A mathematical model for HIV dynamics with multiple infections: implications for immune escape.

Multiple infections enable the recombination of different strains, which may contribute to viral diversity. How multiple infections affect the competition dynamics between the two types of strains, the wild and the immune escape mutant, remains poorly understood. This study develops a novel mathematical model that includes the two strains, two modes of viral infection, and multiple infections. For the representative double-infection case, the reproductive numbers are derived and global stabilities of equilibria are obtained via the Lyapunov direct method and theory of limiting systems. Numerical simulations indicate similar viral dynamics regardless of multiplicities of infections though the competition between the two strains would be the fiercest in the case of quadruple infections. Through sensitivity analysis, we evaluate the effect of parameters on the set-point viral loads in the presence and absence of multiple infections. The model with multiple infections predict that there exists a threshold for cytotoxic T lymphocytes (CTLs) to minimize the overall viral load. Weak or strong CTLs immune response can result in high overall viral load. If the strength of CTLs maintains at an intermediate level, the fitness cost of the mutant is likely to have a significant impact on the evolutionary dynamics of mutant viruses. We further investigate how multiple infections alter the viral dynamics during the combination antiretroviral therapy (cART). The results show that viral loads may be underestimated during cART if multiple-infection is not taken into account.

Dual Molecules Cooperatively Confined In-Between Edge-oxygen-rich Graphene Sheets as Ultrahigh Rate and Stable Electrodes for Supercapacitors.

Noncovalent modification of carbon materials with redox-active organic molecules has been considered as an effective strategy to improve the electrochemical performance of supercapacitors. However, their low loading mass, slow electron transfer rate, and easy dissolution into the electrolyte greatly limit further practical applications. Herein, this work reports dual molecules (1,5-dihydroxyanthraquinone (DHAQ) and 2,6-diamino anthraquinone (DAQ)) cooperatively confined in-between edge-oxygen-rich graphene sheets as high-performance electrodes for supercapacitors. Cooperative electrostatic-interaction on the edge-oxygen sites and π-π interaction in-between graphene sheets lead to the increased loading mass and structural stability of dual molecules. Moreover, the electron tunneling paths constructed between edge-oxygen groups and dual molecules can effectively boost the electron transfer rate and redox reaction kinetics, especially at ultrahigh current densities. As a result, the as-obtained electrode exhibits a high capacitance of 507 F g-1 at 0.5 A g-1 , and an unprecedented rate capability (203 F g-1 at 200 A g-1 ). Moreover, the assembled symmetrical supercapacitor achieves a high energy density of 17.1 Wh kg-1 and an ultrahigh power density of 140 kW kg-1 , as well as remarkable stability with a retention of 86% after 50 000 cycles. This work may open a new avenue for the efficient utilization of organic materials in energy storage and conversion.

A cell model about symmetric and asymmetric stem cell division.

We construct a multi-stage cell lineage model including self-renewal, apoptosis, cell movement and the symmetrical/asymmetrical division of stem cells. The evolution of cell populations can be described by coupled reaction-diffusion partial differential equations, and the propagating wavefront speeds can be obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effect of symmetric/asymmetric division of stem cells on the population and propagating dynamics of cell lineage. It is found that stem cells' asymmetric cell division (ACD) can move the phase boundary of the homogenous solution of the system. The population of the cell lineage will be promoted in presence of ACD. The concentration of stem cells increases with ACD but that of differentiated daughter cells decreases with ACD. In addition, it is found that the propagating speed of the stem cells can be evaluated with ACD. When the daughter cells move fast to a new space, stem cells can catch them up through increasing ACD. Our results may suggest a mechanism of collective migration of cell lineage through cooperation between ACD of stem cells and fast diffusion of the daughter cells.

HIV infection dynamics and viral rebound: Modeling results from humanized mice.

Despite years of combined antiretroviral therapy (cART), HIV persists in infected individuals. The virus also rebounds after the cessation of cART. The sources contributing to viral persistence and rebound are not fully understood. When viral rebound occurs, what affects the time to rebound and how to delay the rebound remain unclear. In this paper, we started with the data fitting of an HIV infection model to the viral load data in treated and untreated humanized myeloid-only mice (MoM) in which macrophages serve as the target of HIV infection. By fixing the parameter values for macrophages from the MoM fitting, we fit a mathematical model including the infection of two target cell populations to the viral load data from humanized bone marrow/liver/thymus (BLT) mice, in which both CD4+ T cells and macrophages are the target of HIV infection. Data fitting suggests that the viral load decay in BLT mice under treatment has three phases. The loss of infected CD4+ T cells and macrophages is a major contributor to the first two phases of viral decay, and the last phase may be due to the latent infection of CD4+ T cells. Numerical simulations using parameter estimates from the data fitting show that the pre-ART viral load and the latent reservoir size at treatment cessation can affect viral growth rate and predict the time to viral rebound. Model simulations further reveal that early and prolonged cART can delay the viral rebound after cessation of treatment, which may have implications in the search for functional control of HIV infection.

Modeling HIV multiple infection.

Multiple infection of target cells by human immunodeficiency virus (HIV) may lead to viral escape from host immune responses and drug resistance to antiretroviral therapy, bringing more challenges to the control of infection. The mechanisms underlying HIV multiple infection and their relative contributions are not fully understood. In this paper, we develop and analyze a mathematical model that includes sequential cell-free virus infection (i.e.one virus is transmitted each time in a sequential infection of target cells by virus) and cell-to-cell transmission (i.e.multiple viral genomes are transmitted simultaneously from infected to uninfected cells). By comparing model prediction with the distribution data of proviral genomes in HIV-infected spleen cells, we find that multiple infection can be well explained when the two modes of viral transmission are both included. Numerical simulation using the parameter estimates from data fitting shows that the majority of T cell infections are attributed to cell-to-cell transmission and this transmission mode also accounts for more than half of cell's multiple infections. These results suggest that cell-to-cell transmission plays a critical role in forming HIV multiple infection and thus has important implications for HIV evolution and pathogenesis.

Dynamics of a new HIV model with the activation status of infected cells.

The activation status can dictate the fate of an HIV-infected CD4+ T cell. Infected cells with a low level of activation remain latent and do not produce virus, while cells with a higher level of activation are more productive and thus likely to transfer more virions to uninfected cells during cell-to-cell transmission. How the activation status of infected cells affects HIV dynamics under antiretroviral therapy remains unclear. We develop a new mathematical model that structures the population of infected cells continuously according to their activation status. The effectiveness of antiretroviral drugs in blocking cell-to-cell viral transmission decreases as the level of activation of infected cells increases because the more virions are transferred from infected to uninfected cells during cell-to-cell transmission, the less effectively the treatment is able to inhibit the transmission. The basic reproduction number [Formula: see text] of the model is shown to determine the existence and stability of the equilibria. Using the principal spectral theory and comparison principle, we show that the infection-free equilibrium is locally and globally asymptotically stable when [Formula: see text] is less than one. By constructing Lyapunov functional, we prove that the infected equilibrium is globally asymptotically stable when [Formula: see text] is greater than one. Numerical investigation shows that even when treatment can completely block cell-free virus infection, virus can still persist due to cell-to-cell transmission. The random switch between infected cells with different activation levels can also contribute to the replenishment of the latent reservoir, which is considered as a major barrier to viral eradication. This study provides a new modeling framework to study the observations, such as the low viral load persistence, extremely slow decay of latently infected cells and transient viral load measurements above the detection limit, in HIV-infected patients during suppressive antiretroviral therapy.

Dynamics of task allocation in social insect colonies: scaling effects of colony size versus work activities.

The mechanisms through which work is organized are central to understanding how complex systems function. Previous studies suggest that task organization can emerge via nonlinear dynamical processes wherein individuals interact and modify their behavior through simple rules. However, there is very limited theory about how those processes are shaped by behavioral variation within social groups. In this work, we propose an adaptive modeling framework on task allocation by incorporating variation both in task performance and task-related metabolic rates. We study the scaling effects of colony size on the resting probability as well as task allocation. We also numerically explore the effects of stochastic noise on task allocation in social insect colonies. Our theoretical and numerical results show that: (a) changes in colony size can regulate the probability of colony resting and the allocation of tasks, and the direction of regulation depends on the nonlinear metabolic scaling effects of tasks; (b) increased response thresholds may cause colonies to rest in varied patterns such as periodicity. In this case, we observed an interesting bubble phenomenon in the task allocation of social insect colonies for the first time; (c) stochastic noise can cause work activities and task demand to fluctuate within a range, where the amplitude of the fluctuation is positively correlated with the intensity of noise.

Tin Nanodots Derived From Sn2+ /Graphene Quantum Dot Complex as Pillars into Graphene Blocks for Ultrafast and Ultrastable Sodium-Ion Storage.

Tin (Sn) is considered to be an ideal candidate for the anode of sodium ion batteries. However, the design of Sn-based electrodes with maintained long-term stability still remains challenging due to their huge volume expansion (≈420%) and easy pulverization during cycling. Herein, a facile and versatile strategy for the synthesis of nitrogen-doped graphene quantum dot (GQD) edge-anchored Sn nanodots as the pillars into reduced graphene oxide blocks (NGQD/Sn-NG) for ultrafast and ultrastable sodium-ion storage is reported. Sn nanodots (2-5 nm) anchored at the edges of "octopus-like" GQDs via covalent SnOC/SnNC bonds function as the pillars that ensure fast Na-ion/electron transport across the graphene blocks. Moreover, the chemical and spatial (layered structure) confinements not only suppress Sn aggregation, but also function as physical barriers for buffering volume change upon sodiation/desodiation. Consequently, the NGQD/Sn-NG with high structural stability exhibits excellent rate performance (555 mAh g-1 at 0.1 A g-1 and 198 mAh g-1 at 10 A g-1 ) and ultra-long cycling stability (184 mAh g-1 remaining even after 2000 cycles at 5 A g-1 ). The confinement-induced synthesis together with remarkable electrochemical performances should shed light on the practical application of highly attractive tin-based anodes for next generation rechargeable sodium batteries.

Modeling the role of macrophages in HIV persistence during antiretroviral therapy.

HIV preferentially infects activated CD4+ T cells. Current antiretroviral therapy cannot eradicate the virus. Viral infection of other cells such as macrophages may contribute to viral persistence during antiretroviral therapy. In addition to cell-free virus infection, macrophages can also get infected when engulfing infected CD4+ T cells as innate immune sentinels. How macrophages affect the dynamics of HIV infection remains unclear. In this paper, we develop an HIV model that includes the infection of CD4+ T cells and macrophages via cell-free virus infection and cell-to-cell viral transmission. We derive the basic reproduction number and obtain the local and global stability of the steady states. Sensitivity and viral dynamics simulations show that even when the infection of CD4+ T cells is completely blocked by therapy, virus can still persist and the steady-state viral load is not sensitive to the change of treatment efficacy. Analysis of the relative contributions to viral replication shows that cell-free virus infection leads to the majority of macrophage infection. Viral transmission from infected CD4+ T cells to macrophages during engulfment accounts for a small fraction of the macrophage infection and has a negligible effect on the total viral production. These results suggest that macrophage infection can be a source contributing to HIV persistence during suppressive therapy. Improving drug efficacies in heterogeneous target cells is crucial for achieving HIV eradication in infected individuals.

Monotone dynamics and global behaviors of a West Nile virus model with mosquito demographics.

In this paper a mathematical model is formulated to study transmission dynamics of West Nile virus (WNv), which incorporates mosquito demographics including pair formation, metamorphic stages and intraspecific competition. The global behaviors of the model are obtained from a geometric approach and theory of monotone dynamics, even though bistability is present due to backward bifurcation. It turns out that the model can be investigated through two auxiliary subsystem, which are cooperative and K-competitive, respectively. Together with implement of compound matrices and Poincaré-Bendixson theorem, a thorough classification of dynamics of the full model is characterized by mosquito reproduction number [Formula: see text], WNv reproduction number [Formula: see text] and a bistability subthreshold [Formula: see text]. The theoretical results show that if [Formula: see text] is not greater than 1, mosquitoes will not survive, and the WNv will die out; if [Formula: see text] is greater than 1, then mosquitoes will persist, and disease may prevail or vanish depending on basin of attraction of the local attractors which are singletons. Our method in this paper can be applied to other mosquito-borne diseases such as malaria, dengue fever which have a similar monotonicity.

COMPUTATION OF ℛ IN AGE-STRUCTURED EPIDEMIOLOGICAL MODELS WITH MATERNAL AND TEMPORARY IMMUNITY.

For infectious diseases such as pertussis, susceptibility is determined by immunity, which is chronological age-dependent. We consider an age-structured epidemiological model that accounts for both passively acquired maternal antibodies that decay and active immunity that wanes, permitting reinfection. The model is a 6-dimensional system of partial differential equations (PDE). By assuming constant rates within each age-group, the PDE system can be reduced to an ordinary differential equation (ODE) system with aging from one age-group to the next. We derive formulae for the effective reproduction number ℛ and provide their biological interpretation in some special cases. We show that the disease-free equilibrium is stable when ℛ < 1 and unstable if ℛ > 1.

Pre-dry heat treatment alters the structure and ultimate in vitro digestibility of wheat starch-lipids complex in hot-extrusion 3D printing.

Herein, we proposed dry heat treatment (DHT) as a pre-treatment method for modifying printed materials, with a particular focus on its application in the control of starch-lipid interactions during hot-extrusion 3D printing (HE-3DP). The results showed that pre-DHT could promote the complexation of wheat starch (WS) and oleic acid (OA)/corn oil (CO) during HE-3DP and thus increase the resistant starch (RS) content. From the structural perspectives, pre-DHT could break starch molecular chains into lower relative molecular weight which enhanced the starch-lipids hydrophobic interactions to form the V-type crystalline structure during HE-3DP. Notably, pre-DHT could also induce the formation of complexed structure which was maintained during HE-3DP. Compared with CO, OA with linear hydrophobic chains was easier to enter the spiral cavity of starch to form more ordered structures, resulting in higher RS content of 27.48 %. Overall, the results could provide basic data for designing nutritional starchy food systems by HE-3DP.

Effect of active carbonyl-carboxyl ratio on dynamic Schiff base crosslinking and its modulation of high-performance oxidized starch-chitosan hydrogel by hot extrusion 3D printing.

The quest to develop 3D starch-based printing hydrogels for the controlled release of active substances with excellent mechanical and printing properties has gained significant attention. This work introduced a facile method based on crosslinking via Schiff base reaction for preparing bicomponent hydrogels. The method involved the utilization of customizable oxidized starch (OS) and chitosan (CS), enabling superior printing performance through the precise control of various active carbonyl-carboxyl ratios (ACR, 2:1, 1:1, and 2:3, respectively) of OS. OS-CS hydrogel (OSC) with an ACR level of 2:1 (OS-2-y%CS) underwent rearrangement during printing environment, fostering increased Schiff base reaction with a higher crosslinking degree and robust high structural recovery (>95 %). However, with decreasing ACR levels (from 2:1 to 2:3), the printing performance and mechanical strength of printed OSC (POSC) declined due to lower Schiff base bonds and increased phase separation. Compared with printed OS, POS-2-2%CS exhibited a remarkable 1250.52 % increase in tensile strength and a substantial 2424.71 % boost in compressive strength, enhanced shape fidelity and notable self-healing properties. Moreover, POS-2-2%CS exhibited stable diffusive drug release, showing potential application in the pH-responsive release of active substances. Overall, controlling the active carbonyl-carboxyl ratios provided an efficient and manageable approach for preparing high-performance 3D-printed hydrogels.

Threshold behaviour of a stochastic SIRS Le´vy jump model with saturated incidence and vaccination.

A stochastic SIRS system with $ \mathrm {L\acute{e}vy} $ process is formulated in this paper, and the model incorporates the saturated incidence and vaccination strategies. Due to the introduction of $ \mathrm {L\acute{e}vy} $ jump, the jump stochastic integral process is a discontinuous martingale. Then the Kunita's inequality is used to estimate the asymptotic pathwise of the solution for the proposed model, instead of Burkholder-Davis-Gundy inequality which is suitable for continuous martingales. The basic reproduction number $ R_{0}^{s} $ of the system is also derived, and the sufficient conditions are provided for the persistence and extinction of SIRS disease. In addition, the numerical simulations are carried out to illustrate the theoretical results. Theoretical and numerical results both show that $ \mathrm {L\acute{e}vy} $ process can suppress the outbreak of the disease.

Towards a new combination therapy with vectored immunoprophylaxis for HIV: Modeling "shock and kill" strategy.

Latently infected cells are considered as a major barrier to curing Human Immunodeficiency Virus (HIV) infection. Reactivation of latently infected cells followed by killing the actively infected cells may be a potential strategy ("shock and kill") to purge the latent reservoir. Based on vectored immunoprophylaxis (VIP) experiment that can elicit bNAbs, in this paper a mathematical model is formulated to explore the efficacy of "shock and kill" strategy with VIP. We derive the basic reproduction number R0 of the model and show that R0 completely determines the dynamics of the model: if R0<1, the disease-free equilibrium is globally asymptotically stable; if R0>1, the system is uniformly persistent. Numerical simulations suggest that the "shock and kill" strategy with VIP can effectively control HIV infection while this strategy cannot eradicate the reservoir without VIP although it can alleviate the HIV infection. To model the administration of drugs and vaccine more realistically, pharmacokinetics and pulse vaccination are incorporated into the model of ordinary differential equations. The resultants are described by impulsive differential equations. The thresholds are obtained for the frequency and strength of the vaccination to eliminate the viruses. Furthermore, the most appropriate times are numerically investigated for starting a short-term latency-reversing agents (LRAs) treatment relative to ART considering the toxicity of LRAs. The results show that LRAs treatment at the beginning of ART might be a better option. These results have important implications for the design of HIV cure-related clinical trials.

Starch-guar gum-ferulic acid molecular interactions alter the ordered structure and ultimate retrogradation properties and in vitro digestibility of chestnut starch under extrusion treatment.

Molecular interactions among starch and multiple-components during food processing determine the retrogradation properties and digestibility of starch. Here, the effects of starch-guar gum (GG)-ferulic acid (FA) molecular interactions on retrogradation properties, digestibility and ordered structural changes of chestnut starch (CS) under extrusion treatment (ET) were investigated by structural analysis and quantum chemistry. Due to the entanglement behaviors and hydrogen bond interactions, GG could inhibit the formation of helical and crystalline structures of CS. When FA was introduced simultaneously, FA could weaken the interactions between GG and CS as well as enter the spiral cavity of starch to increase the single/double helix and V-type crystalline structures while reducing A-type crystalline. Based on the above structural changes, ET with starch-GG-FA molecular interactions resulted in resistant starch content of 20.31% and anti-retrogradation rate of 42.98% for 21-day storage. Overall, the results could provide basic data for creation of chestnut-based food with higher value.

Introduction of chlorogenic acid into thermal processed starch- oleic acid system controls the ordered structure and inhibits oleic acid oxidation through molecular interactions.

In this study, the effects of starch- oleic acid (OA)- chlorogenic acid (CA) molecular interaction on OA oxidation during thermal processing were investigated based on structural analysis, oxidation characteristics and quantum calculations. The results showed that in the ternary system, on the one hand, OA could enter the spiral cavity of starch through hydrophobic forces and form V-type crystalline structure, which delayed its oxidation. On the other hand, CA could further inhibit the oxidation of OA through free radical reaction and did not affect the molecular interactions between OA and starch due to the steric hindrance and hydrophily. Notably, starch-OA-CA interactions could effectively decrease total oxidation value (19.07), prolong the induction time of oxidation (114.6 min) and reduce the abundance of oxidation products through hydrogen atom transfer reactions with active phenolic hydroxyl to protect the α-methylene groups at C=C. Overall, these results provided insights into functional property regulation by the interaction of starch-based multi-component systems.

3D printing-mediated microporous starch hydrogels for wound hemostasis.

Starch hydrogels with biodegradability and cytocompatibility are good alternatives to traditional dressings. Herein, oxidized starch hydrogel loaded with coagulation factor Ca2+ ions (CaOMS) is successfully constructed by green hot-extrusion 3D printing technology (HE-3DP). In vitro study demonstrated the good water absorbing capacity (845.15-1194.20%) and blood cell and platelet adhesion of CaOMS to assist hemostasis owing to the boosted network structure density, gel strength, and the release of activated Ca2+ ions. More importantly, in vivo experiments further demonstrated CaOMS could maintain the weight loss caused by blood loss from wounds and has excellent hemostatic (65 s) and wound healing properties by promoting the secretion of epidermal growth factor (EGF) and vascular endothelial growth factor (VEGF) expression. The advantages of CaOMS, including rapid and effective hemostasis, effective wound healing, low cost, easy usage, and adaptability to fit various wound shapes, make it a promising biomaterial for achieving fast hemostasis and wound healing.

Weighted Gene Co-Expression Network Analysis to Explore Hub Genes of Resveratrol Biosynthesis in Exocarp and Mesocarp of 'Summer Black' Grape.

Resveratrol is a polyphenol compound beneficial to human health, and its main source is grapes. In the present study, the molecular regulation of resveratrol biosynthesis in developing grape berries was investigated using weighted gene co-expression network analysis (WGCNA). At the same time, the reason for the resveratrol content difference between grape exocarp (skin) and mesocarp (flesh) was explored. Hub genes (CHS, STS, F3'5'H, PAL, HCT) related to resveratrol biosynthesis were screened with Cytoscape software. The expression level of hub genes in the exocarp was significantly higher than that in the mesocarp, and the expressions of the hub genes and the content of resveratrol in exocarp peaked at the maturity stage. While the expression levels of PAL, CHS and STS in the mesocarp, reached the maximum at the maturity stage, and F3'5'H and HCT decreased. These hub genes likely play a key role in resveratrol biosynthesis. Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analysis further indicated that resveratrol biosynthesis was related to flavonoid biosynthesis, phenylalanine metabolism, phenylpropanoid biosynthesis, and stilbene biosynthesis pathways. This study has theoretical significance for exploring genes related to resveratrol biosynthesis in the exocarp and mesocarp of grapes, and provides a theoretical basis for the subsequent function and regulatory mechanism of hub genes.

Metal-organic framework-mediated construction of confined ultrafine nickel phosphide immobilized in reduced graphene oxide with excellent cycle stability for asymmetric supercapacitors.

Transition metal phosphides (TMPs) with unique metalloid features have been promised great application potential in developing high-efficiency electrode materials for electrochemical energy storage. Nevertheless, sluggish ion transportation and poor cycling stability are the critical hurdles limiting their application prospects. Herein, we presented the metal-organic framework-mediated construction of ultrafine Ni2P immobilized in reduced graphene oxide (rGO). Nano-porous two-dimensional (2D) Ni-metal-organic framework (Ni-MOF) was grown on holey graphene oxide (Ni(BDC)-HGO), followed by MOF-mediated tandem pyrolysis (carbonization and phosphidation; Ni(BDC)-HGO-X-P, X denoted carbonization temperature and P represented phosphidation). Structural analysis revealed that the open-framework structure in Ni(BDC)-HGO-X-Ps had endowed them with excellent ion conductivity. The Ni2P wrapped by carbon shells and the PO bonds linking between Ni2P and rGO ensured the better structural stability of Ni(BDC)-HGO-X-Ps. The resulting Ni(BDC)-HGO-400-P delivered a capacitance of 2333.3 F g-1 at 1 A g-1 in a 6 M KOH aqueous electrolyte. More importantly, Ni(BDC)-HGO-400-P//activated carbon, the assembled asymmetric supercapacitor with an energy density of 64.5 Wh kg-1 and a power density of 31.7 kW kg-1, almost maintained its initial capacitance after 10,000 cycles. Furthermore, in situ electrochemical-Raman measurements were exploited to demonstrate the electrochemical changes of Ni(BDC)-HGO-400-P throughout the charging and discharging processes. This study has further shed light on the design rationality of TMPs for optimizing supercapacitor performance.