorporating it into a vacuum-formed template. The handpiece sleeve not only guides the head of the handpiece accurately but also enables the cooling water to reach the area of drilling directly.

Stochastic analysis of reaction-diffusion processes.

Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartment size for simulating reaction-diffusion systems and introduce a measure of fluctuations in a discretized system. We then describe a new computational algorithm for implementing a modified Gillespie method for compartmental systems in which reactions are aggregated into equivalence classes and computational cells are searched via an optimized tree structure. Finally, we discuss several examples that illustrate the issues that have to be addressed in general systems.

Empirical application of empathy enhancing program based on movement concept for married couples in conflict.

In the field of marital therapy, it is known that couple movement program helps married couples faced with conflict situation to rebuild the relationship and to maintain a family homeostasis. The purpose of this study was to configure and apply the kinesthetic empathy program and to assess the effectiveness for married couples in conflict. To achieve the research aims, qualitative research method has been conducted, subjecting three couples, 6 people, who are participating in expressive movement program for this study. The study used focus group interview method for collecting date and employed for the interview method by mixing the semi-structured and unstructured questionnaire. The results were followings. First, through kinesthetic empathy enhancing program, one could develop self-awareness and emotional attunement. Second, the result showed the relationship between intention and empathy. It shows that "knowing spouse's hidden intention" is significant factors to understand others. Third, kinesthetic empathy program could complement general marriage counseling program. The results of this study provide empirical evidence that movement program functions as an empathy enhancer through the process of perceiving, feeling, thinking, and interacting with others.

A mathematical model for microRNA in lung cancer.

Lung cancer is the leading cause of cancer-related deaths worldwide. Lack of early detection and limited options for targeted therapies are both contributing factors to the dismal statistics observed in lung cancer. Thus, advances in both of these areas are likely to lead to improved outcomes. MicroRNAs (miRs or miRNAs) represent a class of non-coding RNAs that have the capacity for gene regulation and may serve as both diagnostic and prognostic biomarkers in lung cancer. Abnormal expression patterns for several miRNAs have been identified in lung cancers. Specifically, let-7 and miR-9 are deregulated in both lung cancers and other solid malignancies. In this paper, we construct a mathematical model that integrates let-7 and miR-9 expression into a signaling pathway to generate an in silico model for the process of epithelial mesenchymal transition (EMT). Simulations of the model demonstrate that EGFR and Ras mutations in non-small cell lung cancers (NSCLC), which lead to the process of EMT, result in miR-9 upregulation and let-7 suppression, and this process is somewhat robust against random input into miR-9 and more strongly robust against random input into let-7. We elected to validate our model in vitro by testing the effects of EGFR inhibition on downstream MYC, miR-9 and let-7a expression. Interestingly, in an EGFR mutated lung cancer cell line, treatment with an EGFR inhibitor (Gefitinib) resulted in a concentration specific reduction in c-MYC and miR-9 expression while not changing let-7a expression. Our mathematical model explains the signaling link among EGFR, MYC, and miR-9, but not let-7. However, very little is presently known about factors that regulate let-7. It is quite possible that when such regulating factors become known and integrated into our model, they will further support our mathematical model.

A multiscale approximation in a heat shock response model of E. coli.

BACKGROUND: A heat shock response model of Escherichia coli developed by Srivastava, Peterson, and Bentley (2001) has multiscale nature due to its species numbers and reaction rate constants varying over wide ranges. Applying the method of separation of time-scales and model reduction for stochastic reaction networks extended by Kang and Kurtz (2012), we approximate the chemical network in the heat shock response model. RESULTS: Scaling the species numbers and the rate constants by powers of the scaling parameter, we embed the model into a one-parameter family of models, each of which is a continuous-time Markov chain. Choosing an appropriate set of scaling exponents for the species numbers and for the rate constants satisfying balance conditions, the behavior of the full network in the time scales of interest is approximated by limiting models in three time scales. Due to the subset of species whose numbers are either approximated as constants or are averaged in terms of other species numbers, the limiting models are located on lower dimensional spaces than the full model and have a simpler structure than the full model does. CONCLUSIONS: The goal of this paper is to illustrate how to apply the multiscale approximation method to the biological model with significant complexity. We applied the method to the heat shock response model involving 9 species and 18 reactions and derived simplified models in three time scales which capture the dynamics of the full model. Convergence of the scaled species numbers to their limit is obtained and errors between the scaled species numbers and their limit are estimated using the central limit theorem.