Passive and active reactions of embryonic tissues to the action of dosed mechanical forces

With the help of a suction manometric device, the relation between the deformation of Xenonus laevis embryo at the gastrula and neurula stages and the value of the applied force has been studied. Stiffness modules of embryonic tissues were in the order of several dozens of Pascal and they were inversely proportional during deformation from 40 to 20%. At the gastrula stage, a uniform or an increasing rate of expansion of the embryo body in the suction capillary with the diameter of approximately half that of the embryo was observed for 30 min after the action of the suction forces. The length of the stretched portion of the embryo correlates with the value of its deformation at the first minute. As a result of the expansion, the total body surface area of the deformed embryo increases more than twice compared to intact embryos. After expelling the embryo from the capillary, its surface reduced and the deformation became smoothened within 5 min, which indicates the existence of tensional force in the expanded embryo. These data confirm that, at the embryo gastrula stage, external mechanical forces do not only passively deform the embryo but also initiate the active expansion of the embryo which takes place at zero external force and overcomes the tensional resistance of tissues. The mechanism of active expansion and its link with the processes of normal morphogenesis are discussed.     

A model for estimating the extent of variegation in mosaic tissues

A method is described which allows the size of patches of like cells in mosaic tissues to be estimated from the frequency with which small samples taken from the tissue contain both of the mosaic cell types. The mosaic patches are represented as close-packed geometric figures arranged in twoor three-dimensional tissues. Small samples drawn at random from these tissues will include portions of one or more patches; only those samples which include portions of two or more dissimilar patches (mixed samples) will contain both cell types. The expected frequency of mixed samples is calculated as a function of the shape of the mosaic patches, the frequency of the two mosaic cell types and the sample to patch size ratio. This expected frequency is not strongly dependent on patch shape for triangular, square and hexagonal patches in two dimensions or for cubic and orthotetrakaidekahedral patches in three dimensions. Elongation of square patches along one axis or of cubic patches along one or two axes results in slight increases in the expected frequency of mixed samples for given sample to patch size ratio.     

A simple way to compute protein dynamics without a mechanical model

We found that in proteins the average atomic fluctuation is linearly related to the square of the atomic distance from the center of mass of the protein. Using this simple relation, we can accurately compute the temperature factors of proteins of a wide range of sizes and folds, and the correlation of the fluctuations in proteins. This simple relation provides a direct link between protein dynamics and the static protein's geometrical shape and offers a simple way to compute protein dynamics without either long time trajectory integration or any matrix operations.     

Surprisingly simple mechanical behavior of a complex embryonic tissue

Background

Previous studies suggest that mechanical feedback could coordinate morphogenetic events in embryos. Furthermore, embryonic tissues have complex structure and composition and undergo large deformations during morphogenesis. Hence we expect highly non-linear and loading-rate dependent tissue mechanical properties in embryos.

Methodology/Principal Findings

We used micro-aspiration to test whether a simple linear viscoelastic model was sufficient to describe the mechanical behavior of gastrula stage Xenopus laevis embryonic tissue in vivo. We tested whether these embryonic tissues change their mechanical properties in response to mechanical stimuli but found no evidence of changes in the viscoelastic properties of the tissue in response to stress or stress application rate. We used this model to test hypotheses about the pattern of force generation during electrically induced tissue contractions. The dependence of contractions on suction pressure was most consistent with apical tension, and was inconsistent with isotropic contraction. Finally, stiffer clutches generated stronger contractions, suggesting that force generation and stiffness may be coupled in the embryo.

Conclusions/Significance

The mechanical behavior of a complex, active embryonic tissue can be surprisingly well described by a simple linear viscoelastic model with power law creep compliance, even at high deformations. We found no evidence of mechanical feedback in this system. Together these results show that very simple mechanical models can be useful in describing embryo mechanics.     

A simple model of a vessel with a wall sensitive to mechanical stimuli

Smooth muscles in the walls of small blood vessels under normal conditions are always moderately active, so that there is a certain reserve for blood flow adaptation to changed conditions by either narrowing or expanding of the vessel lumen. The previous studies of small vessel hydrodynamics have shown that the activity can cause specific instability of vessel steady states. In order to trace qualitatively the influence of numerous factors on the active state of the vessel, a simplified model of the vessel was proposed, which is reduced to a nonlinear ordinary equation of the first order with delayed argument.     

A constitutive model for the mechanical behaviour of soft connective tissues

A model of the mechanical behaviour of soft connective tissue has been developed by considering the role of the collagen and glycosaminoglycan (GAG) components within the tissue in order to examine the mechanism by which a variation in the GAG components may exert a control over the mechanical properties of the tissue. It is proposed that the strain energy stored within the collagen fibrils of the loaded tissue can be transferred into a potential field created by the charged GAG components and their electrostatic interaction with the collagen fibrils. A fundamental mechanical unit is described to simulate this energy transfer and a combination of such units is used to represent the tissue. The computer implementation of the proposed tissue model shows it to reproduce many features which have been recognised in the rate dependent mechanical behaviour of soft tissues. These include the characteristic non-linearity of the force-deformation behaviour and the approximate invariance of the stress relaxation behaviour with deformation. The model is also consistent with earlier constitutive representations of tissue behaviour.     

A mechanical model to compute elastic modulus of tissues for harmonic motion imaging

Numerous experimental and computational methods have been developed to estimate tissue elasticity. The existing testing techniques are generally classified into in vitro, invasive in vivo and non-invasive in vivo. For each experimental method, a computational scheme is accordingly proposed to calculate mechanical properties of soft biological tissues. Harmonic motion imaging (HMI) is a new technique that performs radio frequency (RF) signal tracking to estimate the localized oscillatory motion resulting from a radiation force produced by focused ultrasound. A mechanical model and computational scheme based on the superposition principle are developed in this paper to estimate the Young's modulus of a tissue mimicking phantom and bovine liver in vitro tissue from the harmonic displacement measured by HMI. The simulation results are verified by two groups of measurement data, and good agreement is shown in each comparison. Furthermore, an inverse function is observed to correlate the elastic modulus of uniform phantoms with amplitude of displacement measured in HMI. The computational scheme is also implemented to estimate 3D elastic modulus of bovine liver in vitro.     

A recruitment-based rheological model for mechanical behavior of soft tissues

When lung tissue is subjected to finite deformations, phenomena appear that can only be described using nonlinear models. This paper considers the lung as a material composed of two elements, a continuous phase that acts uninterruptedly and a second phase composed of fiber elements that are recruited progressively into the mechanical process. Each individual fiber participates in the mechanical response of the set only when the deformation is above a certain value. A nine-parameter model was designed adopting standard viscoelastic elements both for the matrix and for each of the fibers. The mechanical behavior of the lung can be reproduced by a fitting process with standard numerical procedures in both dynamic-mechanical measurements and stress relaxation processes. Mechanical stress relaxation tests and dynamic-mechanical measurements have been carried out on subpleural parenchymal strips from rat lung. The model permits the reproduction of lung behavior in both types of measurements. The results show a recruitment ratio that decreases with deformation and the nonparticipation of the parallel matrix fraction in the lung's mechanical response so that a uniaxial transmission of force in the lung occurs via the recruited elements and the matrix series.     

A simple mechanochemical model for calcium signalling in embryonic epithelial cells

Journal of Mathematical Biology - Calcium signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between calcium signalling and...     

A simple procedure for estimating the false discovery rate

MOTIVATION: The most used criterion in microarray data analysis is nowadays the false discovery rate (FDR). In the framework of estimating procedures based on the marginal distribution of the P-values without any assumption on gene expression changes, estimators of the FDR are necessarily conservatively biased. Indeed, only an upper bound estimate can be obtained for the key quantity pi0, which is the probability for a gene to be unmodified. In this paper, we propose a novel family of estimators for pi0 that allows the calculation of FDR. RESULTS: The very simple method for estimating pi0 called LBE (Location Based Estimator) is presented together with results on its variability. Simulation results indicate that the proposed estimator performs well in finite sample and has the best mean square error in most of the cases as compared with the procedures QVALUE, BUM and SPLOSH. The different procedures are then applied to real datasets. AVAILABILITY: The R function LBE is available at http://ifr69.vjf.inserm.fr/lbe CONTACT: broet@vjf.inserm.fr.     

A simple model for estimating Ni availability and leaf Ni accumulation for the Ni-hyperaccumulator Leptoplax emarginata

Aims

The aim of the present study was to predict kinetics of both Ni concentration in soil solution and leaf Ni mass for the Ni-hyperaccumulator Leptoplax emarginata cultivated on a fertilized and Ni-contaminated sandy topsoil.

Methods

The 0-D (independent of space) one-site rate-limited desorption model proposed by Ingwersen et al. (J Environ Qual 35:2055–2065, 2006) was modified. The plant sink term of the model was approximated by the biophysical equation which assumes that the leaf nickel mass is equal to the triple product of the Intact Plant Transpiration Stream Concentration Factor for Ni IPTSCF_Ni (xylem:solution Ni concentration ratio), Ni concentration in solution and the volume of transpired water. The model input variables were the constant mean IPTSCF_Ni value, determined from independent leaf Ni accumulation kinetics, and the exponential law fitting the transpiration rate kinetics. Using the best calibration, the model was validated and a sensitivity analysis was carried out thereafter. Models were formulated as sets of ordinary differential equation systems which were solved using the fourth-order Runge–Kutta method.

Results

The best model calibration was the joint parameter optimization: the two parameters of the Freundlich Ni adsorption isotherm and of the Ni desorption rate coefficient are obtained using the kinetics of Ni concentrations in the soil solutions for the reference unplanted Ni-contaminated topsoils. The model was validated reasonably well for both Ni concentration in soil solution and leaf Ni mass.

Conclusions

The joint parameter optimization of the two parameters of the Freundlich nickel sorption isotherm and of the Ni desorption rate was successful whereas the Freundlich batch Ni sorption isotherm dramatically overestimated Ni sorption. This joint approach is therefore recommended for any plant metal uptake model. The 0-D one-site rate-limited desorption model linked to a biophysical coupled Ni and water uptake model reasonably validated the kinetics of both Ni concentration in solution and leaf Ni mass. This promising simplified model for predicting both metal concentration in solution and leaf metal mass for metal needs further validations in culture chambers and further improvements in order to use it in the field as a one-dimensional model, taking into account soil moisture dynamics.     

A simple alternative to line transects of nests for estimating orangutan densities

We conducted a validation of the line transect technique to estimate densities of orangutan (Pongo pygmaeus) nests in a Bornean swamp forest, and compared these results with density estimates based on nest counts in plots and on female home ranges. First, we examined the accuracy of the line transect method. We found that the densities based on a pass in both directions of two experienced pairs of observers was 27% below a combined sample based on transect walks by eight pairs of observers, suggesting that regular line-transect densities may seriously underestimate true densities. Second, we compared these results with those obtained by nest counts in 0.2-ha plots. This method produced an estimated 15.24 nests/ha, as compared to 10.0 and 10.9, respectively, by two experienced pairs of observers who walked a line transect in both directions. Third, we estimated orangutan densities based on female home range size and overlap and the proportion of females in the population, which produced a density of 4.25–4.5 individuals/km² . Converting nest densities into orangutan densities, using locally estimated parameters for nest production rate and proportion of nest builders in the population, we found that density estimates based on the line transect results of the most experienced pairs on a double pass were 2.82 and 3.08 orangutans/km², based on the combined line transect data are 4.04, and based on plot counts are 4.30. In this swamp forest, plot counts therefore give more accurate estimates than do line transects. We recommend that this new method be evaluated in other forest types as well.     

A simple technique for estimating operative environmental temperature

• 1.1.|Operative environmental temperature (T_c) is commonly measured using a taxidermic mount consisting of a hollow copper cast of an animal's body covered by the animal's integument. We compare estimates of T_c made using such mounts with those derived from use of painted metal sphere thermometers, which are easier to construct and more rugged than taxidermic mounts.
• 2.2.|Comparison of data for 4 bird species indicates that metal spheres may be acceptable T_c-thermometers for analyses involving multiple measurements over moderately long time-scales (e.g. several hours).
• 3.3.|In this case, positive and negative differences between operative temperature estimated from use of taxidermic mounts and painted spheres tend to compensate and the average difference is usually less than 2°C. This difference is similar to that resulting from postural variation of taxidermic mounts or variation among individual mounts in identical postures.
• 4.4.|Sensitivity analysis indicates that use of painted spheres is unlikely to be an important source of error in estimates of total daily energy expenditure.
• 5.5.|In contrast, use of painted sphere thermometers in analyses involving fewer measurements over shorter-time scales can produce unacceptable discrepancies from values obtained from taxidermic mounts (i.e. up to 6.3°C).

     

A simple method for estimating cytoplasmic diffusion coefficients

The diffusion coefficients of radioactively labelled substances in cytoplasm or other fluids are determined in vitro. The fluid containing the labelled substance is filled into a cylinder with one open end, through which the labelled substance diffuses out into a stirred outer medium. The diffusion coefficient is calculated by a one-dimensional diffusion equation from the rate of loss from the cylinder, and the length of the cylinder. The diffusion coefficients of tritiated water in several fluids have been determined. The results are in good agreement with those obtained by other methods.     

A fast and simple micromethod for estimating proteins

The assay is based on the property of proteins to form a complex with bromophenol blue. In alkaline solution this complex shows an intensive blue colour which is well measurable at 598 nm. The method is especially useful for small volumes (5-50 microliter) with a content of 5-30 micrograms of protein. By modification the test can be also used for the measurement of higher amounts of protein.     

A test of a model for estimating production in the sea

Primary productivity was measured in the sea off the coasts of Florida and Georgia with the radiocarbon method at four stations during March, 1971. Integral photosynthesis per square meter surface was determined with a mathematical model from empirical data gathered from in situ and shipboard incubation experiments. The mathematical model provided shipboard incubators to be used to estimate primary production rates while overcoming the problem of relating light quality and quantity simulated by the incubators to that found in the euphotic zone. The use of shipboard incubation can allow for measurements to be made on a moving vessel, more stations visited per day and water samples incubated at a constant light intensity. Primary productivity at the four sampling stations ranged from 0.026 to 0.042 mg C/M² hr.     

A simple moder for estimating the ice content of freezing ectotherms

1. 1.Although body ice content is an important variable affecting freeze tolerance, present calorimetric methods for its measurement necessarily require the termination of a freezing protocol.

2. 2.A simple iterative model, based on the colligative properties of solutions and requiring precise measurements of only equilibrium freezing point (of the unfrozen organism) and of core body temperature, allows estimation of the percentage of body water frozen at any time during a freezing episode.

3. 3.This model can also predict the lethal temperature for a freezing ectotherm, assuming that death occurs due to osmotic dehydration when 67% (of any other known lethal fraction) of the body water is frozen.

4. 4.The basic model is easily extended to evaluate the effects of variables such as: body mass, initial body water content, initial osmotic concentration, and test chamber microenvironment.

5. 5.This model is not intended to supplant existing more exact biophysical models of freezing kinetics. Rather it is proposed as a first approximation which is generally supported by published data and which should be of significant practical value for investigators of freeze tolerant organisms.