A Malaria Transmission Model with Temperature-Dependent Incubation Period

Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time delay. We derive the basic reproduction ratio \(R_0\) and establish a threshold type result on the global dynamics in terms of \(R_0\), that is, the unique disease-free periodic solution is globally asymptotically stable if \(R_0<1\); and the model system admits a unique positive periodic solution which is globally asymptotically stable if \(R_0>1\). Numerically, we parameterize the model with data from Maputo Province, Mozambique, and simulate the long-term behavior of solutions. The simulation result is consistent with the obtained analytic result. In addition, we find that using the time-averaged EIP may underestimate the basic reproduction ratio.     

Analysis of two susceptibility SNPs in HLA region and evidence of interaction between rs6457617 in <Emphasis Type="BoldItalic">HLA-DQB1</Emphasis> and <Emphasis Type="BoldItalic">HLA-DRB1</Emphasis>*04 locus on Tunisian rheumatoid arthritis

Previous genomewide association studies (GWAS) and meta-analyses have enumerated several genes/loci in major histocompatibility complex region, which are consistently associated with rheumatoid arthritis (RA) in different ethnic populations. Given the genetic heterogeneity of the disease, it is necessary to replicate these susceptibility loci in other populations. In this case, we investigate the analysis of two SNPs, rs13192471 and rs6457617, from the human leukocyte antigen (HLA) region with the risk of RA in Tunisian population. These SNPs were previously identified to have a strong RA association signal in several GWAS studies. A case–control sample composed of 142 RA patients and 123 healthy controls was analysed. Genotyping of rs13192471 and rs6457617 was carried out using real-time PCR methods by TaqMan allelic discrimination assay. A trend of significant association was found in rs6457617 TT genotype with susceptibility to RA (\(P = 0.04\), \(p_{c} = 0.08\), \(\hbox {OR} = 1.73\)). Moreover, using multivariable analysis, the combination of rs6457617*TT–HLA-DRB1*\(04^{+}\) increased risk of RA (\(\hbox {OR} = 2.38\)), which suggest a gene–gene interaction event between rs6457617 located within the HLA-DQB1 and HLA-DRB1. Additionally, haplotypic analysis highlighted a significant association of rs6457617*T–HLA-DRB1*\(04^{+}\) haplotype with susceptibility to RA (\(P = 0.018\), \(p_{c} = 0.036\), \(\hbox {OR} = 1.72\)). An evidence of association was shown subsequently in \(\hbox {antiCCP}^{+}\) subgroup with rs6457617 both in T allele and TT genotype (\(P = 0.01\), \(p_{c} = 0.03\), \(\hbox {OR} = 1.66\) and \(P = 0.008\), \(p_{c} = 0.024\), \(\hbox {OR} = 1.28\), respectively). However, no association was shown for rs13192471 polymorphism with susceptibility and severity to RA. This study suggests the involvement of rs6457617 locus as risk variant for susceptibility/severity to RA in Tunisian population. Secondly, it highlights the gene–gene interaction between HLA-DQB1 and HLA-DRB1.     

Reproduction Number and Asymptotic Stability for the Dynamics of a Honey Bee Colony with Continuous Age Structure

A system of partial differential equations is derived as a model for the dynamics of a honey bee colony with a continuous age distribution, and the system is then extended to include the effects of a simplified infectious disease. In the disease-free case, we analytically derive the equilibrium age distribution within the colony and propose a novel approach for determining the global asymptotic stability of a reduced model. Furthermore, we present a method for determining the basic reproduction number \(R_0\) of the infection; the method can be applied to other age-structured disease models with interacting susceptible classes. The results of asymptotic stability indicate that a honey bee colony suffering losses will recover naturally so long as the cause of the losses is removed before the colony collapses. Our expression for \(R_0\) has potential uses in the tracking and control of an infectious disease within a bee colony.     

Cell Volume Regulation in the Proximal Tubule of Rat Kidney

We developed a dynamic model of a rat proximal convoluted tubule cell in order to investigate cell volume regulation mechanisms in this nephron segment. We examined whether regulatory volume decrease (RVD), which follows exposure to a hyposmotic peritubular solution, can be achieved solely via stimulation of basolateral K\(^+\) and \(\hbox {Cl}^-\) channels and \(\hbox {Na}^+\)–\(\hbox {HCO}_3^-\) cotransporters. We also determined whether regulatory volume increase (RVI), which follows exposure to a hyperosmotic peritubular solution under certain conditions, may be accomplished by activating basolateral \(\hbox {Na}^+\)/H\(^+\) exchangers. Model predictions were in good agreement with experimental observations in mouse proximal tubule cells assuming that a 10% increase in cell volume induces a fourfold increase in the expression of basolateral K\(^+\) and \(\hbox {Cl}^-\) channels and \(\hbox {Na}^+\)–\(\hbox {HCO}_3^-\) cotransporters. Our results also suggest that in response to a hyposmotic challenge and subsequent cell swelling, \(\hbox {Na}^+\)–\(\hbox {HCO}^-_3\) cotransporters are more efficient than basolateral K\(^+\) and \(\hbox {Cl}^-\) channels at lowering intracellular osmolality and reducing cell volume. Moreover, both RVD and RVI are predicted to stabilize net transcellular \(\hbox {Na}^+\) reabsorption, that is, to limit the net \(\hbox {Na}^+\) flux decrease during a hyposmotic challenge or the net \(\hbox {Na}^+\) flux increase during a hyperosmotic challenge.     

Glutathione <Emphasis Type="BoldItalic">S</Emphasis>-transferase P1 gene polymorphisms and susceptibility to coronary artery disease in a subgroup of north Indian population

The present study aimed to investigate the association of \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) and \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) polymorphisms of GSTP1 with coronary artery disease (CAD) in a subgroup of north Indian population. In the present case–control study, CAD patients (\(n = 200\)) and age-matched, sex-matched and ethnicity-matched healthy controls (\(n = 200\)) were genotyped for polymorphisms in GSTP1 using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) method. Genotype distribution of \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) and \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) polymorphisms of GSTP1 gene was significantly different between cases and controls (\(P = 0.005\) and 0.024, respectively). Binary logistic regression analysis showed significant association of A/G (odds ratio (OR): 1.6, 95% CI: 1.08–2.49, \(P = 0.020\)) and G/G (OR: 3.1, 95% CI: 1.41–6.71, P \(=\) 0.005) genotypes of GSTP1 \(\hbox {g}.313\hbox {A}{\!>\!}\hbox {G}\), and C/T (OR: 5.8, 95% CI: 1.26–26.34, \(P = 0.024\)) genotype of GSTP1 \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) with CAD. The A/G and G/G genotypes of \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) and C/T genotype of \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) conferred 6.5-fold increased risk for CAD (OR: 6.5, 95% CI: 1.37–31.27, \(P = 0.018\)). Moreover, the recessive model of GSTP1 \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) is the best fit inheritance model to predict the susceptible gene effect (OR: 2.3, 95% CI: 1.11–4.92, \(P = 0.020\)). In conclusion, statistically significant associations of GSTP1 \(\hbox {g}.313\hbox {A}{>}\hbox {G}\) (A/G, G/G) and \(\hbox {g}.341\hbox {C}{>}\hbox {T}\) (C/T) genotypes with CAD were observed.     

Oestrogen regulates the expression of cathepsin E-A-like gene through ER$$\upbeta $$ in liver of chicken ( Gallus gallus)

The cathepsin E-A-like, also known as ‘similar to nothepsin’, is a new member of the aspartic protease family, which may take part in processing of egg yolk macromolecules, due to it was identified in the chicken egg-yolk. Previously, studies have suggested that the expression of cathepsin E-A-like increased gradually during sexual maturation of pullets, but the exact regulation mechanism is poorly understood. In this study, to gain insight into the function and regulation mechanism of the gene in egg-laying hen, we cloned the cathepsin E-A-like gene and evaluated its evolutionary origin by using both phylogenetic and syntenic methods. The mode of the gene expression regulation was analysed through stimulating juvenile hens with \(17\upbeta \)-estradiol and chicken embryo hepatocytes with \(17\upbeta \)-estradiol combined with oestrogen receptor antagonists including MPP, ICI 182,780 and tamoxifen. Our results showed that cathepsin E-A-like was an orthologoues gene with nothepsin, which is present in birds but not in mammals. The expression of cathepsin E-A-like significantly increased in a dose-dependent manner after the juvenile hens were treated with \(17\upbeta \)-estradiol (\(P~<~0.05\)). Compared with the \(17\upbeta \)-estradiol treatment group, the expression of cathepsin E-A-like was not significantly changed when the hepatocytes were treated with \(17\upbeta \)-estradiol combined with MPP (\(P~<~0.05\)). In contrast, compared with the \(17\upbeta \)-estradiol combined with MPP treatment group, the expression of cathepsin E-A-like was significantly downregulated when the hepatocytes were treated with \(17\upbeta \)-estradiol combined with tamoxifen or ICI 182,780 (\(P~<~0.05\)). These results demonstrated that cathepsin E-A-like shared the same evolutionary origin with nothepsin. The expression of cathepsin E-A-like was regulated by oestrogen, and the regulative effect was predominantly mediated through ER-\(\upbeta \) in liver of chicken.     

Trend analysis of variations in carbon stock using stock big data

Changes in land use affect the terrestrial carbon stock through changes in the land cover. Research on land use and analysis of variations in carbon stock have practical applications in the optimization of land use and the mitigation of climate change effects. This study was conducted in Baixiang and Julu counties in the Taihang Piedmont by employing the trend analysis method to characterize the variation in county land use and carbon stock. The findings show that in both counties, agricultural and unused land areas decreased while built-up land area increased, and the reduction in cropland was the main reason behind the agricultural land reduction. An inflection point appeared on the cropland curves of Julu, because the cropland area decreased by 1576.97 hm\(^{2}\) from 2004 to 2006. Cropland area in Baixiang decreased from 1996 to 1998 by a total of 129.89 hm\(^{2}\) and then remained relatively stable after 1998. The total carbon storage and variation in land use in the two counties displayed similar trends. Total carbon reserves in Julu increased by 2.76 \(\times \) 10\(^{4}\) tC (carbon equivalent), while those in Baixiang decreased by 0.63 \(\times \) 10\(^{4}\) tC. Carbon stock of built-up land in Julu and Baixiang increased by 2.44 \(\times \) 10\(^{4}\) and 1.22 \(\times \) 10\(^{4}\) tC, respectively.     

Caspase-1-Mediated Pyroptosis of the Predominance for Driving CD4$$^{}$$ T Cells Death: A Nonlocal Spatial Mathematical Model

Caspase-1-mediated pyroptosis is the predominance for driving CD4\(^{+}\) T cells death. Dying infected CD4\(^{+}\) T cells can release inflammatory signals which attract more uninfected CD4\(^{+}\) T cells to die. This paper is devoted to developing a diffusive mathematical model which can make useful contributions to understanding caspase-1-mediated pyroptosis by inflammatory cytokines IL-1\(\beta \) released from infected cells in the within-host environment. The well-posedness of solutions, basic reproduction number, threshold dynamics are investigated for spatially heterogeneous infection. Travelling wave solutions for spatially homogeneous infection are studied. Numerical computations reveal that the spatially heterogeneous infection can make \(\mathscr {R}_0>1\), that is, it can induce the persistence of virus compared to the spatially homogeneous infection. We also find that the random movements of virus have no effect on basic reproduction number for the spatially homogeneous model, while it may result in less infection risk for the spatially heterogeneous model, under some suitable parameters. Further, the death of infected CD4\(^{+}\) cells which are caused by pyroptosis can make \(\mathscr {R}_0<1\), that is, it can induce the extinction of virus, regardless of whether or not the parameters are spatially dependent.     

Improved identifiability of myocardial material parameters by an energy-based cost function

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were \(C_1=3000\pm 1700\,\hbox {Pa}\) and \(\alpha =45\pm 25\) (\(b_f=25\pm 14\), \(b_{ft}=11\pm 6\), \(b_{t}=9\pm 5\)) for the HF cases and \(C_1=1700\,\hbox {Pa}\) and \(\alpha =15\) (\(b_f=8\), \(b_{ft}=4\), \(b_{t}=3\)) for the healthy case.     

Genetic variability and structure of an isolated population of <Emphasis Type="Italic">Ambystoma altamirani</Emphasis>, a mole salamander that lives in the mountains of one of the largest urban areas in the world

Amphibians are globally threatened by habitat loss and fragmentation; species within the order Ambystoma are not the exception, as there are 18 species of mole salamanders in México, of which 16 are endemic and all species are under some national or international status of protection. The mole salamander, Ambystoma altamirani is a microendemic species, which is distributed in central México, within the trans-Mexican volcanic belt, and is one of the most threatened species due to habitat destruction and the introduction of exotic species. Nine microsatellite markers were used to determine the genetic structure, genetic variability, effective population size, presence of bottlenecks and inbreeding coefficient of one population of A. altamirani to generate information which might help to protect and conserve this threatened species. We found two genetic subpopulations with significant level of genetic structure (\(F_{\mathrm{ST}}= 0.005\)) and high levels of genetic variability (\(H_{\mathrm{o}}= 0.883\); \(H_{\mathrm{e}}= 0.621\)); we also found a small population size (\(N_{\mathrm{e}} = 8.8\)), the presence of historical (\(M =\) 0.486) and recent bottlenecks under IAM and TPM models, with a low, but significant coefficient of inbreeding (\(F_{\mathrm{IS}} = -\)0.451). This information will help us to raise conservation strategies of this microendemic mole salamander species.     

Forecasting next season’s <Emphasis Type="Italic">Ixodes ricinus</Emphasis> nymphal density: the example of southern Germany 2018

The castor bean tick, Ixodes ricinus (L.) (Ixodida: Ixodidae), is the principal vector of pathogens causing tick-borne encephalitis or Lyme borreliosis in Europe. It is therefore of general interest to make an estimate of the density of I. ricinus for the whole year at the beginning of the tick season. There are two necessary conditions for making a successful prediction: a long homogeneous time series of observed tick density and a clear biological relationship between environmental predictors and tick density. A 9-year time series covering the period 2009–2017 of nymphal I. ricinus flagged at monthly intervals in southern Germany has been used. With the hypothesis that I. ricinus density is triggered by the fructification of the European beech 2 years before, the mean annual temperature of the previous year, and the current mean winter temperature (December–February), a forecast of the annual nymphal tick density has been made. Therefore, a Poisson regression model was generated resulting in an explained variance of 93.4% and an error of \(\hbox {RMSE} = 21\) ticks per \(100\,\hbox {m}^2\) (annual \(\hbox {MEAN} = 260\) collected ticks/\(100\,\hbox {m}^2\)). An independent verification of the forecast for the year 2017 resulted in 187 predicted versus 180 observed nymphs per \(100\,\hbox {m}^2\). For the year 2018 a relatively high number of 443 questing I. ricinus nymphs per \(100\,\hbox {m}^2\) is forecasted, i.e., a “good” tick year.     

Joint non-uniform sampling of all incremented time delays for quicker acquisition in protein relaxation studies

NMR relaxometry plays crucial role in studies of protein dynamics. The measurement of longitudinal and transverse relaxation rates of \(^{15}\)N is the main source of information on backbone motions. However, even the most basic approach exploiting a series of \(^{15}\)N HSQC spectra can require several hours of measurement time. Standard non-uniform sampling (NUS), i.e. random under-sampling of indirect time domain, typically cannot reduce this by more than 2–4\(\times\) due to relatively low “compressibility” of these spectra. In this paper we propose an extension of NUS to relaxation delays. The two-dimensional space of \(t_1\)/\(t_{relax}\) is sampled in a way similar to NUS of \(t_1\)/\(t_2\) domain in 3D spectra. The signal is also processed in a way similar to that known from 3D NUS spectra i.e. using one of the most popular compressed sensing algorithms, iterative soft thresholding. The 2D Fourier transform matrix is replaced with mixed inverse Laplace-Fourier transform matrix. The peak positions in resulting 3D spectrum are characterized by two frequency coordinates and relaxation rate and thus no additional fitting of exponential curves is required. The method is tested on three globular proteins, providing satisfactory results in a time corresponding to acquisition of two conventional \(^{15}\)N HSQC spectra.     

Backbone resonance assignments for the SET domain of the human methyltransferase NSD2

Aberrant NSD2 methyltransferase activity is implicated as the oncogenic driver in multiple myeloma, suggesting opportunities for novel therapeutic intervention. The methyltransferase activity of NSD2 resides in its catalytic SET domain, which is conserved among most lysine methyltransferases. Here we report the backbone \(\hbox {H}^{\mathrm{N}}\), N, C\(^{\prime }\), \(\hbox {C}^\alpha\) and side-chain \(\hbox {C}^\beta\) assignments of a 25 kDa NSD2 SET domain construct, spanning residues 991–1203. A chemical shift analysis of C\(^{\prime }\), \(\hbox {C}^\alpha\) and \(\hbox {C}^\beta\) resonances predicts a secondary structural pattern that is in agreement with homology models.     

Invasions Slow Down or Collapse in the Presence of Reactive Boundaries

Motivated by the propagation of thin bacterial films around planar obstacles, this paper considers the dynamics of travelling wave solutions to the Fisher–KPP equation \(u_t = u(1-u) + u_{xx} + u_{yy}\) in a planar strip \(-\infty< x < \infty \), \(0 \le y \le L\). We examine the propagation of fronts in the presence of a mixed boundary condition (also referred to as a ‘partially absorbing’ or ‘reactive’ boundary) \(u_y = \alpha u\), with \(\alpha >0\), at \(y=0\). The presence of boundary conditions of this kind leads to the development of front solutions that propagate in x but contain transverse structure in y. Motivated by the observation that the speed of propagation in the Fisher–KPP equation is determined (for exponentially decaying initial conditions) by the behaviour at the leading edge, we analyse the linearised Fisher–KPP equation in order to estimate the speed of the stable travelling front, a function of the width L and the imposed boundary conditions. For wide strips the speed estimate based on the linearised equation agrees well with the results of numerical simulations. For narrow channels numerical simulations indicate that the stable front propagates more slowly, and for sufficiently small L or sufficiently large \(\alpha \) the front speed falls to zero and the front collapses. The reason for the collapse is the non-existence, far behind the front, of a stable positive equilibrium solution u(x, y). While existence of these equilibrium states can be demonstrated via phase plane arguments, the investigation of stability is similar to calculations of critical patch sizes carried out in similar ecological models.     

Association of <Emphasis Type="BoldItalic">lactase</Emphasis> 13910 C/T polymorphism with bone mineral density and fracture risk: a meta-analysis

A number of studies have investigated the association of lactase (LCT, C/T-13910) gene polymorphism with bone mineral density (BMD) and fracture risk, but previous results were inconclusive. In this study, a meta-analysis was performed to quantify the association of LCT (C/T-13910) polymorphism with BMD and fracture risk. Eligible publications were searched in the PubMed, Web of Science, Embase databases, Google Scholar, Yahoo and Baidu. Pooled weighed mean difference (WMD) or odds ratio (OR) with their 95% confidence interval (CI) were calculated using a fixed-effects or random-effects model. A total of nine articles with 8871 subjects were investigated in the present meta-analysis. Overall, the TT/TC genotypes of LCT 13910 C/T polymorphism showed significantly higher BMD than those with the CC genotype at femur neck (FN) (\(\hbox {WMD} = 0.011\,\hbox {g/cm}^{2}\), 95% CI \(=\) 0.004–0.018, \(P = 0.003\)). Besides, LCT 13910 C/T polymorphism may decrease the risk of any site fractures (for TT versus TC \(+\) CC, OR \(=\) 0.813, 95% CI \(=\) 0.704–0.938, \(P = 0.005\); for T allele versus C allele, OR \(=\) 0.885, 95% CI \(=\) 0.792–0.989, \(P = 0.032\)). However, there was no significant association of LCT 13910 C/T polymorphism with BMD at lumbar spine and risk of vertebral fractures under all genetic contrast models (all P values were \({>}0.05\)). The meta-analysis suggests that there are significant effects of LCT 13910 C/T polymorphism on BMD and fracture risk. Large-scale studies with different ethnic populations will be needed to further investigate the possible race-specific effect of LCT 13910 C/T polymorphism on BMD and fracture risk.     

Transmission Fitness in Co-colonization and the Persistence of Bacterial Pathogens

Humans are often colonized by polymorphic bacteria such as Streptococcus pneumoniae, Bordetella pertussis, Staphylococcus Aureus, and Haemophilus influenzae. Two co-colonizing pathogen clones may interact with each other upon host entry and during within-host dynamics, ranging from competition to facilitation. Here we examine the significance of these exploitation strategies for bacterial spread and persistence in host populations. We model SIS epidemiological dynamics to capture the global behavior of such multi-strain systems, focusing on different parameters of single and dual colonization. We analyze the impact of heterogeneity in clearance and transmission rates of single and dual colonization and find the criteria under which these asymmetries enhance endemic persistence. We obtain a backward bifurcation near \(R_0 = 1\) if the reproductive value of the parasite in dually infected hosts is sufficiently higher than that in singly infected ones. In such cases, the parasite is able to persist even in sub-threshold conditions, and reducing the basic reproduction number below 1 would be insufficient for elimination. The fitness superiority in co-colonized hosts can be attained by lowering net parasite clearance rate (\(\gamma _\mathrm{{d}}\)), by increasing transmission rate (\(\beta _\mathrm{{d}}\)), or both, and coupling between these traits critically constrains opportunities of pathogen survival in the \(R_0<1\) regime. Finally, using an adaptive dynamics approach, we verify that despite their importance for sub-threshold endemicity, traits expressed exclusively in coinfection should generally evolve independently of single infection traits. In particular, for \(\beta _\mathrm{{d}}\) a saturating parabolic or hyperbolic function of \(\gamma _\mathrm{{d}}\), co-colonization traits evolve to an intermediate optimum (evolutionarily stable strategy, ESS), determined only by host lifespan and the trade-off parameters linking \(\beta _\mathrm{{d}}\) and \(\gamma _\mathrm{{d}}\). Our study invites more empirical attention to the dynamics and evolution of parasite life-history traits expressed exclusively in coinfection.     

Towards the prediction of flow-induced shear stress distributions experienced by breast cancer cells in the lymphatics

Tumour metastasis in the lymphatics is a crucial step in the progression of breast cancer. The dynamics by which breast cancer cells (BCCs) travel in the lymphatics remains poorly understood. The goal of this work is to develop a model capable of predicting the shear stresses metastasising BCCs experience using numerical and experimental techniques. This paper models the fluidic transport of large particles (\(\eta =d_{\mathrm{p}}/W=0.1-0.4\) where \(d_{\mathrm{p}}\) is the particle diameter and W is the channel width) subjected to lymphatic flow conditions (\({ Re}=0.04\)), in a \(100\times 100\,\upmu \hbox {m}\) microchannel. The feasibility of using the dynamic fluid body interaction (DFBI) method to predict particle motion was assessed, and particle tracking experiments were performed. The experiments found that particle translational velocity decreased from the undisturbed fluid velocity with increasing particle size (5–14% velocity lag for \(\eta =0.1-0.3\)). DFBI simulations were found to better predict particle behaviour than theoretical predictions; however, mesh restrictions in the near-wall region (\(0.2\,\mathrm{W}>y>0.8\,\mathrm{W}\)) result in computationally expensive models. The simulations were in good agreement with the experiments (\(<12\%\) difference) across the channel (\(0.2\,\mathrm{W}\le y\le 0.8\,\mathrm{W}\)), with differences up to 25% in the near-wall region. Particles experience a range of shear stresses (0.002–0.12 Pa) and spatial shear gradients (\(0.004-0.137\,\hbox {Pa}/\upmu \hbox {m}\)) depending on their size and radial position. The predicted shear gradients are far in excess of values associated with BCC apoptosis (\(0.004-0.023\,\hbox {Pa}/\upmu \hbox {m}\)). Increasing our understanding of the shear stress magnitudes and gradients experienced by BCCs could be leveraged to elucidate whether a particular BCC size or location exists that encourages metastasis within the lymphatics.     

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, \(A_\mathrm{R}\) and \(B_\mathrm{R}\), each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for \(A_\mathrm{R}\) and \(B_\mathrm{R}\), we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., \(f \Delta t\)-long for DrugA and \((1-f) \Delta t\)-long for DrugB with \(0 \le f \le 1\) and \(\Delta t \ge 0\)). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, \(\mathcal {A/B} = A_\mathrm{R}/B_\mathrm{R}\), and the effect of each drug. We determine a critical ratio, which we term \(\mathcal {(A/B)}^{*}\), at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, \(\mathcal {A/B}\) changes monotonically to \(\mathcal {(A/B)}^{*}\) and then, during the second stage, remains at \(\mathcal {(A/B)}^{*}\) thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.