Cellular mechanosensitivity to substrate stiffness decreases with increasing dissimilarity to cell stiffness

Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus \(\textit{E}_\mathrm{s}\) on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of \(\lambda =1.1\), were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and \(\textit{E}_\mathrm{s}\,=\,\)140 KPa and (2) \(\textit{E}_\mathrm{s}\,=\,10\), 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35\(\text {e}^{-2}\), 0.235\(\text {e}^{-2}\) and 0.6\(\text {e}^{-2}\)) than for FA attachment (0.0952\(\text {e}^{-2}\), 0.0472\(\text {e}^{-2}\) and 0.05\(\text {e}^{-2}\)). For increasing \(\textit{E}_\mathrm{s}\), the largest maximum principal strain was 4.4\(\text {e}^{-4}\), 5\(\text {e}^{-4}\), 5.3\(\text {e}^{-4}\) and 5.3\(\text {e}^{-4}\) in the membrane, 9.5\(\text {e}^{-4}\), 1.1\(\text {e}^{-4}\), 1.2\(\text {e}^{-3}\) and 1.2\(\text {e}^{-3}\) in the cytosol, and 4.5\(\text {e}^{-4}\), 5.3\(\text {e}^{-4}\), 5.7\(\text {e}^{-4}\) and 5.7\(\text {e}^{-4}\) in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.     

A Mathematical Model for the Macrophage Response to Respiratory Viral Infection in Normal and Asthmatic Conditions

Respiratory viral infections are common in the general population and one of the most important causes of asthma aggravation and exacerbation. Despite many studies, it is not well understood how viral infections cause more severe symptoms and exacerbations in asthmatics. We develop a mathematical model of two types of macrophages that play complementary roles in fighting viral infection: classically \((\hbox {CA}\)-\(\hbox {M}\Phi )\) and alternatively activated macrophages \((\hbox {AA}\)-\(\hbox {M}\Phi )\). \(\hbox {CA}\)-\(\hbox {M}\Phi \) destroy infected cells and tissues to remove viruses, while \(\hbox {AA}\)-\(\hbox {M}\Phi \) repair damaged tissues. We show that a higher viral load or longer duration of infection provokes a stronger immune response from the macrophage system. By adjusting the parameters, we model the differences in response to respiratory viral infection in normal and asthmatic subjects and show how this skews the system toward a response that generates more severe symptoms in asthmatic patients.     

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.     

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.     

Isolation and characterization of microsatellite markers in the spiny lobster, <Emphasis Type="Italic">Panulirus echinatus</Emphasis> Smith, 1869 (Decapoda: Palinuridae) by Illumina MiSeq sequencing

Okra’s (Abelmoschus esculentus (L.) Moench) commercial cultivation is threatened in the tropics due to high incidence of yellow vein mosaic virus (YVMV) disease. Okra geneticists across the world tried to understand the inheritance pattern of YVMV disease tolerance without much success. Therefore, the inheritance pattern of YVMV disease in okra was revisited by employing six generations (\(\hbox {P}_{1}\), \(\hbox {P}_{2}\), \(\hbox {F}_{1}\), \(\hbox {F}_{2}\), \(\hbox {BC}_{1}\) and \(\hbox {BC}_{2}\)) of four selected crosses (one tolerant \(\times \) tolerant, two tolerant \(\times \) susceptible and one susceptible \(\times \) susceptible) using two tolerant (BCO-1 and Lal Bhendi) and two susceptible (Japanese Jhar Bhendi and PAN 2127) genotypes. Qualitative genetic analysis was done on the basis of segregation pattern of tolerant and susceptible plants in \(\hbox {F}_{2}\) and backcross generations of all the four crosses. It revealed that a single dominant gene along with some minor factors governed the disease tolerant trait in both the tolerant parents used. However, it was observed that genes governing disease tolerance identified in both the tolerant variety used was different. It could be concluded that the gene governing YVMV disease tolerance in okra was genotype specific. Further, duplicate gene action as evident from an approximate ratio of 15 : 1 (tolerant : susceptible) in the \(\hbox {F}_{2}\) population in the cross of two tolerant varieties gave a scope of increasing the tolerance level of the hybrid plants when both the tolerant genes are brought together. However, generation mean analysis revealed involvement of both additive and nonadditive effects in the inheritance of disease tolerance. Thus, the present study confirms that a complicated genetic inheritance pattern is involved in the disease tolerance against YVMV trait. The major tolerance genes could be transferred to other okra varieties, but the tolerance breaking virus strains might not allow them to achieve tolerance in stable condition. Therefore, accumulation of additional genes may be needed for a sustainable tolerance phenotype in okra.     

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.     

Genomewide identification of PPR gene family and prediction analysis on restorer gene in <Emphasis Type="BoldItalic">Gossypium</Emphasis>

Pentatricopeptide repeat (PPR) gene family plays an essential role in the regulation of plant growth and organelle gene expression. Some PPR genes are related to fertility restoration in plant, but there is no detailed information in Gossypium. In the present study, we identified 482 and 433 PPR homologues in Gossypium raimondii (\(\hbox {D}_{5}\)) and G. arboreum (\(\hbox {A}_{2}\)) genomes, respectively. Most PPR homologues showed an even distribution on the whole chromosomes. Given an evolutionary analysis to PPR genes from G. raimondii (\(\hbox {D}_{5}\)), G. arboreum (\(\hbox {A}_{2}\)) and G. hirsutum genomes, eight PPR genes were clustered together with restoring genes of other species. Most cotton PPR genes were qualified with no intron, high proportion of \(\upalpha \)-helix and classical tertiary structure of PPR protein. Based on bioinformatics analyses, eight PPR genes were targeted in mitochondrion, encoding typical P subfamily protein with protein binding activity and organelle RNA metabolism in function. Further verified by RNA-seq and quantitative real-time PCR (qRT-PCR) analyses, two PPR candidate genes, Gorai.005G0470 (\(\hbox {D}_{5}\)) and Cotton_A_08373 (\(\hbox {A}_{2}\)), were upregulated in fertile line than sterile line. These results reveal new insights into PPR gene evolution in Gossypium.     

Resolving the viscoelasticity and anisotropy dependence of the mechanical properties of skin from a porcine model

The mechanical response of skin to external loads is influenced by anisotropy and viscoelasticity of the tissue, but the underlying mechanisms remain unclear. Here, we report a study of the main effects of tissue orientation (TO, which is linked to anisotropy) and strain rate (SR, a measure of viscoelasticity), as well as the interaction effects between the two factors, on the tensile properties of skin from a porcine model. Tensile testing to rupture of porcine skin tissue was conducted to evaluate the sensitivity of the tissue modulus of elasticity (E) and fracture-related properties, namely maximum stress \((\sigma _{U})\) and strain \((\varepsilon _{U})\) at \(\sigma _{U}\), to varying SR and TO. Specimens were excised from the abdominal skin in two orientations, namely parallel (P) and right angle (R) to the torso midline. Each TO was investigated at three SR levels, namely 0.007–0.015 \(\hbox {s}^{-1}\) (low), 0.040 \(\hbox {s}^{-1}\) (mid) and 0.065 \(\hbox {s}^{-1}\) (high). Two-factor analysis of variance revealed that the respective parameters responded differently to varying SR and TO. Significant changes in the \(\sigma _{U}\) were observed with different TOs but not with SR. The \(\varepsilon _{U}\) decreased significantly with increasing SR, but no significant variation was observed for different TOs. Significant changes in E were observed with different TOs; E increased significantly with increasing SR. More importantly, the respective mechanical parameters were not significantly influenced by interactions between SR and TO. These findings suggest that the trends associated with the changes in the skin mechanical properties may be attributed partly to differences in the anisotropy and viscoelasticity but not through any interaction between viscoelasticity and anisotropy.     

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.     

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

Boundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from \(\mu \hbox {CT}\) scans of femoral heads and vertebral bodies. They were converted into \(\mu \hbox {FE}\) models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs- and KUBCs-based tensors were determined for each sample. “In situ” stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset–Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors, and model parameters \(\nu _{0}\) (Poisson’s ratio) \(E_{0}\) and \(\mu _{0}\) (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on \(\nu _{0}\). However, KUBCs- and PMUBCs-based \(E_{0}\) and \(\mu _{0}\), respectively, decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.     

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.     

Complexity and algorithms for copy-number evolution problems

Background

Cancer is an evolutionary process characterized by the accumulation of somatic mutations in a population of cells that form a tumor. One frequent type of mutations is copy number aberrations, which alter the number of copies of genomic regions. The number of copies of each position along a chromosome constitutes the chromosome’s copy-number profile. Understanding how such profiles evolve in cancer can assist in both diagnosis and prognosis.

Results

We model the evolution of a tumor by segmental deletions and amplifications, and gauge distance from profile \(\mathbf {a}\) to \(\mathbf {b}\) by the minimum number of events needed to transform \(\mathbf {a}\) into \(\mathbf {b}\). Given two profiles, our first problem aims to find a parental profile that minimizes the sum of distances to its children. Given k profiles, the second, more general problem, seeks a phylogenetic tree, whose k leaves are labeled by the k given profiles and whose internal vertices are labeled by ancestral profiles such that the sum of edge distances is minimum.

Conclusions

For the former problem we give a pseudo-polynomial dynamic programming algorithm that is linear in the profile length, and an integer linear program formulation. For the latter problem we show it is NP-hard and give an integer linear program formulation that scales to practical problem instance sizes. We assess the efficiency and quality of our algorithms on simulated instances.

Availability

https://github.com/raphael-group/CNT-ILP

     

Comparison of the Functional Activities of Xanthine Oxidases Isolated from Microorganisms and from Cow’s Milk

The characteristics of the formation of the superoxide radical anion (\(\rm{O}_2^{\bullet-}\)) and hydrogen peroxide by xanthine oxidases isolated from microorganisms and from cow’s milk were investigated. The increase in pH led to an increase in the rate of xanthine oxidation with oxygen by both xanthine oxidases. The functioning of xanthine oxidase from milk along with the two-electron reduction of O₂ to H₂O₂ carries through the one-electron reduction of O₂ to \(\rm{O}_2^{\bullet-}\), and the rate and the fraction of generation of \(\rm{O}_2^{\bullet-}\) increased with increasing pH. Under operation of the microbial xanthine oxidase, the \(\rm{O}_2^{\bullet-}\) radical was not detected in the medium. The results suggest a difference in the operation of active centers of enzyme from different sources.     

A Mathematical Model Supports a Key Role for Ae4 (Slc4a9) in Salivary Gland Secretion

We develop a mathematical model of a salivary gland acinar cell with the objective of investigating the role of two \(\mathrm{Cl}^-/\mathrm{HCO}_3^-\) exchangers from the solute carrier family 4 (Slc4), Ae2 (Slc4a2) and Ae4 (Slc4a9), in fluid secretion. Water transport in this type of cell is predominantly driven by \(\mathrm{Cl}^-\) movement. Here, a basolateral \(\mathrm{Na}^+/ \mathrm{K}^+\) adenosine triphosphatase pump (NaK-ATPase) and a \(\mathrm{Na}^+\)–\(\mathrm{K}^+\)–\(2 \mathrm{Cl}^-\) cotransporter (Nkcc1) are primarily responsible for concentrating the intracellular space with \(\mathrm{Cl}^-\) well above its equilibrium potential. Gustatory and olfactory stimuli induce the release of \(\mathrm{Ca}^{2+}\) ions from the internal stores of acinar cells, which triggers saliva secretion. \(\mathrm{Ca}^{2+}\)-dependent \(\mathrm{Cl}^-\) and \(\mathrm{K}^+\) channels promote ion secretion into the luminal space, thus creating an osmotic gradient that promotes water movement in the secretory direction. The current model for saliva secretion proposes that \(\mathrm{Cl}^-/ \mathrm{HCO}_3^-\) anion exchangers (Ae), coupled with a basolateral \(\mathrm{Na}^+/\hbox {proton}\) (\(\hbox {H}^+\)) (Nhe1) antiporter, regulate intracellular pH and act as a secondary \(\mathrm{Cl}^-\) uptake mechanism (Nauntofte in Am J Physiol Gastrointest Liver Physiol 263(6):G823–G837, 1992; Melvin et al. in Annu Rev Physiol 67:445–469, 2005.  https://doi.org/10.1146/annurev.physiol.67.041703.084745). Recent studies demonstrated that Ae4 deficient mice exhibit an approximate \(30\%\) decrease in gland salivation (Peña-Münzenmayer et al. in J Biol Chem 290(17):10677–10688, 2015). Surprisingly, the same study revealed that absence of Ae2 does not impair salivation, as previously suggested. These results seem to indicate that the Ae4 may be responsible for the majority of the secondary \(\mathrm{Cl}^-\) uptake and thus a key mechanism for saliva secretion. Here, by using ‘in-silico’ Ae2 and Ae4 knockout simulations, we produced mathematical support for such controversial findings. Our results suggest that the exchanger’s cotransport of monovalent cations is likely to be important in establishing the osmotic gradient necessary for optimal transepithelial fluid movement.     

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.     

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.     

Study of biological communities subject to imperfect detection: bias and precision of community <Emphasis Type="Italic">N</Emphasis>-mixture abundance models in small-sample situations

Community N-mixture abundance models for replicated counts provide a powerful and novel framework for drawing inferences related to species abundance within communities subject to imperfect detection. To assess the performance of these models, and to compare them to related community occupancy models in situations with marginal information, we used simulation to examine the effects of mean abundance \((\bar{\lambda }\): 0.1, 0.5, 1, 5), detection probability \((\bar{p}\): 0.1, 0.2, 0.5), and number of sampling sites (n _site : 10, 20, 40) and visits (n _visit : 2, 3, 4) on the bias and precision of species-level parameters (mean abundance and covariate effect) and a community-level parameter (species richness). Bias and imprecision of estimates decreased when any of the four variables \((\bar{\lambda }\), \(\bar{p}\), n _site , n _visit ) increased. Detection probability \(\bar{p}\) was most important for the estimates of mean abundance, while \(\bar{\lambda }\) was most influential for covariate effect and species richness estimates. For all parameters, increasing n _site was more beneficial than increasing n _visit . Minimal conditions for obtaining adequate performance of community abundance models were n _site  ≥ 20, \(\bar{p}\) ≥ 0.2, and \(\bar{\lambda }\) ≥ 0.5. At lower abundance, the performance of community abundance and community occupancy models as species richness estimators were comparable. We then used additive partitioning analysis to reveal that raw species counts can overestimate β diversity both of species richness and the Shannon index, while community abundance models yielded better estimates. Community N-mixture abundance models thus have great potential for use with community ecology or conservation applications provided that replicated counts are available.