An autologistic model for the genetic analysis of familial binary data.

Regressive logistic models specify the probability distribution of familial binary traits by conditioning each individual's phenotype on those of preceding relatives; therefore, the expression of the joint probability of the familial data necessitates ordering the observations. In the present paper, we propose an autologistic model of this familial dependence structure, which does not require specification of a particular ordering of the phenotypic observations. Genetic effects are introduced into the model in order to perform segregation analysis that is aimed at detecting the role of a major locus in the expression of familial phenotypes. In this model, the conditional probabilities have a logistic form, and large patterns of dependence between relatives can be considered with a simple interpretation of the parameters measuring the relationship between two phenotypes. The model is compared with the regressive logistic approach in terms of odds ratios and by using a simulation study.     

Transmembrane electric potential as a regulator of functional activity of biomembranes

The role of the transmembrane electric potential difference in producing structural tension of biological membranes is analysed. A suggestion is made that delta psi can optimize conditions of protein-protein interactions by ordering the membrane lipid. For energy-coupling membranes this makes it possible to explain the dependence of ATP synthesis on both electron transport and delta psi in terms of local bioenergetic coupling. The energized biomembrane is considered as a self-supporting structure, delta psi being a regulator of efficiency of molecular machines performing different membrane functions, including energization as well.     

A qualitative comparison of some diffusion models for neural activity via stochastic ordering

A number of diffusion processes have been proposed as a continuous analog of Stein's model for the subthreshold membrane potential of a neuron. Interspike intervals are then described as the first-passage-time of the corresponding diffusion model through a suitable threshold. Various biological considerations suggest the use of more sophisticated models in lieu of the Ornstein-Uhlenbeck model. However, the advantages of the additional complexity are not always clear. Comparisons among different models generally use numerical methods in specific examples without a general sensitivity analysis on the role of the model parameters. Here, we compare the distribution of interspike intervals from different models using the method of stochastic ordering. The qualitative comparison of the role of each parameter extends the results obtained from numerical simulations. One result on neurons with high positive net excitation is that the reversal potential models considered do not greatly differ from the Ornstein-Uhlenbeck model. For neurons with increased inhibition, the models give greater differences among the interspike interval distributions. In particular, when the mean trajectories are matched, the Feller model gives shorter times than the Ornstein-Uhlenbeck model but longer times than our double reversal potential model. Received: 5 August 1999 / Accepted in revised form: 8 May 2000     

Feedforward origins of response variability underlying contrast invariant orientation tuning in cat visual cortex

Contrast invariant orientation tuning in simple cells of the visual cortex depends critically on contrast dependent trial-to-trial variability in their membrane potential responses. This observation raises the question of whether this variability originates from within the cortical circuit or the feedforward inputs from the lateral geniculate nucleus (LGN). To distinguish between these two sources of variability, we first measured membrane potential responses while inactivating the surrounding cortex, and found that response variability was nearly unaffected. We then studied variability in the LGN, including contrast dependence, and the trial-to-trial correlation in responses between nearby neurons. Variability decreased significantly with contrast, whereas correlation changed little. When these experimentally measured parameters of variability were applied to a feedforward model of simple cells that included realistic mechanisms of synaptic integration, contrast-dependent, orientation independent variability emerged in the membrane potential responses. Analogous mechanisms might contribute to the stimulus dependence and propagation of variability throughout the neocortex.     

A geometrical model for DNA organization in bacteria

Recent experimental studies have revealed that bacteria, such as C. crescentus, show a remarkable spatial ordering of their chromosome. A strong linear correlation has been found between the position of genes on the chromosomal map and their spatial position in the cellular volume. We show that this correlation can be explained by a purely geometrical model. Namely, self-avoidance of DNA, specific positioning of one or few DNA loci (such as origin or terminus) together with the action of DNA compaction proteins (that organize the chromosome into topological domains) are sufficient to get a linear arrangement of the chromosome along the cell axis. We develop a Monte-Carlo method that allows us to test our model numerically and to analyze the dependence of the spatial ordering on various physiologically relevant parameters. We show that the proposed geometrical ordering mechanism is robust and universal (i.e. does not depend on specific bacterial details). The geometrical mechanism should work in all bacteria that have compacted chromosomes with spatially fixed regions. We use our model to make specific and experimentally testable predictions about the spatial arrangement of the chromosome in mutants of C. crescentus and the growth-stage dependent ordering in E. coli.     

Thermodynamics and Energetics of the Tonoplast Membrane Operating as a Hysteresis Switch in an Oscillatory Model of Crassulacean Acid Metabolism

The observed endogenous circadian rhythm in plants performing Crassulacean acid metabolism is effected by malate transport at the tonoplast membrane. Experimental and theoretical work asks for a hysteresis switch, regulating this transport via the ordering state of the membrane. We apply a schematic molecular model to calculate the thermally averaged order parameter of the membrane lipid structure in its dependence on external parameters temperature and area per molecule. The model shows a first order structural phase transition in a biologically relevant temperature range. Osmotic consequences of malate accumulation can trigger a transition between the two phases by changing the surface area of the cell vacuole. Estimation of the energy needed to expand the vacuole under turgor pressure because of osmotic changes while acidifying shows that energy needed as latent heat for the calculated change between phases can easily be afforded by the cell. Thus, malate content and the coexisting two phases of lipid order, showing hysteretic behavior, can serve as a feedback system in an oscillatory model of Crassulacean acid metabolism, establishing the circadian clock needed for endogenous rhythmicity. Received: 2 September 1997/Revised: 24 April 1998     

Cholesterol in model membranes. A molecular dynamics simulation.

Molecular dynamics simulations of a model membrane with inserted cholesterol molecules have been performed to study the perturbing influence of cholesterol. In the fluid phase of a lipid bilayer at 13 mol% concentration of cholesterol, local ordering of the hydrocarbon chains is induced. This perturbation decays with the distance from the cholesterol, and the effect extends 1.25 nm. It can be monitored in several ways, e.g., by an order parameter corresponding to deuterium nuclear magnetic resonance quadrupolar splittings, by the fraction of gauche bonds, or by the local bilayer thickness. At constant surface density, the local ordering is accompanied by disordering of the bulk phase, and, consequently, the net ordering effect is small. After compressing the system laterally in accordance with experimentally known surface areas, the bulk order parameters agree with those of a pure system, and the average order parameters are in accordance with experimental data. The necessity for this lateral compression is supported by calculated lateral pressures. At lower cholesterol concentration (3%), no direct perturbing effect is observed. A smaller lateral pressure than in a pure system indicates that the system with cholesterol is expected to have a smaller surface area, which would result in an increase of the order parameters, thus accounting for the experimental observations. The lack of spatial variation is, however, puzzling and may indicate a cooperative ordering effect.     

Spin-labeling study of membranes in wheat embryo axes. 1. Partitioning of doxyl stearates into the lipid domains

The interaction of lipid soluble spin labels with wheat embryo axes has been investigated to obtain insight into the structural organization of lipid domains in embryo cell membranes, using conventional electron paramagnetic resonance (EPR) and saturation transfer EPR (ST-EPR) spectroscopy. Stearic acid spin labels (n-SASL) and their methylated derivatives (n-MeSASL), labelled at different positions of their doxyl group (n=5, 12 and 16), were used to probe the ordering and molecular mobility in different regions of the lipid moiety of axis cell membranes. The ordering and local polarity in relation to the position of the doxyl group along the hydrocarbon chain of SASL, determined over the temperature range from -50 to +20 degrees C, are typical for biological and model lipid membranes, but essentially differ from those in seed oil droplets. Positional profiles for ST-EPR spectra show that the flexibility profile along the lipid hydrocarbon chain does exist even at low temperatures, when most of the membrane lipids are in solid state (gel phase). The ordering of the SASL nitroxide radical in the membrane surface region is essentially higher than that in the depth of the membrane. The doxyl groups of MeSASLs are less ordered (even at low temperatures) than those of the corresponding SASLs, indicating that the MeSASLs are located in the bulk of membrane lipids rather than in the protein boundary lipids. The analysis of the profiles of EPR and ST-EPR spectral parameters allows us to conclude that the vast majority of SASL and MeSASL molecules accumulated in embryo axes is located in the cell membranes rather than in the interior of the oil bodies. The preferential partitioning of the doxyl stearates into membranes demonstrates the potential of the EPR spin-labelling technique for the in situ study of membrane behavior in seeds of different hydration levels.     

Sine wave electropermeabilization reveals the frequency-dependent response of the biological membranes

The permeabilization of biological membranes by electric fields, known as electroporation, has been traditionally performed with square electric pulses. These signals distribute the energy applied to cells in a wide frequency band. This paper investigates the use of sine waves, which are narrow band signals, to provoke electropermeabilization and the frequency dependence of this phenomenon.Single bursts of sine waves at different frequencies in the range from 8 kHz–130 kHz were applied to cells in vitro. Electroporation was studied in the plasma membrane and the internal organelles membrane using calcium as a permeabilization marker. Additionally, a double-shell electrical model was simulated to give a theoretical framework to our results.The electroporation efficiency shows a low pass filter frequency dependence for both the plasma membrane and the internal organelles membrane. The mismatch between the theoretical response and the observed behavior for the internal organelles membrane is explained by a two-step permeabilization process: first the permeabilization of the external membrane and afterwards that of the internal membranes. The simulations in the model confirm this two-step hypothesis when a variable plasma membrane conductivity is considered in the analysis.This study demonstrates how the use of narrow-band signals as sine waves is a suitable method to perform electroporation in a controlled manner. We suggest that the use of this type of signals could bring a simplification in the investigations of the very complex phenomenon of electroporation, thus representing an interesting option in future fundamental studies.     

Chloride channels in toad skin

A study of the voltage and time dependence of a transepithelial Cl- current in toad skin (Bufo bufo) by the voltage-clamp method leads to the conclusion that potential has a dual role for Cl- transport. One is to control the permeability of an apical membrane Cl-pathway, the other is to drive Cl- ions through this pathway. Experimental analysis of the gating kinetics is rendered difficult owing to a contamination of the gated currents by cellular ion redistribution currents. To obtain insight into the effects of accumulation-depletion currents on voltage clamp currents of epithelial membranes, a mathematical model of the epithelium has been developed for computer analysis. By assuming that the apical membrane Cl- permeability is governed by a single gating variable (Hodgkin-Huxley kinetics), the model predicts fairly well steady-state current-voltage curves, the time course of current activations from a closed state, and the dependence of unidirectional fluxes on potential. Other predictions of the model do not agree with experimental findings, and it is suggested that the gating kinetics are governed by rate coefficients that also depend on the holding potential. Evidence is presented that Cl- transport through open channels does not obey the constant-field equation.     

Membrane Potential Fluctuations Determine the Precision of Spike Timing and Synchronous Activity: A Model Study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.     

Measurement of diffusion potentials in liposomes. Origin and properties of the threshold level in the oxonol VI response

A model is presented for the response of the membrane potential probe oxonol VI on diffusion potentials in liposomes. In this model the dependence of the probe response on the initial ion gradient is explained in terms of internal volume, internal ion concentration, membrane capacity and initial membrane potential. It is found that in the presence of an initial membrane potential (positive outside) there is a threshold value of the ion gradient needed for a probe response, which increases when the internal volume or the internal ion concentration decrease. The model is confirmed by experiments with liposomes of different sizes and internal KCl concentrations, prepared from asolectin or lipids isolated from the thermophilic cyanobacterium Synechococcus 6716. The significance of the model for threshold values observed in other energy-dependent phenomena is discussed.     

A kinetic model of the cytochrome bf complex. Evaluation of kinetic parameters

A kinetic model of the cytochrome bf complex was developed on the assumption that the Q-cycle operates. The bf complex was considered as a membrane enzyme catalyzing the electron transfer from plastoquinol to plastocyanine, which is coupled with proton translocation from the chloroplast stroma to the thylakoid lumen. The dependence of the electron transfer rates on the value of the transmembrane electric potential was taken into account. The model was applied to describe the experimental data on the flash-induced turnover of cytochromes b, plastocyanine, and the kinetics of proton deposition in the thylakoid lumen. The estimation of model parameters was performed.     

Towards a molecular theory of the nerve membrane: Prediction of the maximum negative conductance

A model of the squid axon membrane based on the theory of absolute reaction rates generates the rapid potential dependence of the membrane properties from the statistics of a simple gate-closing mechanism. It is shown that the peak negative transient conductance, normalized to the peak inward transient current, has a maximum value which is only weakly dependent upon parameter values, and is basically a property of the proposed mechanism. Those parameters which do influence the normalized peak conductance also affect the potential at which the maximum occurs, enabling an upper limit of 0.10 ± 0.02 mV^?1 to be established. Published data are consistent with this value but more precise measurements are desirable. The same limit should be observed in all excitable tissues which depend on the postulated central mechanism. Since other models do not predict such a maximum, experimental measurements of this property can provide a stringent test of the unifying principle suggested.     

On spontaneous discharge obtained from a physicochemical model of excitation

It is shown that a slight modification of a model of excitatory phenomena in irritable tissues, which has been treated before, exhibits spontaneous oscillations. The frequency of these oscillations and the time-course of the potential across the model membrane have been determined, together with the dependence of some of their characteristics on some important parameters, particularly (Ca⁺⁺).     

Predicting the effect of steroids on membrane biophysical properties based on the molecular structure

The relationship between sterol structure and the resulting effects on membrane physical properties is still unclear, owing to the conflicting results found in the current literature. This study presents a multivariate analysis describing the physical properties of 83 steroid membranes. This first structure-activity analysis supports the generally accepted physical effects of sterols in lipid bilayers. The sterol chemical substituents and the sterol/phospholipid membrane physical properties were encoded by defining binary variables for the presence/absence of those chemical substituents in the polycyclic ring system and physical parameters obtained from phospholipid mixtures containing those sterols. Utilizing Principal Coordinates Analysis, the steroid population was grouped into five well-defined clusters according to their chemical structures. An examination of the membrane activity of each sterol structural cluster revealed that a hydroxyl group at C3 and an 8-10 carbon isoalkyl side-chain at C17 are mainly present in membrane active sterols having rigidifying, molecular ordering/condensing effects and/or a raft promoting ability. In contrast, sterol chemical structures containing a keto group at C3, a C4-C5-double bond, and polar groups or a short alkyl side-chain at C17 (3 to 7 atoms) are mostly found in sterols having opposite effects. Using combined multivariate approaches, it was concluded that the most important structural determinants influencing the physical properties of sterol-containing mixtures were the presence of an 8-10 carbon C17 isoalkyl side-chain, followed by a hydroxyl group at C3 and a C5-C6 double bond. Finally, a simple Logistic Regression model predicting the dependence of membrane activity on sterol chemical structure is proposed.     

Negatively charged residues in the membrane ordering activity of SARS-CoV-1 and -2 fusion peptides

Entry of coronaviruses into host cells is mediated by the viral spike protein. Previously, we identified the bona fide fusion peptides (FPs) for severe acute respiratory syndrome coronavirus (“SARS-1”) and severe acute respiratory syndrome coronavirus-2 (“SARS-2”) using electron spin resonance spectroscopy. We also found that their FPs induce membrane ordering in a Ca²⁺-dependent fashion. Here we study which negatively charged residues in SARS-1 FP are involved in this binding, to build a topological model and clarify the role of Ca²⁺. Our systematic mutation study on the SARS-1 FP shows that all six negatively charged residues contribute to the FP’s membrane ordering activity, with D812 the dominant residue. The corresponding SARS-2 residue D830 plays an equivalent role. We provide a topological model of how the FP binds Ca²⁺ ions: its two segments FP1 and FP2 each bind one Ca²⁺. The binding of Ca²⁺, the folding of FP (both studied by isothermal titration calorimetry experiments), and the ordering activity correlate very well across the mutants, suggesting that the Ca²⁺ helps the folding of FP in membranes to enhance the ordering activity. Using a novel pseudotyped viral particle-liposome methodology, we monitored the membrane ordering induced by the FPs in the whole spike protein in its trimer form in real time. We found that the SARS-1 and SARS-2 pseudotyped viral particles also induce membrane ordering to the extent that separate FPs do, and mutations of the negatively charged residues also significantly suppress the membrane ordering activity. However, the slower kinetics of the FP ordering activity versus that of the pseudotyped viral particle suggest the need for initial trimerization of the FPs.     

SARS-CoV-2 Fusion Peptide has a Greater Membrane Perturbating Effect than SARS-CoV with Highly Specific Dependence on Ca2+

Coronaviruses are a major infectious disease threat, and include the zoonotic-origin human pathogens SARS-CoV-2, SARS-CoV, and MERS-CoV (SARS-2, SARS-1, and MERS). Entry of coronaviruses into host cells is mediated by the spike (S) protein. In our previous ESR studies, the local membrane ordering effect of the fusion peptide (FP) of various viral glycoproteins including the S of SARS-1 and MERS has been consistently observed. We previously determined that the sequence immediately downstream from the S2′ cleavage site is the bona fide SARS-1 FP. In this study, we used sequence alignment to identify the SARS-2 FP, and studied its membrane ordering effect. Although there are only three residue differences, SARS-2 FP induces even greater membrane ordering than SARS-1 FP, possibly due to its greater hydrophobicity. This may be a reason that SARS-2 is better able to infect host cells. In addition, the membrane binding enthalpy for SARS-2 is greater. Both the membrane ordering of SARS-2 and SARS-1 FPs are dependent on Ca²⁺, but that of SARS-2 shows a greater response to the presence of Ca²⁺. Both FPs bind two Ca²⁺ ions as does SARS-1 FP, but the two Ca²⁺ binding sites of SARS-2 exhibit greater cooperativity. This Ca²⁺ dependence by the SARS-2 FP is very ion-specific. These results show that Ca²⁺ is an important regulator that interacts with the SARS-2 FP and thus plays a significant role in SARS-2 viral entry. This could lead to therapeutic solutions that either target the FP-calcium interaction or block the Ca²⁺ channel.