A viscoplastic model for the active component in cardiac muscle

The HMK model (Hunter et al. in Prog Biophys Mol Biol 69:289–331, 1998) proposes mechanobiological equations for the influence of intracellular calcium concentration \(\hbox {Ca}_\mathrm{i}\) on the evolution of bound calcium concentration \(\hbox {Ca}_\mathrm{b}\) and the tropomyosin kinetics parameter z, which model processes in the active component of the tension in cardiac muscle. The inelastic response due to actin-myosin crossbridge kinetics is modeled in the HMK model with a function Q that depends on the history of the rate of total stretch of the muscle fiber. Here, an alternative model is proposed which models the active component of the muscle fiber as a viscoplastic material. In particular, an evolution equation is proposed for the elastic stretch \(\lambda _\mathrm{a} \) in the active component. Specific forms of the constitutive equations are proposed and used to match experimental data. The proposed viscoplastic formulation allows for separate modeling of three processes: the high rate deactivation of crossbridges causing rapid reduction in active tension; the high but lower rate reactivation of crossbridges causing recovery of active tension; and the low rate relaxation effects characterizing the Hill model of muscles.     

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.     

Dynamic permeability of the lacunar–canalicular system in human cortical bone

A new method for the experimental determination of the permeability of a small sample of a fluid-saturated hierarchically structured porous material is described and applied to the determination of the lacunar–canalicular permeability \((K_\mathrm{LC})\) in bone. The interest in the permeability of the lacunar–canalicular pore system (LCS) is due to the fact that the LCS is considered to be the site of bone mechanotransduction due to the loading-driven fluid flow over cellular structures. The permeability of this space has been estimated to be anywhere from \(10^{-17}\;\) to \(10^{-25}\; \hbox {m}^{2}\) . However, the vascular pore system and LCS are intertwined, rendering the permeability of the much smaller-dimensioned LCS challenging to measure. In this study, we report a combined experimental and analytical approach that allowed the accurate determination of the \(K_\mathrm{LC}\) to be on the order of \(10^{-22}\; \hbox {m}^{2}\) for human osteonal bone. It was found that the \(K_\mathrm{LC}\) has a linear dependence on loading frequency, decreasing at a rate of \(2 \times 10^{-24}\; \hbox {m}^{2}\) /Hz from 1 to 100 Hz, and using the proposed model, the porosity alone was able to explain 86 % of the \(K_\mathrm{LC}\) variability.     

Interaction-induced electric (hyper)polarizability in the dihydrogen–neon pair: basis set and electron correlation effects

We investigated the interaction (hyper)polarizability of neon–dihydrogen pairs by performing high-level ab initio calculations with atom/molecule-specific, purpose-oriented Gaussian basis sets. We obtained interaction-induced electric properties at the SCF, MP2, and CCSD levels of theory. At the CCSD level, for the T-shaped configuration, around the respective potential minimum of 6.437 a₀, the interaction-induced mean first hyperpolarizability varies for 5?<? R/a₀?<?10 as

$$ \left[{\overline{\beta}}_{\mathrm{int}}(R)\hbox{-} {\overline{\beta}}_{\mathrm{int}}\left({R}_{\mathrm{e}}\right)\right]/{e}^3{a_0}^3{E_{\mathrm{h}}}^{-2}=-0.91\left(R\hbox{-} {R}_{\mathrm{e}}\right)+0.50{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^2\hbox{--} 0.13{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^3+0.01{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^4. $$

Again, at the CCSD level, but for the L-shaped configuration around the respective potential minimum of 6.572 a₀, this property varies for 5?<? R/a₀?<?10 as

$$ \left[{\overline{\beta}}_{\mathrm{int}}(R)\hbox{-} {\overline{\beta}}_{\mathrm{int}}\left({R}_{\mathrm{e}}\right)\right]/{e}^3{a_0}^3{E_{\mathrm{h}}}^{-2}=-1.33\left(R\hbox{-} {R}_{\mathrm{e}}\right)+0.75{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^2-0.20{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^3+0.02{\left(R\hbox{-} {R}_{\mathrm{e}}\right)}^4. $$

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Graphical Abstract Interaction-induced mean dipole polarizability (\( \overline{a} \)) for the T-shaped configuration of H₂–Ne calculated at the SCF, MP2, and CCSD levels of theory

     

LPC$$_\mathrm{}$$: A local power controller using the frequency scheduling approach for virtualized servers

For more than a decade, the power consumption of data centers has been addressed from different perspectives. Many solutions have been proposed to reduce (or optimize) this power consumption, such as controlling the operation of the servers in data centers. However, these approaches have not yet reached their optimum goals. Existing power control solutions using CPU frequency with an ad hoc or frequency modulator approach are not sufficient. In this paper, we review the power consumption effects of different configuration settings applied to the server’s CPU. We propose our local power controller using frequency scheduling (LPC\(_\mathrm{FreqSchd}\)), which is a server-level power controller that depends on an extended gain scheduling technique. Our proposed LPC\(_\mathrm{FreqSchd}\) considers the impact of different CPU configuration settings that are typically not considered simultaneously, such as the allocated CPU credits and CPU frequency level. Through a real experimental test bed, our LPC\(_\mathrm{FreqSchd}\) exhibits effective power management of different types of machines and outperforms other existing approaches, such as ad hoc and frequency modulation, when the power budget is low. Moreover, our proposed LPC\(_\mathrm{FreqSchd}\) has a very lightweight control actuation overhead compared with other approaches: approximately \(1/10 \mathrm{th}\) of the ad hoc approach’s overhead and \(1/100 \mathrm{th}\) of the frequency modulator approach’s overhead. This lightweight control actuation overhead reduces the power consumption overhead caused by the controller, and it could be used by other controllers, such as performance or thermal controllers running on the same server.     

A simulation of rat edl force output based on intrinsic muscle properties

Force-velocity and force-length relations were obtained for the edl of four Wistar rats in order to characterise the contractile properties (CE) of these muscle-tendon complexes. Compliances of the undamped part of the series components (SE) were measured in quick length decreases. Force-extension relations of SEs were obtained by integration of compliance to force. A muscle model consisting of CE, SE and a visco-elastic element was used to simulate the force output of the muscle tendon complex in response to a changing muscle length lOI as input. This simulated force was compared with the experimental force of the same muscle measured in response to the same lOI as input. Tetanic contractions were used in all experiments. The results show that this muscle model can predict the experimental force within a mean maximal error not larger than approximately 14% of the force amplitude. However the comparison of simulated force with experimental force and a few additional experiments show that the muscles do not have a unique instantaneous force-velocity characteristic. As shown by several other studies, force seems to be influenced by many other variables (time, history etc.) than CE length and velocity.     

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.     

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.     

E-waste projection using life-span and population statistics

Purpose

E-waste is the most rapidly growing problem throughout the world, which has serious future concerns over its management and recycling. This article proposes a simple approach for future e-waste projection which can be obtained by using life-span data of various electronic items along with incorporation of population statistics.

Methods

For this purpose, 7-year sales data of electronic items were collected, which is then used to generate various mathematical equations. These mathematical relations are then modified by incorporating life-span and population data.

Results and discussion

By comparing sales data with their life-span (average) and population statistics, future e-waste can be quantified both in terms of specified area under investigation and proposed estimation area. The following equation is thus proposed: E - waste In terms of quantity = m Waste projection year ? Life - span ? Initial data collection year + C × Population of estimation area Population of study area $$ \begin{array}{c}\mathrm{E}-\mathrm{waste}\;\\ {}\left(\mathrm{In}\ \mathrm{terms}\ \mathrm{of}\ \mathrm{quantity}\right)=\left[m\left\{\mathrm{Waste}\;\mathrm{projection}\;\mathrm{year}-\mathrm{Life}-\mathrm{span}\right\}-\mathrm{Initial}\ \mathrm{data}\ \mathrm{collection}\ \mathrm{year}+C\right]\times \frac{\mathrm{Population}\ \mathrm{of}\ \mathrm{estimation}\ \mathrm{area}}{\mathrm{Population}\ \mathrm{of}\ \mathrm{study}\ \mathrm{area}\ }\end{array} $$ Where m and C can be obtained from plotting year-wise sales data over Excel sheet.

Conclusions

Local as well as global projection of future e-waste can be possible with the help of final equation.     

Measuring the signs of the methyl <Superscript>1</Superscript>H chemical shift differences between major and ‘invisible’ minor protein conformational states using methyl <Superscript>1</Superscript>H multi-quantum spectroscopy

Carr–Purcell–Meiboom–Gill (CPMG) type relaxation dispersion experiments are now routinely used to characterise protein conformational dynamics that occurs on the μs to millisecond (ms) timescale between a visible major state and ‘invisible’ minor states. The exchange rate(s) (\( k_{{{\text{ex}}}} \)), population(s) of the minor state(s) and the absolute value of the chemical shift difference \(|{\Delta \varpi }|\) (ppm) between different exchanging states can be extracted from the CPMG data. However the sign of \({\Delta \varpi }\) that is required to reconstruct the spectrum of the ‘invisible’ minor state(s) cannot be obtained from CPMG data alone. Building upon the recently developed triple quantum (TQ) methyl \( ^{1} {\text{H}} \) CPMG experiment (Yuwen in Angew Chem 55:11490–11494, 2016) we have developed pulse sequences that use carbon detection to generate and evolve single quantum (SQ), double quantum (DQ) and TQ coherences from methyl protons in the indirect dimension to measure the chemical exchange-induced shifts of the SQ, DQ and TQ coherences from which the sign of \({\Delta \varpi }\) is readily obtained for two state exchange. Further a combined analysis of the CPMG data and the difference in exchange induced shifts between the SQ and DQ resonances and between the SQ and TQ resonances improves the estimates of exchange parameters like the population of the minor state. We demonstrate the use of these experiments on two proteins undergoing exchange: (1) the ~ 18 kDa cavity mutant of T4 Lysozyme (\( k_{{{\text{ex}}}} \sim\,3500{\text{ s}}^{{ - 1}} \)) and (2) the \(\sim\,4.7\) kDa Peripheral Sub-unit Binding Domain (PSBD) from the acetyl transferase of Bacillus stearothermophilus (\(k_{ex} \sim\,13,000\hbox { s}^{-1}\)).     

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.     

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.     

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.     

Decomposition-rate estimation of leaf litter in karst forests in China based on a mathematical model

Aims

The objectives of the study were to analyze the relationship between decomposition rates and initial chemistry of leaf litter and to establish an optimal model to predict the decomposition rates of a large number of plant species in karst forests of China.

Methods

We determined the decomposition rate of leaf litter from 21 representative species in karst forests through a litterbag experiment. Using Akaike information criteria, we selected an optimal model among 925 regression models of decomposition rate based on initial chemistry indexes to estimate annual leaf-litter-decomposition rate for an additional 96 important species.

Results

Of the 21 representative species, Elaeocarpus decipiens and Phoebe sheareri exhibited the highest (62.85 %) and lowest (23.50 %) annual decomposition rates, respectively. In the first and second quarters, climatic conditions were not advantageous to decomposition, but 20 species reached their highest decomposition rate. Most of 117 tested species accumulated fewer nutrients and more non-easily-decomposed materials in their leaf litter than plant species in non-karst forests. The selected optimal model was: $ \mathrm{annual} \ \mathrm{decomposition} \ \mathrm{rate}=111.838-0.114\;\left( {\mathrm{total} \ \mathrm{carbon}} \right)+0.021\;\left( {\mathrm{total} \ \mathrm{nitrogen}} \right)+0.068\;\left( {\mathrm{total} \ \mathrm{potassium}} \right)-0.027\;\left( {\mathrm{lignin}} \right)-0.398\;\left( {\mathrm{tannin}} \right)-0.015\;\left( {\mathrm{starch}} \right) $ . Predicted annual leaf-litter-decomposition rates of the additional 96 tree species were 20–80 %.

Conclusions

This study enhances our understanding of leaf-litter decomposition for plant species in karst forests and provides a method for estimating annual leaf-litter-decomposition rates.     

Uncertainty quantification and sensitivity analysis of an arterial wall mechanics model for evaluation of vascular drug therapies

Quantification of the uncertainty in constitutive model predictions describing arterial wall mechanics is vital towards non-invasive assessment of vascular drug therapies. Therefore, we perform uncertainty quantification to determine uncertainty in mechanical characteristics describing the vessel wall response upon loading. Furthermore, a global variance-based sensitivity analysis is performed to pinpoint measurements that are most rewarding to be measured more precisely. We used previously published carotid diameter–pressure and intima–media thickness (IMT) data (measured in triplicate), and Holzapfel–Gasser–Ogden models. A virtual data set containing 5000 diastolic and systolic diameter–pressure points, and IMT values was generated by adding measurement error to the average of the measured data. The model was fitted to single-exponential curves calculated from the data, obtaining distributions of constitutive parameters and constituent load bearing parameters. Additionally, we (1) simulated vascular drug treatment to assess the relevance of model uncertainty and (2) evaluated how increasing the number of measurement repetitions influences model uncertainty. We found substantial uncertainty in constitutive parameters. Simulating vascular drug treatment predicted a 6% point reduction in collagen load bearing (\(L_\mathrm {coll}\)), approximately 50% of its uncertainty. Sensitivity analysis indicated that the uncertainty in \(L_{\mathrm {coll}}\) was primarily caused by noise in distension and IMT measurements. Spread in \(L_{\mathrm {coll}}\) could be decreased by 50% when increasing the number of measurement repetitions from 3 to 10. Model uncertainty, notably that in \(L_{\mathrm {coll}}\), could conceal effects of vascular drug therapy. However, this uncertainty could be reduced by increasing the number of measurement repetitions of distension and wall thickness measurements used for model parameterisation.     

The force-length relationship of a muscle-tendon complex: experimental results and model calculations

Models are useful when studying how architectural and physiological properties of muscle-tendon complexes are related to function, because they allow for the simulation of the behaviour of such complexes during natural movements. In the construction of these models, evaluation of their accuracy is an important step. In the present study, a model was constructed to calculate the isometric force-length relationship of the rat extensor digitorum longus muscle-tendon complex. The model is based on the assumption that a muscle-tendon complex is a collection of independent units, each consisting of a muscle fibre in series with a tendon fibre. By intention, values for model parameters were derived indirectly, using only the measured maximal isometric tetanic force, the distance between origin and insertion at which it occurred (optimum lOI) and an estimate of muscle fibre optimal length. The accuracy of the calculated force-length relationship was subsequently evaluated by comparing it to the relationship measured in isometric tetanic contractions of a real complex in the rat. When the length of distal muscle fibres, measured during isometric contraction at optimal lOI of the whole complex, was used as an estimate for muscle fibre optimal length of all muscle fibre-tendon fibre units in the model, the calculated relationship was too narrow. That is, both on the ascending limb and on the descending limb the calculated tetanic force was lower than the measured tetanic force.(ABSTRACT TRUNCATED AT 250 WORDS)     

Long-term grazing affects relationships between nitrogen form uptake and biomass of alpine meadow plants

Trade-off between nutrient uptake rate and product accumulation has been found among species characterized as acquisitive and conservative strategies in resource utilization. However, long-term grazing causes changes in soil nutrient availability and plant species abundance by selective foraging and resource allocation between above- and belowground organs, which may cover up such trade-off. However, little is known whether the trade-off can be observed among species in community without grazing disturbance, and how grazing influences the trade-off. We conducted a ¹⁵N labelling experiment in winter grazing and grazing release alpine meadow communities on the Tibet Plateau. We examined changes in N form uptake of 11 common species and relationship of N chemical uptake rate with aboveground biomass. Grazing release increased soil \({\text{NH}}_{4}^{ + }\)–N and \({\text{NO}}_{3}^{ - }\)–N, and increased \({\text{NO}}_{3}^{ - }\)–N uptake rate in two species and \({\text{NH}}_{4}^{ + }\)–N uptake rate in three species. Meanwhile, grazing release decreased aboveground biomass of three species and two of them belong to those species’ increased N uptake rate. Contrarily, grazing release increased aboveground biomass of four species and none belongs to the changed N uptake rate. Thus, grazing release caused changes of plant nutrient uptake rate and aboveground production in different directions, which explains the negative relationship of N uptake rate with aboveground biomass in ungrazed community. Our results indicate that the increase in nutrient uptake is probably one of the mechanisms for acquisitive species to cope with the raising nutrient availability and/or competition from the conservative dominant grasses after grazing release.