On proper linearization, construction and analysis of the Boyle-van't Hoff plots and correct calculation of the osmotically inactive volume

The Boyle–van’t Hoff (BVH) law of physics has been widely used in cryobiology for calculation of the key osmotic parameters of cells and optimization of cryo-protocols. The proper use of linearization of the Boyle–vant’Hoff relationship for the osmotically inactive volume (v_b) has been discussed in a rigorous way in (Katkov, Cryobiology, 2008, 57:142–149). Nevertheless, scientists in the field have been continuing to use inappropriate methods of linearization (and curve fitting) of the BVH data, plotting the BVH line and calculation of v_b. Here, we discuss the sources of incorrect linearization of the BVH relationship using concrete examples of recent publications, analyze the properties of the correct BVH line (which is unique for a given v_b), provide appropriate statistical formulas for calculation of v_b from the experimental data, and propose simplistic instructions (standard operation procedure, SOP) for proper normalization of the data, appropriate linearization and construction of the BVH plots, and correct calculation of v_b. The possible sources of non-linear behavior or poor fit of the data to the proper BVH line such as active water and/or solute transports, which can result in large discrepancy between the hyperosmotic and hypoosmotic parts of the BVH plot, are also discussed.     

Challenge from the simple: some caveats in linearization of the Boyle-van't Hoff and Arrhenius plots

Some aspects of proper linearization of the Boyle-van’t Hoff (BVH) relationship for calculation of the osmotically inactive volume v_b, and Arrhenius plot (AP) for the activation energy E_a are discussed. It is shown that the commonly used determination of the slope and the intercept (v_b), which are presumed to be independent from each other, is invalid if the initial intracellular molality m₀ is known. Instead, the linear regression with only one independent parameter (v_b) or the Least Square Method (LSM) with v_b as the only fitting LSM parameter must be applied. The slope can then be calculated from the BVH relationship as the function of v_b. In case of unknown m₀ (for example, if cells are preloaded with trehalose, or electroporation caused ion leakage, etc.), it is considered as the second independent statistical parameter to be found. In this (and only) scenario, all three methods give the same results for v_b and m₀. AP can be linearized only for water hydraulic conductivity (L_p) and solute mobility (ω_s) while water and solute permeabilities P_w ≡ L_pRT and P_s ≡ ω_sRT cannot be linearized because they have pre-exponential factor (RT) that depends on the temperature T.     

Osmometric behavior of mouse oocytes in the presence of different intracellular sugars

In order to successfully cryopreserve oocytes using low concentrations of intracellular sugars, it is important to characterize their osmotic response in the presence of these intracellular sugars. In the present study, murine (B6D2F1) oocytes were microinjected with 0.8M glucose, trehalose or stachyose solutions to achieve an intracellular concentration equivalent to 0.1M, and then exposed to hypertonic solutions of increasing strength by supplementing an isotonic solution with 0.2, 0.3, 0.5, and 0.7 M of trehalose. Analysis of volumetric response of microinjected oocytes showed that the oocytes behaved as ideal osmometers in the presence of intracellular sugars and satisfied the Boyle van't Hoff relationship. Extrapolation of the osmotically inactive fraction (V macro b) from the Boyle van't Hoff relationship yielded values of 0.188+/-0.028, 0.212+/-0.042, 0.197+/-0.044, and 0.211+/-0.042 for control, glucose, trehalose and stachyose-injected oocytes, respectively. The present data revealing osmometric behavior of mouse oocytes in the presence of different intracellular sugars are important for the optimization of cryopreservation protocols using sugars.     

Rationally optimized cryopreservation of multiple mouse embryonic stem cell lines: I—Comparative fundamental cryobiology of multiple mouse embryonic stem cell lines and the implications for embryonic stem cell cryopreservation protocols

The post-thaw recovery of mouse embryonic stem cells (mESCs) is often assumed to be adequate with current methods. However as this publication will show, this recovery of viable cells actually varies significantly by genetic background. Therefore there is a need to improve the efficiency and reduce the variability of current mESC cryopreservation methods. To address this need, we employed the principles of fundamental cryobiology to improve the cryopreservation protocol of four mESC lines from different genetic backgrounds (BALB/c, CBA, FVB, and 129R1 mESCs) through a comparative study characterizing the membrane permeability characteristics and membrane integrity osmotic tolerance limits of each cell line. In the companion paper, these values were used to predict optimal cryoprotectants, cooling rates, warming rates, and plunge temperatures, and then these predicted optimal protocols were validated against standard freezing protocols.     

Curve fitting approach for measurement of cellular osmotic properties by the electrical sensing zone method. I. Osmotically inactive volume

We have investigated the confounding effects of dynamic range limitations on measurement of the osmotically inactive volume using electrical sensing zone instruments (e.g., Coulter counters), and propose an improved approach to parameter estimation. The conventional approach for analysis of cell size distributions measured by such particle sizing instruments requires data truncation: the mean cell volume is computed after exclusion of data below a specified lower bound (typically chosen to remove artifacts due to small-volume noise) and above an upper bound (typically governed by instrument limitations). The osmotically inactive volume is then estimated from a Boyle–van’t Hoff plot of the averaged volume data obtained after exposure to various solution osmolalities. We demonstrate that systematic exclusion of data in the conventional approach introduces bias that results in erroneously high estimates of the osmotically inactive volume fraction. To minimize this source of error, we have devised a new algorithm based on fitting a bimodal distribution model to the non-truncated volume data. In experiments with mouse insulinoma (MIN6) cells, the osmotically inactive volume fraction was estimated to be 0.15 ± 0.01 using the new method, which was significantly smaller than the estimate of 0.37 ± 0.02 obtained using the conventional method (p < 0.05). In silico experiments indicated that the parameter estimate obtained by the new method was accurate within 5%, whereas the error associated with the conventional approach was approximately 150%. Parametric analysis was used to elucidate the sensitivity of errors to variations in instrument dynamic range and cell volume distribution width.     

A theory for the membrane potential of living cells

We give an explicit formula for the membrane potential of cells in terms of the intracellular and extracellular ionic concentrations, and derive equations for the ionic currents that flow through channels, exchangers and electrogenic pumps. We demonstrate that the work done by the pumps equals the change in potential energy of the cell, plus the energy lost in downhill ionic fluxes through the channels and exchangers. The theory is illustrated in a simple model of spontaneously active cells in the cardiac pacemaker. The model predicts the experimentally observed intracellular ionic concentration of potassium, calcium and sodium. Likewise, the shapes of the simulated action potential and five membrane currents are in good agreement with experiment. We do not see any drift in the values of the concentrations in a long time simulation, and we obtain the same asymptotic values when starting from the full equilibrium situation with equal intracellular and extracellular ionic concentrations. Received: 9 December 1998 / Revised version: 30 August 1999 / Accepted: 15 October 1999     

A method for studying the depolarization-induced calcium ion release from fragmented sarcoplasmic reticulum

An optical method of studying the ‘depolarization’-induced Ca²⁺ release from isolated sarcoplasmic reticulum was presented. The method, which involves the use of metallochromic indicators, has the advantage of being able to perform the rapid kinetic measurement of the release. It was suggested that the velocity of the ‘depolarization’-induced Ca²⁺ release was rapid enough to account for the velocity of muscle contraction if the phenomenon is involved in the contraction mechanism. The change of membrane potential was also measured optically using a potential-sensitive dye. The possibility that this type of release is caused by osmotic effects is discussed.     

Fluid Transport: A Guide for the Perplexed

Readers of the physiological literature may be excused if they feel that fluid transport has become a complex and confusing field that is difficult to understand and to assess. The major theories of fluid-transporting epithelia are examined here with respect to their ability to explain quasi-isotonic fluid transport and its modulation by salt transport, osmotic permeability and basal tonicity. The basics of each theory are set out concisely, and their pros and cons are made explicit. Finally, a comparison is made in table form indicating their overall performance in relation to the problems of this difficult but important field.     

Analytical solution for the extremums of cell water volume and cell volume using a two-parameter model

Based on a two-parameter model [Cryobiology 37 (1998) 271-289], the analytical solution for the extremums of cell water volume and cell volume for a two-solute system are obtained. Compared with the numerical solution, the analytical solution offers an accurate but simple choice. The approximate solution [Cryobiology 40 (2000) 64-83] for the extremum of cell water volume is also discussed, the reason for the deviation is presented.     

A straightforward multiallelic significance test for the Hardy-Weinberg equilibrium law

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of "biallelic" tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes.     

Nitrite infusion increases cerebral blood flow and decreases mean arterial blood pressure in rats: A role for red cell NO

It has been proposed that the reduction of nitrite by red cells producing NO plays a role in the regulation of vascular tone. This hypothesis was investigated in rats by measuring the effect of nitrite infusion on mean arterial blood pressure (MAP), cerebral blood flow (CBF) and cerebrovascular resistance (CVR) in conjunction with the accumulation of red cell NO. The relative magnitude of the effects on MAP and CBF as well as the time dependent changes during nitrite infusion are used to distinguish between the effects on the peripheral circulation and the effects on the cerebral circulation undergoing cerebral autoregulation. The nitrite infusion was found to reverse the 96% increase in MAP and the 13% decrease in CBF produced by L-NAME inhibition of e-NOS. At the same time there was a 20-fold increase in oxygen stable red cell NO. Correlations of the red cell NO for individual rats support a role for red cell nitrite reduction in regulating vascular tone in both the peripheral and the cerebral circulation. Furthermore, data obtained prior to treatment is consistent with a contribution of red cell reduced nitrite in regulating vascular tone even under normal conditions.     

A sizeable decrease in the electric conductance of the thylakoid lumen as an early event during reaction center and Q cycle turnover

A patch-clamp method was used for measuring light-induced currents (photocurrents) in single dark-adapted Peperomia metallica chloroplasts in a 'whole-thylakoid' configuration. The multi-phasic photocurrent profiles upon a train of multiple flashes (time separation between flashes in the train 1 s) show the following characteristics: (i) photocurrent generation originates from trans-thylakoid charge transfer accompanying reaction center (RC)- and Q-cycle turnover; (ii) a 15–30% decrease in the amplitude of the RC-driven current in the second and following flashes, concomitantly with an increase in the dark recovery time of the current; and (iii) a binary oscillation of the Q-cycle current generator with high activity in even numbered flashes. The decrease in amplitude and decay rate constant of the photocurrent in a double flash after dark adaptation are interpreted in terms of a change in the electric conductance of the thylakoid lumen. Data are interpreted to indicate a light control of the thylakoid lumen via a narrowing of the planar sheet-like structures by 1 to 3 single turnover flashes. A simple method is given to determine the bioenergetic and electric parameters of the thylakoid membrane of a single chloroplast from the current profiles in a double flash. The data indicate that 1 s after a saturating flash the fraction of closed inactive centers is less than 3%.     

Population-specific material properties of the implantation site for transcatheter aortic valve replacement finite element simulations

Patient-specific computational models are an established tool to support device development and test under clinically relevant boundary conditions. Potentially, such models could be used to aid the clinical decision-making process for percutaneous valve selection; however, their adoption in clinical practice is still limited to individual cases. To be fully informative, they should include patient-specific data on both anatomy and mechanics of the implantation site. In this work, fourteen patient-specific computational models for transcatheter aortic valve replacement (TAVR) with balloon-expandable Sapien XT devices were retrospectively developed to tune the material parameters of the implantation site mechanical model for the average TAVR population.Pre-procedural computed tomography (CT) images were post-processed to create the 3D patient-specific anatomy of the implantation site. Balloon valvuloplasty and device deployment were simulated with finite element (FE) analysis. Valve leaflets and aortic root were modelled as linear elastic materials, while calcification as elastoplastic. Material properties were initially selected from literature; then, a statistical analysis was designed to investigate the effect of each implantation site material parameter on the implanted stent diameter and thus identify the combination of material parameters for TAVR patients.These numerical models were validated against clinical data. The comparison between stent diameters measured from post-procedural fluoroscopy images and final computational results showed a mean difference of 2.5 ± 3.9%. Moreover, the numerical model detected the presence of paravalvular leakage (PVL) in 79% of cases, as assessed by post-TAVR echocardiographic examination.The final aim was to increase accuracy and reliability of such computational tools for prospective clinical applications.     

A Finite Element Analysis Methodology for Representing the Articular Cartilage Functional Structure

Recognising that the unique biomechanical properties of articular cartilage are a consequence of its structure, this paper describes a finite element methodology which explicitly represents this structure using a modified overlay element model. The validity of this novel concept was then tested by using it to predict the axial curling forces generated by cartilage matrices subjected to saline solutions of known molality and concentration in a novel experimental protocol. Our results show that the finite element modelling methodology accurately represents the intrinsic biomechanical state of the cartilage matrix and can be used to predict its transient load-carriage behaviour. We conclude that this ability to represent the intrinsic swollen condition of a given cartilage matrix offers a viable avenue for numerical analysis of degenerate articular cartilage and also those matrices affected by disease.     

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

A computer program for the implicit regression of the Hill equation]

A computer program for implicit regression of the Hill equation. The fundamentals for the regression of implicit functions following the Gauss method are dealt with. Basing on these fundamentals a program for the regression of the Hill equation is described. The binding constant, the Hill coefficient and end extinction can be estimated. The mean errors of parameters were calculated in the linear model. The program was written in ALGOL 60 for the computer Robotron 300. The program is available on request.     

A new look at the hemolytic effect of local anesthetics, considering their real membrane/water partitioning at pH 7.4

The interaction of local anesthetics (LA) with biological and phospholipid bilayers was investigated regarding the contribution of their structure and physicochemical properties to membrane partition and to erythrocyte solubilization. We measured the partition into phospholipid vesicles—at pH 5.0 and 10.5—and the biphasic hemolytic effect on rat erythrocytes of: benzocaine, chloroprocaine, procaine, tetracaine, bupivacaine, mepivacaine, lidocaine, prilocaine, and dibucaine. At pH 7.4, the binding of uncharged and charged LA to the membranes was considered, since it results in an ionization constant (pK_app) different from that observed for the anesthetic in the aqueous phase (pK_w). Even though it occurred at a pH at which there is a predominance of the charged species, hemolysis was greatly influenced by the uncharged species, revealing that the disrupting effect of LA on these membranes is mainly a consequence of hydrophobic interactions. The correlation between the hemolytic activity and the LA potency shows that hemolytic experiments could be used for the prediction of activity in the development of new LA molecules.     

Investigating the potential for cryopreservation of human granulocytes with concentrated glycerol

The purpose of this study was to investigate the potential for cryopreservation of granulocytes using 30% glycerol. Recently reported permeability data was used to design two different methods for addition and removal of glycerol: a fast method that is predicted to keep cell volumes between 80% and 150% of the isotonic volume and a slow method that is predicted to keep cell volumes between 80% and 115% of the isotonic volume. The fast method resulted in cell recoveries of 31% ± 9% and 11% ± 3% before and after freezing, respectively, whereas the slow method resulted in even lower cell recoveries of 5% ± 2% and 4% ± 2%. The reduced cell recovery for the slow method is consistent with an increase in damage as a result of glycerol toxicity. Our results suggest that cryopreservation of granulocytes in concentrated glycerol is not feasible.