Understanding the Role of Environmental Transmission on COVID-19 Herd Immunity and Invasion Potential.

COVID-19 is caused by the SARS-CoV-2 virus, which is mainly transmitted directly between humans. However, it is observed that this disease can also be transmitted through an indirect route via environmental fomites. The development of appropriate and effective vaccines has allowed us to target and anticipate herd immunity. Understanding of the transmission dynamics and the persistence of the virus on environmental fomites and their resistive role on indirect transmission of the virus is an important scientific and public health challenge because it is essential to consider all possible transmission routes and route specific transmission strength to accurately quantify the herd immunity threshold. In this paper, we present a mathematical model that considers both direct and indirect transmission modes. Our analysis focuses on establishing the disease invasion threshold, investigating its sensitivity to both transmission routes and isolate route-specific transmission rate. Using the tau-leap algorithm, we perform a stochastic model simulation to address the invasion potential of both transmission routes. Our analysis shows that direct transmission has a higher invasion potential than that of the indirect transmission. As a proof of this concept, we fitted our model with early epidemic data from several countries to uniquely estimate the reproduction numbers associated with direct and indirect transmission upon confirming the identifiability of the parameters. As the indirect transmission possess lower invasion potential than direct transmission, proper estimation and necessary steps toward mitigating it would help reduce vaccination requirement.

Probing the Ionic Atmosphere and Hydration of the c-MYC i-Motif.

G-quadruplexes and i-motifs are noncanonical secondary structures of DNA that appear to play a number of regulatory roles in the genome with clear connection to disease. Characterization of the forces stabilizing these structures is necessary for developing an ability to induce G-quadruplex and/or i-motif structures at selected genomic loci in a controlled manner. We report here the results of pH-dependent acoustic and densimetric measurements and UV melting experiments at elevated pressures to scrutinize changes in hydration and ionic atmosphere accompanying i-motif formation by the C-rich DNA sequence from the promoter region of the human c-MYC oncogene [5'-d(TTACCCACCCTACCCACCCTCA)] (ODN). We also conducted pH-dependent acoustic and densimetric characterizations of two DNA molecules that are compositionally identical to ODN but do not adopt the i-motif conformation, 5'-d(CTCTCACCACACCACACCTCTC) (ODN1) and 5'-d(CACACTCCTCACCTCTCCACAC) (ODN2). Our results reveal that i-motif formation by ODN is not accompanied by changes in volume and compressibility. The volumetric similarity of the i-motif and coil states of ODN implies a fortuitous compensation between changes in the intrinsic and hydration contributions to volume and compressibility. Analysis of the pH-dependent volumetric profiles of ODN, ODN1, and ODN2, along with the data on volumetric changes accompanying the protonation of isolated cytosine and deoxycytidine, suggests that protonation of the cytosines in the oligonucleotides causes release of the majority if not all of their counterions to the bulk. Thus, in the i-motif conformation, the oligomer no longer acts as a polyelectrolyte insofar as counterions are concerned. We discuss the biological ramifications of our results.

Effect of Urea on G-Quadruplex Stability.

G-quadruplexes represent a class of noncanonical nucleic acid structures implicated in transcriptional regulation, cellular function, and disease. An understanding of the forces involved in stabilization and destabilization of the G-quadruplex conformation relative to the duplex or single-stranded conformation is a key to elucidating the biological role of G-quadruplex-based genomic switches and the quest for therapeutic means for controlled induction or suppression of a G-quadruplex at selected genomic loci. Solute-solvent interactions provide a ubiquitous and, in many cases, the determining thermodynamic force in maintaining and modulating the stability of nucleic acids. These interactions involve water as well as water-soluble cosolvents that may be present in the solution or in the crowded environment in the cell. We present here the first quantitative investigation of the effect of urea, a destabilizing cosolvent, on the conformational preferences of a G-quadruplex formed by the telomeric d[A(G3T2A)3G3] sequence (Tel22). At 20 mM NaCl and room temperature, Tel22 undergoes a two-state urea-induced unfolding transition. An increase in salt mitigates the deleterious effect of urea on Tel22. The urea m-value of Tel22 normalized per change in solvent-accessible surface area, ΔSA, is similar to those for other DNA and RNA structures while being several-fold larger than that of proteins. Our results suggest that urea can be employed as an analytical tool in thermodynamic characterizations of G-quadruplexes in a manner similar to the use of urea in protein studies. We emphasize the need for further studies involving a larger selection of G-quadruplexes varying in sequence, topology (parallel, antiparallel, hybrid), and molecularity (monomolecular, bimolecular, tetramolecular) to outline the advantages and the limits of the use of urea in G-quadruplex studies. A deeper understanding of the effect of solvent and cosolvents on the differential stability of the G-quadruplex and duplex conformations is a step toward elucidation of the modulating influence of different types of cosolvents on duplex-G-quadruplex molecular switches triggering genomic events.

Optimal control problems of mosquito-borne disease subject to changes in feeding behavior of Aedes mosquitoes.

Dengue viruses (DENV) are transmitted to humans by the bite of Aedes mosquitoes. It is known that dengue virus infection in Aedes aegypti female mosquitoes makes a change in the feeding behavior of the infected mosquitoes. In this study, using the forces of infection, we incorporated the effect of changes in the feeding behavior of mosquitoes into the standard vector-borne SIR-SI model. It has been proved that both a single-strain model and a two-strain model exhibit forward bifurcations. Moreover, optimal implementations of control with specific prevention measures for dengue transmission are analyzed. As a result we found that more implementation of controls on the secondary infection of humans should be considered for the behavioral changes in feeding of the infected mosquitoes.

Istamycin aminoglycosides profiling and their characterization in Streptomyces tenjimariensis ATCC 31603 culture using high-performance liquid chromatography with tandem mass spectrometry.

A high-performance liquid chromatography with electrospray ionization ion trap tandem mass spectrometry method was developed and validated for the robust profiling and characterization of biosynthetic congeners in the 2-deoxy-aminocyclitol istamycin pathway, from the fermentation broth of Streptomyces tenjimariensis ATCC 31603. Gradient elution on an Acquity CSH C18 column was performed with a gradient of 5 mM aqueous pentafluoropropionic acid and 50% acetonitrile. Sixteen natural istamycin congeners were profiled and quantified in descending order; istamycin A, istamycin B, istamycin A0 , istamycin B0 , istamycin B1 , istamycin A1 , istamycin C, istamycin A2 , istamycin C1 , istamycin C0 , istamycin X0 , istamycin A3 , istamycin Y0 , istamycin B3 , and istamycin FU-10 plus istamycin AP. In addition, a total of five sets of 1- or 3-epimeric pairs were chromatographically separated using a macrocyclic glycopeptide-bonded chiral column. The lower limit of quantification of istamycin-A present in S. tenjimariensis fermentation was estimated to be 2.2 ng/mL. The simultaneous identification of a wide range of 2-deoxy-aminocyclitol-type istamycin profiles from bacterial fermentation was determined for the first time by employing high-performance liquid chromatography with tandem mass spectrometry analysis and the separation of istamycin epimers.

Kinetic studies on recombinant UDP-glucose: sterol 3-O-ß-glycosyltransferase from Micromonospora rhodorangea and its bioconversion potential.

Kinetics of a recombinant uridine diphosphate-glucose: sterol glycosyltransferase from Micromonospora rhodorangea ATCC 27932 (MrSGT) were studied using a number of sterols (including phytosterols) as glycosyl acceptors. The lowest K m value and the highest catalytical efficiency (k cat/K m) were found when ß-sitosterol was the glycosyl acceptor in the enzymatic reaction. In contrast to the enzyme's flexibility toward the glycosyl acceptor substrate, this recombinant enzyme was highly specific to uridine diphosphate (UDP)-glucose as the donor substrate. Besides, the UDP-glucose-dependent MrSGT was able to attach one glucose moiety specifically onto the C-3 hydroxyl group of other phytosterols such as fucosterol and gramisterol, yielding stereo-specific fucosterol-3-O-ß-D-glucoside and gramisterol-3-O-ß-D-glucoside, respectively. Based on kinetic data obtained from the enzyme's reactions using five different sterol substrates, the significance of the alkene (or ethylidene) side chains on the C-24 position in the sterol scaffolds was described and the possible relationship between the substrate structure and enzyme activity was discussed. This is the first report on the enzymatic bioconversion of the above two phytosteryl 3-O-ß-glucosides, as well as on the discovery of a stereospecific bacterial SGT which can attach a glucose moiety in ß-conformation at the C-3 hydroxyl group of diverse sterols, thus highlighting the catalytic potential of this promiscuous glycosyltransferase to expand the structural diversity of steryl glucosides.

Thermodynamic linkage analysis of pH-induced folding and unfolding transitions of i-motifs.

We describe the pH-induced folding/unfolding transitions of i-motifs by a linkage thermodynamics-based formalism in terms of three pKa's of cytosines, namely, an apparent pKa in the unfolded conformation, pKau, and two apparent pKa's in the folded state, pKaf1 and pKaf2. For the 5'-TTACCCACCCTACCCACCCTCA-3' sequence from the human c-MYC oncogene promoter region, the values of pKau, pKaf1, and pKaf2 are 4.8, 6.0, and 3.6, respectively. With these pKa's, we calculate the differential number of protons bound to the folded and unfolded states as a function of pH. Analysis along these lines offers an alternative interpretation to the experimentally observed shift in the pH-induced unfolded-to-i-motif transitions to neutral pH in the presence of cosolvents and crowders.

Ionic Effects on VEGF G-Quadruplex Stability.

In a potassium solution, a modified 22-meric DNA sequence Pu22-T12T13 from a region proximal to the transcription initiation site of the human VEGF gene adopts a single parallel-stranded G-quadruplex conformation with a 1:4:1 loop-size arrangement. We measured the thermal stability, TM, of the K(+)-stabilized Pu22-T12T13 G-quadruplex as a function of stabilizing K(+) ions and nonstabilizing Cs(+) and TMA(+) ions. The thermal stability, TM, of the Pu22-T12T13 G-quadruplex increases with the concentration of the stabilizing potassium ions, while it sharply decreases upon the addition of the nonstabilizing cations. We interpret these results as underscoring the opposing effects of internal binding and counterion condensation on the stability of the Pu22-T12T13 G-quadruplex. While centrally bound ions stabilize the G-quadruplex conformation, counterion condensation destabilizes it, favoring the coil conformation. From the initial slopes of the dependences of TM on the concentration of Cs(+) and TMA(+) cations, we estimate that the deleterious effect of counterion condensation stems from roughly one extra counterion associated with the coil relative to the G-quadruplex state of Pu22-T12T13. The reduced accumulation of counterions around the G-quadruplex state of Pu22-T12T13 relative to its coil state is due to the low surface charge density of the G-quadruplex reflecting its structural characteristics. On the basis of the analysis of our data along with the results of a previous study, we propose that the differential effect of internally (stabilizing) and externally (destabilizing) bound cations may be a general feature of parallel intramolecular G-quadruplexes.

Effects of Salt on the Stability of a G-Quadruplex from the Human c-MYC Promoter.

In an atmosphere of potassium ions, a modified c-MYC NHE III1 sequence with two G-to-T mutations (MYC22-G14T/G23T) forms a highly stable parallel-stranded G-quadruplex. The G-quadruplex exhibits a steady increase in its melting temperature, T(M), with an increase in the concentration of the stabilizing cation K(+). On the other hand, an increase in the concentration of nonstabilizing Cs(+) or TMA(+) cations at a constant concentration of K(+) causes a sharp decline in T(M) followed by a leveling off at ∼200 mM Cs(+) or TMA(+). At 51 °C and 600 µM K(+), an increase in Cs(+) concentration from 0 to 800 mM leads to a complete unfolding of the G-quadruplex. These observations are consistent with the picture in which more counterions accumulate in the vicinity of the unfolded state of MYC22-G14T/G23T (nonspecific ion binding) than in that of the G-quadruplex state. We estimate that the unfolded state condenses one extra counterion compared to the G-quadruplex state. Taken together with our earlier results, our data suggest that sodium or potassium cations sequestered inside the central cavity stabilize the G-quadruplex conformation acting as specifically bound ligands. Nonspecifically bound (condensed) counterions may slightly stabilize, exert no influence (human telomeric G-quadruplexes), or strongly destabilize (MYC22-G14T/G23T) the G-quadruplex conformation. We offer a structural rationalization for the enhanced thermal stability of the MYC22-G14T/G23T G-quadruplex.

Optimal implementation of intervention strategies for elderly people with ludomania.

OBJECTIVES: Now-a-days gambling is growing especially fast among older adults. To control the gratuitous growth of gambling, well-analyzed scientific strategies are necessary. We tried to analyze the adequacy of the health of society mathematically through immediate treatment of patients with early prevention. METHODS: The model from Lee and Do was modified and control parameters were introduced. Pontryagin's Maximum Principle was used to obtain an optimal control strategy. RESULTS: Optimal control can be achieved through simultaneous use of the control parameters, though it varies from society to society. The control corresponding to prevention needed to be implemented in full almost all the time for all types of societies. In the case of the other two controls, the scenario was greatly affected depending on the types of societies. CONCLUSION: Prevention and treatment for elderly people with ludomania are the main intervention strategies. We found that optimal timely implementation of the intervention strategies was more effective. The optimal control strategy varied with the initial number of gamblers. However, three intervention strategies were considered, among which, preventing people from engaging in all types of gambling proved to be the most crucial.

Optimal Implementation of Intervention to Control the Self-harm Epidemic.

OBJECTIVES: Deliberate self-harm (DSH) of a young person has been a matter of growing concern to parents and policymakers. Prevention and early eradication are the main interventional techniques among which prevention through reducing peer pressure has a major role in reducing the DSH epidemic. Our aim is to develop an optimal control strategy for minimizing the DSH epidemic and to assess the efficacy of the controls. METHODS: We considered a deterministic compartmental model of the DSH epidemic and two interventional techniques as the control measures. Pontryagin's Maximum Principle was used to mathematically derive the optimal controls. We also simulated the model using the forward-backward sweep method. RESULTS: Simulation results showed that the controls needed to be used simultaneously to reduce DSH successfully. An optimal control strategy should be adopted, depending on implementation costs for the controls. CONCLUSION: The long-term success of the optimum control depends on the implementation cost. If the cost is very high, the control could be used for a short term, even though it fails in the long run. The control strategy, most importantly, should be implemented as early as possible to attack a comparatively fewer number of addicted individuals.

Polyelectrolyte effects in G-quadruplexes.

The role of counterion condensation as a dominant force governing the stability of DNA duplexes and triplexes is well established. In contrast, the effect of counterion condensation on the stability of G-quadrupex conformations is poorly understood. Unlike other ordered nucleic acid structures, G-quadruplexes exhibit a specific binding of counterions (typically, Na(+) or K(+)) which are buried inside the central cavity and coordinated to the O6 carbonyls of the guanines forming the G-quartets. While it has been known that the G-quadruplex-to-coil transition temperature, TM, increases with an increase in the concentration of the stabilizing ion, the contributions of the specific (coordination in the central cavity) and nonspecific (condensation) ion binding have not been resolved. In this work, we separate the two contributions by studying the change in TM of preformed G-quadruplexes following the addition of nonstabilizing ions Li(+), Cs(+), and TMA(+) (tetramethylammonium). In our studies, we used two G-quadruplexes formed by the human telomeric sequences which are distinct with respect to the folding topology and the identity and the number of sequestered stabilizing ions. Our data suggest that the predominant ionic contribution to G-quadruplex stability comes from the specifically bound Na(+) or K(+) ions and not from counterion condensation. We offer molecular rationalizations to the observed insensitivity of G-quadruplex stability to counterion condensation and emphasize the need to expand such studies to assess the generality of our findings.

Optimal Control Strategy of Plasmodium vivax Malaria Transmission in Korea.

OBJECTIVE: To investigate the optimal control strategy for Plasmodium vivax malaria transmission in Korea. METHODS: A Plasmodium vivax malaria transmission model with optimal control terms using a deterministic system of differential equations is presented, and analyzed mathematically and numerically. RESULTS: If the cost of reducing the reproduction rate of the mosquito population is more than that of prevention measures to minimize mosquito-human contacts, the control of mosquito-human contacts needs to be taken for a longer time, comparing the other situations. More knowledge about the actual effectiveness and costs of control intervention measures would give more realistic control strategies. CONCLUSION: Mathematical model and numerical simulations suggest that the use of mosquito-reduction strategies is more effective than personal protection in some cases but not always.

A model for the transmission dynamics of Orientia tsutsugamushi among its natural reservoirs.

The bacteria Orientia tsutsugamushi is the causative agent of scrub typhus, a prevalent disease in Asian countries that can affect humans and which shows an alarming increase of cases during the last years, especially in rural areas. Unfortunately, there is no vaccine for scrub typhus, and antibiotic treatments successfully used in the past appear to be inefficient to treat some strains of O. tsutsugamushi. We introduce a mathematical model that approximates the dynamics of the bacteria among its natural reservoirs. After computing the basic reproductive number from the proposed model, we explore its sensitivity to the parameter values that may be affected by application of control measures. This theoretical model may be of interest to pest managers as well as health authorities interested in gaining insight into the public management of the disease, through a better understanding of its qualitative dynamics.