Nonlinear viscoelastic characterization of bovine trabecular bone

The time-independent elastic properties of trabecular bone have been extensively investigated, and several stiffness–density relations have been proposed. Although it is recognized that trabecular bone exhibits time-dependent mechanical behaviour, a property of viscoelastic materials, the characterization of this behaviour has received limited attention. The objective of the present study was to investigate the time-dependent behaviour of bovine trabecular bone through a series of compressive creep–recovery experiments and to identify its nonlinear constitutive viscoelastic material parameters. Uniaxial compressive creep and recovery experiments at multiple loads were performed on cylindrical bovine trabecular bone samples (\(n = 19\)). Creep response was found to be significant and always comprised of recoverable and irrecoverable strains, even at low stress/strain levels. This response was also found to vary nonlinearly with applied stress. A systematic methodology was developed to separate recoverable (nonlinear viscoelastic) and irrecoverable (permanent) strains from the total experimental strain response. We found that Schapery’s nonlinear viscoelastic constitutive model describes the viscoelastic response of the trabecular bone, and parameters associated with this model were estimated from the multiple load creep–recovery (MLCR) experiments. Nonlinear viscoelastic recovery compliance was found to have a decreasing and then increasing trend with increasing stress level, indicating possible stiffening and softening behaviour of trabecular bone due to creep. The obtained parameters from MLCR tests, expressed as second-order polynomial functions of stress, showed a similar trend for all the samples, and also demonstrate stiffening–softening behaviour with increasing stress.     

Mathematical modelling of bone adaptation of the metacarpal subchondral bone in racehorses

In Thoroughbred racehorses, fractures of the distal limb are commonly catastrophic. Most of these fractures occur due to the accumulation of fatigue damage from repetitive loading, as evidenced by microdamage at the predilection sites for fracture. Adaptation of the bone in response to training loads is important for fatigue resistance. In order to better understand the mechanism of subchondral bone adaptation to its loading environment, we utilised a square root function defining the relationship between bone volume fraction \((f_{BM} )\) and specific surface \((S_v )\) of the subchondral bone of the lateral condyles of the third metacarpal bone (MCIII) of the racehorse, and using this equation, developed a mathematical model of subchondral bone that adapts to loading conditions observed in vivo. The model is expressed as an ordinary differential equation incorporating a formation rate that is dependent on strain energy density. The loading conditions applied to a selected subchondral region, i.e. volume of interest, were estimated based on joint contact forces sustained by racehorses in training. For each of the initial conditions of \(f_{BM} \) we found no difference between subsequent homoeostatic \(f_{BM} \) at any given loading condition, but the time to reach equilibrium differed by initial \(f_{BM} \) and loading condition. We found that the observed values for \(f_{BM} \) from the mathematical model output were a good approximation to the existing data for racehorses in training or at rest. This model provides the basis for understanding the effect of changes to training strategies that may reduce the risk of racehorse injury.     

Informing phenomenological structural bone remodelling with a mechanistic poroelastic model

Studies suggest that fluid motion in the extracellular space may be involved in the cellular mechanosensitivity at play in the bone tissue adaptation process. Previously, the authors developed a mesoscale predictive structural model of the femur using truss elements to represent trabecular bone, relying on a phenomenological strain-based bone adaptation algorithm. In order to introduce a response to bending and shear, the authors considered the use of beam elements, requiring a new formulation of the bone adaptation drivers. The primary goal of the study presented here was to isolate phenomenological drivers based on the results of a mechanistic approach to be used with a beam element representation of trabecular bone in mesoscale structural modelling. A single-beam model and a microscale poroelastic model of a single trabecula were developed. A mechanistic iterative adaptation algorithm was implemented based on fluid motion velocity through the bone matrix pores to predict the remodelled geometries of the poroelastic trabecula under 42 different loading scenarios. Regression analyses were used to correlate the changes in poroelastic trabecula thickness and orientation to the initial strain outputs of the beam model. Linear (\(R^2>0.998\)) and third-order polynomial (\(R^2 >0.98\)) relationships were found between change in cross section and axial strain at the central axis, and between beam reorientation and ratio of bending strain to axial strain, respectively. Implementing these relationships into the phenomenological predictive algorithm for the mesoscale structural femur has the potential to produce a model combining biofidelic structure and mechanical behaviour with computational efficiency.     

Prediction of apparent trabecular bone stiffness through fourth-order fabric tensors

The apparent stiffness tensor is an important mechanical parameter for characterizing trabecular bone. Previous studies have modeled this parameter as a function of mechanical properties of the tissue, bone density, and a second-order fabric tensor, which encodes both anisotropy and orientation of trabecular bone. Although these models yield strong correlations between observed and predicted stiffness tensors, there is still space for reducing accuracy errors. In this paper, we propose a model that uses fourth-order instead of second-order fabric tensors. First, the totally symmetric part of the stiffness tensor is assumed proportional to the fourth-order fabric tensor in the logarithmic scale. Second, the asymmetric part of the stiffness tensor is derived from relationships among components of the harmonic tensor decomposition of the stiffness tensor. The mean intercept length (MIL), generalized MIL (GMIL), and fourth-order global structure tensor were computed from images acquired through microcomputed tomography of 264 specimens of the femur. The predicted tensors were compared to the stiffness tensors computed by using the micro-finite element method (\(\upmu \)FE), which was considered as the gold standard, yielding strong correlations (\(R^2\) above 0.962). The GMIL tensor yielded the best results among the tested fabric tensors. The Frobenius error, geodesic error, and the error of the norm were reduced by applying the proposed model by 3.75, 0.07, and 3.16 %, respectively, compared to the model by Zysset and Curnier (Mech Mater 21(4):243–250, 1995) with the second-order MIL tensor. From the results, fourth-order fabric tensors are a good alternative to the more expensive \(\upmu \)FE stiffness predictions.     

Estimation of the effective yield properties of human trabecular bone using nonlinear micro-finite element analyses

Micro-finite element (\(\upmu \)FE) analyses are often used to determine the apparent mechanical properties of trabecular bone volumes. Yet, these apparent properties depend strongly on the applied boundary conditions (BCs) for the limited size of volumes that can be obtained from human bones. To attenuate the influence of the BCs, we computed the yield properties of samples loaded via a surrounding layer of trabecular bone (“embedded configuration”). Thirteen cubic volumes (10.6 mm side length) were collected from \(\upmu \)CT reconstructions of human vertebrae and femora and converted into \(\upmu \)FE models. An isotropic elasto-plastic material model was chosen for bone tissue, and nonlinear \(\upmu \)FE analyses of six uniaxial, shear, and multi-axial load cases were simulated to determine the yield properties of a subregion (5.3 mm side length) of each volume. Three BCs were tested. Kinematic uniform BCs (KUBCs: each boundary node is constrained with uniform displacements) and periodicity-compatible mixed uniform BCs (PMUBCs: each boundary node is constrained with a uniform combination of displacements and tractions mimicking the periodic BCs for an orthotropic material) were directly applied to the subregions, while the embedded configuration was achieved by applying PMUBCs on the larger volumes instead. Yield stresses and strains, and element damage at yield were finally compared across BCs. Our findings indicate that yield strains do not depend on the BCs. However, KUBCs significantly overestimate yield stresses obtained in the embedded configuration (+43.1 ± 27.9%). PMUBCs underestimate (?10.0 ± 11.2%), but not significantly, yield stresses in the embedded situation. Similarly, KUBCs lead to higher damage levels than PMUBCs (+51.0 ± 16.9%) and embedded configurations (+48.4 ± 15.0%). PMUBCs are better suited for reproducing the loading conditions in subregions of the trabecular bone and deliver a fair estimation of their effective (asymptotic) yield properties.     

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.     

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.     

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.     

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.     

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.     

Ultrasound palpation for fast in-situ quantification of articular cartilage stiffness,thickness and relaxation capacity

Most current cartilage testing devices require the preparation of excised samples and therefore do not allow intra-operative application for diagnostic purposes. The gold standard during open or arthroscopic surgery is still the subjective perception of manual palpation. This work presents a new diagnostic method of ultrasound palpation (USP) to acquire applied stress and strain data during manual palpation of articular cartilage. With the proposed method, we obtain cartilage thickness and stiffness. Moreover, repeated palpations allow the quantification of relaxation effects. USP measurements on elastomer phantoms demonstrated very good repeatability for both, stage-guided (97.2%) and handheld (96.0%) applications. The USP measurements were compared with conventional indentation experiments and revealed very good agreement on elastomer phantoms (\(r = 0.98\)) and good agreement on porcine cartilage samples (\(r = 0.76\)). Artificially degenerated cartilage samples showed reduced stiffness, weak capacity to relax after palpation and an increase of stiffness of approximately 50% with each single palpation. Intact cartilage was measured by USP directly at the patella (in situ) and after excision and removal of the subchondral bone (ex situ), leading to stiffness values of \(12.1\pm 5.5\) and \(8.5\pm 5.9\,\hbox {MPa}\) (\(p<0.05\)), respectively. The results demonstrate the potential of the USP system for cartilage testing, its sensitivity to degenerative changes and as a method for quantifying relaxation processes by means of repeated palpations. Furthermore, the differences in the results of in-situ and ex-situ measurements are of general interest, since such comparison has not been reported previously. We point out the limited comparability of ex-situ cartilage with its in-situ biomechanical behavior.     

Optimal foraging behavior with an explicit consideration of within-individual behavioral variation: an example of predation

Animal behavior is flexible, and the same individual can exhibit variable expressions under the equivalent ecological situations (i.e., within-individual behavioral variation). This study examines the evolution of within-individual behavioral variation using an individual-based model. A common predation scenario is considered where a predator spends a period h to handle and consume a captured prey. The model assumes the handling time of the predator to be a random variable. The average and within-individual variance of handling time are described by \(\mu _h\) and \(\sigma _h^2\), respectively, where each individual has its own unique \(\mu _h\) and \(\sigma _h^2\). Using a genetic algorithm, the evolution of \(\sigma _h^2\) is traced. The results show that natural selection acts on both \(\mu _h\) and \(\sigma _h^2\), and the optimal behavioral variation depends on the density of prey. In particular, individuals with high behavioral variance \(\sigma _h^2\) are more likely selected when prey density is low. Individual based modeling can be a useful tool for studying the ultimate significance of within-individual behavioral variation and generating empirically testable predictions. The mechanisms of the evolution of within-individual behavioral variation and their ecological implications are discussed.     

Influence of muscle groups’ activation on proximal femoral growth tendency

Muscle and joint contact force influence stresses at the proximal growth plate of the femur and thus bone growth, affecting the neck shaft angle (NSA) and femoral anteversion (FA). This study aims to illustrate how different muscle groups’ activation during gait affects NSA and FA development in able-bodied children. Subject-specific femur models were developed for three able-bodied children (ages 6, 7, and 11 years) using magnetic resonance images. Contributions of different muscle groups—hip flexors, hip extensors, hip adductors, hip abductors, and knee extensors—to overall hip contact force were computed. Specific growth rate for the growth plate was computed, and the growth was simulated in the principal stress direction at each element in the growth front. The predicted growth indicated decreased NSA and FA (of about \(0.1 {^{\circ }}\) over a four-month period) for able-bodied children. Hip abductors contributed the most, and hip adductors, the least, to growth rate. All muscles groups contributed to a decrease in predicted NSA (\(\sim \)0.01\({^{\circ }}\)–0.04\({^{\circ }})\) and FA (\(\sim \)0.004\({^{\circ }}\)–\(0.2{^{\circ }}\)), except hip extensors and hip adductors, which showed a tendency to increase the FA (\(\sim \)0.004\({^{\circ }}\)–\(0.02{^{\circ }}\)). Understanding influences of different muscle groups on long bone growth tendency can help in treatment planning for growing children with affected gait.     

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.     

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.     

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.     

A finite-element model of mechanosensation by a Pacinian corpuscle cluster in human skin

The Pacinian corpuscle (PC) is the cutaneous mechanoreceptor responsible for sensation of high-frequency (20–1000 Hz) vibrations. PCs lie deep within the skin, often in multicorpuscle clusters with overlapping receptive fields. We developed a finite-element mechanical model of one or two PCs embedded within human skin, coupled to a multiphysics PC model to simulate action potentials elicited by each PC. A vibration was applied to the skin surface, and the resulting mechanical signal was analyzed using two metrics: the deformation amplitude ratio (\({\rho }_{\mathrm{1S}} \), \({\rho }_{\mathrm{2S}} )\) and the phase shift of the vibration (\({\delta }_{\mathrm{S}1}^{\mathrm{mech}} \), \({\delta }_{\mathrm{S}2}^{\mathrm{mech}} )\) between the stimulus and the PC. Our results showed that the amplitude attenuation and phase shift at a PC increased with distance from the stimulus to the PC. Differences in amplitude (\(\rho _{12} )\) and phase shift (\({\delta }_{12}^{\mathrm{mech}} )\) between the two PCs in simulated clusters directly affected the interspike interval between the action potentials elicited by each PC (\({\delta }_{12}^{\mathrm{spike}} )\). While \({\delta }_{12}^{\mathrm{mech}} \) had a linear relationship with \({\delta }_{12}^{\mathrm{spike}} \), \(\rho _{12} \)’s effect on \({\delta }_{12}^{\mathrm{spike}} \) was greater for lower values of \(\rho _{12} \). In our simulations, the separation between PCs and the distance of each PC from the stimulus location resulted in differences in amplitude and phase shift at each PC that caused \({\delta }_{12}^{\mathrm{spike}} \) to vary with PC location. Our results suggest that PCs within a cluster receive different mechanical stimuli which may enhance source localization of vibrotactile stimuli, drawing parallels to sound localization in binaural hearing.