A study of statistical error in isothermal titration calorimetry

In isothermal titration calorimetry (ITC), the two main sources of random (statistical) error are associated with the extraction of the heat q from the measured temperature changes and with the delivery of metered volumes of titrant. The former leads to uncertainty that is approximately constant and the latter to uncertainty that is proportional to q. The role of these errors in the analysis of ITC data by nonlinear least squares is examined for the case of 1:1 binding, M+X right arrow over left arrow MX. The standard errors in the key parameters-the equilibrium constant Ko and the enthalpy DeltaHo-are assessed from the variance-covariance matrix computed for exactly fitting data. Monte Carlo calculations confirm that these "exact" estimates will normally suffice and show further that neglect of weights in the nonlinear fitting can result in significant loss of efficiency. The effects of the titrant volume error are strongly dependent on assumptions about the nature of this error: If it is random in the integral volume instead of the differential volume, correlated least-squares is required for proper analysis, and the parameter standard errors decrease with increasing number of titration steps rather than increase.     

Seasonal changes in silicon content of diatoms estimated from the ratio of particulate silicon to diatom volume under silicon sufficiency in diatom-rich Lake Barato

To clarify the changes in Si content of diatoms, the particulate silicon (PSi) concentration and total diatom volume (TDV) were determined in Lake Barato, Japan, from April to July 1998–2000. The soluble reactive silicon (SRSi) concentration decreased markedly with the rapid increase in TDV in May and June in all three years, although the value did not fall below that at which diatom growth might be limited. The proliferation of small discoid diatoms contributed to the decrease in SRSi concentration each year. The Si content of diatoms may not be constant as indicated by the changes in PSi:TDV ratio. The low PSi:TDV ratio and the fact that PSi concentration was lower than diatom PSi concentration (calculated from the volume of diatom species) accompanying the decrease in TDV suggests the possibility of a disturbance in the silicification in May and June 1999. These parameter changes accompanying the increase in TDV suggest that the silicification did not catch up with the cell division in early April 1998, early May 1999, and mid-June 2000. In addition, the PSi:TDV ratio increased rapidly and showed large fluctuations in July 1998 and 1999. This may have been caused by a change in dominant species from small discoid diatoms to Aulacoseira granulata because of the differences in Si content per unit cell volume.     

Slow-folding kinetics of ribonuclease-A by volume change and circular dichroism: evidence for two independent reactions.

The slow refolding of guanidine-HCl-denatured ribonuclease-A was studied by volume change and by kinetic CD at 222 and 276 nm. Dilatometric measurements revealed that on refolding there is a fast volume change of +232 mL/mol of protein. This is followed by a very slow nonexponential change that takes about 25 min to reach equilibrium. By adding varying amounts of (NH4)2SO4, the slow volume change curve was resolved into 2 concurrent reactions. The faster of the 2 slow events entails a negative volume change of -64 mL/mol of protein and appears to arise from proline isomerization. The slower process, attended by a positive change of +53 mL/mol of protein, has properties consistent with the "XY" reaction of Lin and Brands (1983, Biochemistry 22:563-573). This reaction is so named because the conformational nature of neither its initial (Y) nor its final state (X) is known; the transition is characterized solely by its absorbance and fluorescence kinetics. These are the first direct physical measures attributable to the "XY" process. The early formation of a compact structure in the event responsible for the rapid +232-mL/mol volume change, however, is consistent with the sequential model of folding (Cook KH, Schmid FX, Baldwin RL, 1979, Proc Natl Acad Sci USA 76:6157-6161; Kim PS, Baldwin RL, 1980, Biochemistry 19:6124-6129). The usefulness of volume change measurements as a method of detecting structural rearrangements was confirmed by finding agreement between time constants obtained from parallel volume change and kinetic CD experiments. The measured volume changes arise from both changes in hydration and changes in the packing of atoms in the interior of the protein.     

Muscle Volume Changes

Measurements have been made of the volume changes accompanying single isometric and isotonic twitches of frog sartorius muscle. The volume change consists of a rapid increase, a subsequent decrease, and a return to the initial volume; the order of magnitude of increase and decrease is 10^-5 cc/g of muscle. This volume change is length-dependent: the initial increase becomes more pronounced as the initial length of the muscle is decreased, while the volume decrease is greatest at reference length and is diminished for longer and shorter initial lengths. Muscle volume changes are also dependent upon temperature and amount of shortening: the return phase is prolonged as the temperature is lowered; and, in an isotonic twitch, a volume increase accompanying muscle shortening is superimposed upon the volume change described for an isometric twitch. These "shortening volume changes" may correspond to the volume decrease observed in frog muscle under a passive stretch. If the active state is prolonged by the use of a frog Ringer solution in which iodide ions have been substituted for chloride ions, the time course of the volume decrease is likewise prolonged; this suggests a relationship between the volume decrease and the active state of the muscle.     

The Investigation of Stomatal Ionic Relations using Guard Cell Protoplasts: II. OSMOTIC RELATIONS OF GUARD CELL PROTOPLASTS IN SHORT AND LONG-TERM INCUBATION

Clint, G. M. 1985. The investigation of stomatal ionic relationsusing guard cell protoplasts. II. Osmotic relations of guardcell protoplasts in short and long-term incubation.—J.exp. Bot 36: 1739–1748 Measurements were made of the volume changes exhibited by isolatedguard cell protoplasts (GCPs) of Commelina communis L, whenexposed to a range of concentrations of external osmotica Inshort-term incubation, GCPs behaved as osmometers and showedrapid volume changes in response to changing external osmoticpressure (₀). In long-term incubation, GCPs prepared and incubatedwith added external KCl showed further slow changes in volume,in a manner suggesting that regulation of volume occurred. Protoplastsprepared and incubated without added external KCl had smallervolumes for a given value of ₀, and their ability to regulatevolume in long-term incubation was reduced or absent. Treatment with fusicoccin caused an increase in both the volumeand the K⁺ content of GCPs. The increase in volume continuingafter the increase in K⁺ content had ceased, in a manner similarto that observed in walled guard cells in epidermal strips. Key words: Guard cell protoplasts, volume regulation, Commelina communis     

Applications of pressure perturbation calorimetry to study factors contributing to the volume changes upon protein unfolding

BackgroundPressure perturbation calorimetry (PPC) is a biophysical method that allows direct determination of the volume changes upon conformational transitions in macromolecules.Scope of this reviewThis review provides novel details of the use of PPC to analyze unfolding transitions in proteins. The emphasis is made on the data analysis as well as on the validation of different structural factors that define the volume changes upon unfolding. Four case studies are presented that show the application of these concepts to various protein systems.Major conclusionsThe major conclusions are:

• 1.Knowledge of the thermodynamic parameters for heat induced unfolding facilitates the analysis of the PPC profiles.
• 2.The changes in the thermal expansion coefficient upon unfolding appear to be temperature dependent.
• 3.Substitutions on the protein surface have negligible effects on the volume changes upon protein unfolding.
• 4.Structural plasticity of proteins defines the position dependent effect of amino acid substitutions of the residues buried in the native state.
• 5.Small proteins have positive volume changes upon unfolding which suggests difference in balance between the cavity/void volume in the native state and the hydration volume changes upon unfolding as compared to the large proteins that have negative volume changes.

General significanceThe information provided here gives a better understanding and deeper insight into the role played by various factors in defining the volume changes upon protein unfolding. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences — Principles and Applications, edited by Fadi Bou-Abdallah.     

Percutaneous disc decompression with nucleoplasty-volumetry of the nucleus pulposus using ultrahigh-field MRI

Purpose

To evaluate changes in nucleus pulposus volume as a potential parameter for the effects of disc decompression.

Methods

Fifty-two discs (T8 to L1) were extracted from 26 pigs and separated into thoracic (T8 to T11) and thoracolumbar discs (T12 to L1). The discs were imaged using 7.1 Tesla ultrahigh-field magnetic resonance imaging (MRI) with acquisition of axial T2-weighted turbo spin-echo sequences for determination of baseline and postinterventional nucleus pulposus volumes. Volumes were calculated using OsiriX® (http://www.osirix-viewer.com). After randomization, one group was treated with nucleoplasty, while the placebo group was treated with an identical procedure but without coblation current. The readers analyzing the MR images were blinded to the kind of procedure performed. Baseline and postinterventional volumes were compared between the nucleoplasty and placebo group.

Results

Average preinterventional nucleus volume was 0.799 (SD: 0.212) ml. Postinterventional volume reduction in the nucleoplasty group was significant at 0.052 (SD: 0.035) ml or 6.30% (p<0.0001) (thoracic discs) and 0.082 (SD: 0.042) ml or 7.25% (p = 0.0078) (thoracolumbar discs). Nucleoplasty achieved volume reductions of 0.114 (SD: 0.054) ml or 14.72% (thoracic) and 0.093 (SD: 0.081) ml or 11.61% (thoracolumbar) compared with the placebo group.

Conclusions

Nucleoplasty significantly reduces thoracic and thoracolumbar nucleus pulposus volumes in porcine discs.     

Biomechanical properties of human cranium: Age-relayed aspects

Biomechanical properties of the human skull affect its dynamic tensility (pliability or compliance) at changes of intracranial volume and pressure (ΔV/ΔP). The work substantiates a possibility of noninvasive and dynamic evaluation of cranial compliance by synchronous recording of transcranial dopplerogram of middle cerebral artery and cranial bioimpedance that provides information about pulsative changes of intracranial pressure and volume, respectively, with subsequent computer pattern and phasic analysis of these processes. The characteristic peculiarities of the cranial compliance at rest and during action of functional hemo- and liquorodynamic tests were traced in people of the middle (40–50 years) and elderly (70–85 years) age groups as compared with the young group (20–30 years). A relative decrease of this parameter has been revealed in the middle age group due to an increase of rigidity of skull bones and ligaments, which indicates a decrease of tolerance of the intracranial circulatory system. However, in the group of 70–85 years the compliance parameters rose due to an increase of intracranial liquor volume and activation of liquor circulation inside the craniospinal space, which is a compensatory mechanism for maintenance of the adequate brain circulatory-metabolic activity.     

Physiological significance of volume-regulatory transporters

Research over thepast 25 years has identified specific ion transporters and channelsthat are activated by acute changes in cell volume and that serve torestore steady-state volume. The mechanism by which cells sense changesin cell volume and activate the appropriate transporters remains amystery, but recent studies are providing important clues. A curiousaspect of volume regulation in mammalian cells is that it is oftenabsent or incomplete in anisosmotic media, whereas complete volumeregulation is observed with isosmotic shrinkage and swelling. The basisfor this may lie in an important role of intracellularCl in controllingvolume-regulatory transporters. This is physiologically relevant, sincethe principal threat to cell volume in vivo is not changes inextracellular osmolarity but rather changes in the cellular content ofosmotically active molecules. Volume-regulatory transporters are alsoclosely linked to cell growth and metabolism, producing requisitechanges in cell volume that may also signal subsequent growth andmetabolic events. Thus, despite the relatively constant osmolarity inmammals, volume-regulatory transporters have important roles inmammalian physiology.     

pH-dependent changes in mitochondrial membrane structure

The pH-dependent changes in structure of submitochondrial vesicles prepared from rat liver have been investigated by a variety of structural probes. The main changes are: (a) the volume of the vesicles as assessed by electron microscopy and packed volume is dependent upon pH, being a minimum at pH 5. Between pH 5 and pH 9 the changes are reversible; (b) the accompanying light-scattering changes are also sensitive to divalent cations; (c) the binding characteristics of 8-anilinonaphthalene-1-sulfonic acid indicate pH-dependent changes in the amount of net charge on the membrane; (d) above pH 4, circular dichroism spectra show alterations characteristic of changes in quaternary protein structure; (e) below pH 4, infrared studies indicate changes in protein secondary conformation are also taking place. From these results, the nature and limits of conformational (molecular) and configurational (morphological) changes in mitochondrial membranes following changes in H⁺ activity are better defined. In the physiological range, pH-dependent conformational changes are confined to reversible changes in quaternary structure resulting from alterations in membrane charge.     

Network thermodynamic analysis and stimulation of isotonic solute-coupled volume flow in leaky epithelia: an example of the use of network theory to provide the qualitative aspects of a complex system and its verification by stimulation

A network thermodynamic model was developed to provide insights into the nature of isotonic solute-coupled volume flow in "leaky" epithelia, where the transepithelial volume flow is assumed to be primarily through the cellular pathway. The coupled flows of solute and volume at each membrane in this four membrane model are described by the practical phenomenological equations as developed by Kedem & Katchalsky (1958). The model contains one permeable non-electrolyte solute (s) and a fixed amount of an impermeable non-electrolyte (i) inside the cell. The cell is assumed to be capable of volume regulation under the steady-state experimental conditions simulated. A solute-pump, located in the basolateral membrane, uses feedback regulation to adjust Cs in the cell in order to maintain cell volume at or near control levels in all simulations. Model behavior is, in general, very consistent with experimental observations with respect to tonicity and magnitude of volume flow over a wide range of experimental conditions. Examination of the parameter space suggests the following important features when isotonic solute-coupled volume flow moves primarily through the cellular pathway: (1) the apical membrane reflection coefficient must be less than that of the basolateral membrane; (2) the basement membrane reflection coefficient must be small; (3) the apical membrane solute permeability and reflection coefficient are the two most "sensitive" parameters and need to vary in an inverse manner in order to maintain isotonicity when both solute and volume flows increase; and (4) relationships (1) and (3) above imply the need for at least two separate solute pathways in the apical membrane, one that is shared with volume flow and one that is not.     

Glomerular morphometry in biopsy evaluation of minimal change disease, membranous glomerulonephritis, thin basement membrane disease and Alport's syndrome

OBJECTIVE: To assess the role of glomerular morphometry in biopsy evaluation in renal disorders in addition to conventional diagnostic procedures. STUDY DESIGN: The study includes 10 cases each of minimal change disease (MCD), idiopathic membranous glomerulonephritis (idiopathic MGN), thin basement membrane disease (TBMD) and Alport's syndrome. Renal biopsies for normal study were obtained from age- and sex-matched autopsy cases without any renal disorder, confirmed histologically and ultrastructurally. Glomerular morphometry was performed by semiautomatic procedure using Quantimet-600 image analysis system (Leica, Cambridge, United Kingdom). RESULTS: Morphometric findings revealed significant increase in glomerular "diameter and area" and "tuft diameter and area" in patients of idiopathic MGN, but no significant difference was found in patients of MCD, TBMD and Alport's syndrome. Evaluation of glomerular volume fractions revealed a decrease in capillary space volume fraction and an increase in "membranes and mesangial matrix" volume fraction in patients with idiopathic MGN. Significant decrease in capillary space volume fraction was also observed in patients of MCD. Patients with Alport's syndrome showed variable changes. CONCLUSION: Glomerular morphometry could be considered as an adjunct to the diagnostic armamentarium of light microscopy, immunofluorescence and electron microscopy because it provides deep insight into quantitative parameters.     

Determination of membrane permeability to water from osmotically induced light-scattering changes of membrane vesicles: Analysis of the method

The kinetics of osmotically induced changes in vesicular volume and internal solute concentration were analyzed for membrane vesicles containing fixed quantity of impermeable osmoticum in the lumen. The kinetic curves of the concentration and volume changes were shown to be dissimilar. The average durations of these two processes may differ by several tens of percents, depending on the extent and polarity of the initially imposed osmotic gradient. For vesicles containing identical solutes in the internal and external solutions, the problem is analyzed of how the concentration and volume changes are manifested in changes of the effective scattering cross-section of the vesicle. The light scattering changes, directed oppositely to volume changes, were found to coincide roughly with the kinetics of volume changes. The analysis shows that calculations of water permeability coefficient should be based on average duration of volume changes rather than the duration of concentration changes. The replacement in calculations of the first parameter with the second one may result in overestimation of water permeability by a factor of 1.5. This might be relevant to the reported discrepancies in water permeability values determined by the osmotic and isotope methods. Although the allowance for 1.5-fold overestimation cannot fully account for the differences observed, it significantly lowers the discrepancy between these estimates in some cases. The opposite signs of light scattering and volume changes originate from the presence of two components in the optical path of the vesicle, i.e., the membrane and the lumenal solution.     

Tracer measurements of non-equilibrium volumes of distribution

According to conventional theory the product of the transport flowrate and the mean transit time of a tracer through a system yields the equilibrium volume of distribution for the tracer, regardless of tracer kinetics or space geometry. Experimental results do not support this notion. The influence of measurement time on the volume measured with a bolus technique is addressed using systems theory to analyze a tissue-impedance form of the Sangren-Sheppard model. Assymptotic solutions show that the volume estimates are governed by a time constant, tau, related to diffusion in the tissue, to tissue capacity, and to wall permeability, and by a dimensionless ratio, f, describing a relation of tau to vascular transport time. A third parameter, g, describing the relative contributions to overall resistance to diffusion of effective permeability and of limited diffusivity in the tissue, is shown to be of less importance. The derived tau is similar to but not equivalent to the often cited "characteristic time". The "equilibrium" volume of distribution is defined as that which would be measured if equilibrium were allowed to establish. The "non-equilibrium" volume of distribution is defined as that which would be measured given finite times and is shown to approach the "equilibrium" volume as such times increase. Tracer equilibration is not required to accurately measure the "equilibrium" volume. When there is no flow limitation (f much less than 1) a measurement time of tau (plus vascular transit time) would yield a "non-equilibrium" volume only 33% of the "equilibrium" volume; a time of 2 tau would yield 55%; a time of 10 tau would yield effectively the total equilibrium volume. Finite diffusivity in tissue and permeability restrictions can have significant effects on the proportion of the volume measured.     

Patterns in the structural homeostasis of cardiomyocytes

Results of quantitative analysis of the ultrastructura organization (UO) of animal (rabbit, rat, dog) and human cardiomyocytes carried out by means of the point method are presented. A number of stereometric constants which provide structural cardiomyocyte homeostasis (SCH) were revealed: the sum total mitochondrial (MT) and myofibril (MF) volume is a constant value- a "cardiomyocytic constant" (Vmt + Vmf=Kcm); the total growth of MT and MF volumes in different functional states is equal to "0" (dVmt + dVmf=0); adaptational MT and MF rearrangement takes place during an interval of 11% of the volume (deltaVmt=deltaVmf=11 percent; the SCH is maintained by the changes of the UO within the limits of the law of "constancy of volume interrelations" (80; 10; 10), according to which 80 percent of the volume falls on Kcm, 10 percent of the remaining organellae and cell inclusions (Vi) and 10 percent on the plasma cell (Vpl). The assumption on a possibility of universality of the stereometric constants is suggested.     

General continuum analysis of transport through pores. II. Nonuniform pores.

A general continuum derivation of the nonelectrolyte (Js) and volume (Jv) flux through a pore whose cross section is a function of axial position (nonuniform) is given. In general, the flux equations cannot be reduced to the same form as for a uniform pore and it is not possible to characterize the pore kinetics by three constants as in the uniform pore case. However, it is shown that under certain conditions, the nonuniform pore equations can be approximated by the uniform pore form and can be characterized by three constants (omega, sigma, Lp). The only condition needed to reduce the Jv equation to the uniform form is that the solution be dilute. The deviation of the Js equation from the uniform form is characterized by an asymmetrical function of Jv whose maximum value is estimated. It is shown that the maximum posible fractional deviation of the Js equation from the uniform form is given by the parameter: 0:5sigmaJv/omegaRT. Since this parameter is less then 0.15 for most membrane studies, the nonuniform Js equation can usually be approximated by the uniform pore form. The general results are illustrated by explicit calculations on several models of nonuniform pores. It is shown, for example, that the "equivalent pore radius" defined in the usual way is a function of the experimental parameter that is measured and is not unique.     

The Response of Duck Erythrocytes to Nonhemolytic Hypotonic Media : Evidence for a volume-controlling mechanism

Duck erythrocytes were incubated in hypotonic media at tonicities which do not produce hemolysis. The cells'' response can be divided into two phases: an initial rapid phase of osmotic swelling and a second more prolonged phase (volume regulatory phase) in which the cells shrink until they approach their initial isotonic volume. Shrinkage associated with the volume regulatory phase is the consequence of a nearly isosmotic loss of KCl and water from the cell. The potassium loss results from a transient increase in K efflux. There is also a small reduction in Na permeability. Changes in cell size during the volume regulatory phase are not altered by 10^-4 M ouabain although this concentration of ouabain does change the cellular cation content. The over-all response of duck erythrocytes is considered as an example of "isosmotic intracellular regulation," a term used to describe a form of volume regulation common to euryhaline invertebrates which is achieved by adjusting the number of effective intracellular osmotic particles. The volume regulatory phase is discussed as the product of a membrane mechanism which is sensitive to some parameter associated with cell volume and is capable of regulating the loss of potassium from the cell. This mechanism is able to regulate cell size when the Na-K exchange, ouabain-inhibitable pump mechanism is blocked.     

Paradoxical effects and interactions in food webs: a commentary on Nilsson and McCann (2016)

Counter-intuitive responses of population density to changes in parameter values were used by Nilsson and McCann (Theor Ecol 9:59–71, 2016, Theoretical Ecology) to argue for the superiority of a recently proposed measure of interaction strength. They argued that one of these responses (decreasing consumer density in response to increasing per capita resource attack rate) is rarely or never discussed and is distinct from responses to consumer mortality. In fact, there is a long history of work on responses to altered attack rates, and they are linked to responses to mortality because the latter very often produce coupled changes in attack rate. This earlier literature does not support a qualitative difference between the impacts of these two types of parameter change and does not clearly support the desirability of any particular measure of interaction strength.     

Herbivory damage does not indirectly influence the composition or excretion of aphid honeydew

Recent research has shown that extrafloral nectar secretion by plants, which also attracts ants, is a defense inducible by herbivory damage. Our research addresses the question of whether plants can manipulate the honeydew secretions of homopterans as an inducible defense in response to herbivory in the same manner as extrafloral nectaries. We investigated changes in honeydew composition and excretion rate by the facultatively ant-attended aphid Chaitophorus saliniger Shinji (Homoptera: Aphididae) depending on the presence or absence of herbivory by caterpillars (Clostera anastomosis L.; Lepidoptera: Notodontidae) on their host plant, the willow Salix gilgiana Seemen. Our results found no evidence to suggest that herbivory damage to the aphids host plant causes significant changes in aphid population growth, honeydew droplet volume, volume of honeydew excreted per aphid per hour, or composition of three abundant sugars in aphid honeydew as a result of herbivory damage to the aphids host plant, suggesting that, in this particular system, the plant is not manipulating the aphids honeydew output for its own benefit.