Discrete probability of a model for information provision on early embryonic development

A percolation model of the diffuse redistribution of morphogenetic information in early regulative development is analyzed. It is demonstrated that the statistical average values of cell connectedness remaining below the percolation threshold of the spatial redistribution of developmental determinants do not provide for the formation of cell structures of the necessary size. The average number of cell interactions should exceed the percolation threshold, and, therefore, the carriers of morphogenetic information in early development can move over distances comparable with the size of the entire embryo. The assumption concerning the percolation mechanism of cell death is used as a basis for estimating the statistical average value of cell connectedness at which the predicted number of cells theoretically isolated from the flow of signal molecules corresponds to the observed frequencies of dying embryonic cells. The estimated average number of cell interactions significantly exceeds the threshold of information resource percolation in the embryonic space and agrees with estimations of other authors, based on direct observations. The probable role of the diffusion front, or percolation cluster shell, in the regionalization of embryonic structures differing in their prospective values is discussed. It is shown that the duration of the communicative period, along with the statistical average number of channels providing for the intercellular transfer of signal molecules by diffusion, is a parameter controlling the processes of determination of embryonic structures.     

Systematic screening for signaling molecules expressed during somitogenesis by the signal sequence trap method

We describe a systematic screening to search for molecules that act as an extracellular signal during somitogenesis in vertebrates. Somitogenesis, which gives rise to segmented structures of axial bones and muscles, is a consequence of cooperative morphogenetic movements caused by precisely regulated cell and tissue interactions. We employed a strategy that combined subtractive hybridization to enrich paraxial mesoderm/somite-specific cDNAs and the signal sequence trap method, which selects signal sequence-containing molecules. Ninety-two independent cDNAs found to possess a putative signal sequence or a transmembrane domain are presented with a data base accession number for each. These clones include cDNAs which were previously identified with a function characterized, cDNAs previously identified with an undetermined function, and also cDNAs with no similarity to known sequences. Among them, 16 clones exhibited peculiar patterns of expression in the presomitic mesoderm/somites revealed by whole-mount and section in situ hybridization techniques, with some clones also being expressed in the forming neural tube. This is the first report in which an elaborate strategy combining three different screening steps was employed to identify signaling molecules relevant to a particular morphogenetic process.     

Cell surface labeling and mass spectrometry reveal diversity of cell surface markers and signaling molecules expressed in undifferentiated mouse embryonic stem cells

Although interactions between cell surface proteins and extracellular ligands are key to initiating embryonic stem cell differentiation to specific cell lineages, the plasma membrane protein components of these cells are largely unknown. We describe here a group of proteins expressed on the surface of the undifferentiated mouse embryonic stem cell line D3. These proteins were identified using a combination of cell surface labeling with biotin, subcellular fractionation of plasma membranes, and mass spectrometry-based protein identification technology. From 965 unique peptides carrying biotin labels, we assigned 324 proteins including 235 proteins that have putative signal sequences and/or transmembrane segments. Receptors, transporters, and cell adhesion molecules were the major classes of proteins identified. Besides known cell surface markers of embryonic stem cells, such as alkaline phosphatase, the analysis identified 59 clusters of differentiation-related molecules and more than 80 components of multiple cell signaling pathways that are characteristic of a number of different cell lineages. We identified receptors for leukemia-inhibitory factor, interleukin 6, and bone morphogenetic protein, which play critical roles in the maintenance of undifferentiated mouse embryonic stem cells. We also identified receptors for growth factors/cytokines, such as fibroblast growth factor, platelet-derived growth factor, ephrin, Hedgehog, and Wnt, which transduce signals for cell differentiation and embryonic development. Finally we identified a variety of integrins, cell adhesion molecules, and matrix metalloproteases. These results suggest that D3 cells express diverse cell surface proteins that function to maintain pluripotency, enabling cells to respond to various external signals that initiate differentiation into a variety of cell types.     

Cell adhesion in embryo morphogenesis

Visualizing and analyzing shape changes at various scales, ranging from single molecules to whole organisms, are essential for understanding complex morphogenetic processes, such as early embryonic development. Embryo morphogenesis relies on the interplay between different tissues, the properties of which are again determined by the interaction between their constituent cells. Cell interactions, on the other hand, are controlled by various molecules, such as signaling and adhesion molecules, which in order to exert their functions need to be spatiotemporally organized within and between the interacting cells. In this review, we will focus on the role of cell adhesion functioning at different scales to organize cell, tissue and embryo morphogenesis. We will specifically ask how the subcellular distribution of adhesion molecules controls the formation of cell-cell contacts, how cell-cell contacts determine tissue shape, and how tissue interactions regulate embryo morphogenesis.     

Morphogens: experimental illusion or reality?

The main attention is paid to the critical analysis of experimental data on morphogenetically active substances, so called "morphogens". It is proposed to consider the morphogens as specific transmitters providing for definite phases of morphogenetic tissues interactions, rather than as vectors of "morphogenetic information". In the normal development, the most studied morphogenetic tissue interactions can be referred to as so called permissive inductions, since the cells of the vertebrate embryos (amphibians, avians) are early determined for development in the ectomeso--and endodermal directions. A slow progress in studying the morphogens can be due to the following causes. 1. Theoretical "inadequacy" of the former concepts on the essence and mechanisms of embryonic induction. The necessity to develop a new system of concepts in this area of developmental biology is stressed. 2. Incompleteness of knowledge about the properties of reacting tissues and the mechanisms of action of morphogens. The early gastrula ectoderm of amphibians, most frequently used for testing the morphogens, appears to be a heterogenous population of the cells with different properties and potencies. It is, therefore, impossible to standardize strictly the biotesting of morphogens. It is suggested that the use to this end of aggregates of cell "strains" from the gastrula ectoderm, rather than of the gastrula ectoderm itself, may be more adequate 3. Insufficiency of embryonic material for biochemical identification and isolation of natural morphogens. A study of so called heterogenous inductors might be of help; these latter can be considered as analogs of natural morphogens. But the similarity of natural and heterogenous inductors can be limited only by their final effect on target tissue. The data are provided on the chemical nature, properties and mechanisms of action for a number of natural and heterogenous inductors (vegetalizing, neuralizing, mesodermalizing, lens-inducing factors). A conclusion is drawn that specific antigens do exist normally but they should not be established as a special class of "informationally important" molecules. The information necessary for development is contained in target cells and the function of a morphogen consists in providing for a definite link in the chain of processes leading to the switching on or expression of one or another programme. Only syntheses of specific proteins can, apparently, be programmed, thus reflecting the "onset" of differentiation path for a cell.     

Influence of water clustering on the dynamics of hydration water at the surface of a lysozyme

Dynamics of hydration water at the surface of a lysozyme molecule is studied by computer simulations at various hydration levels in relation with water clustering and percolation transition. Increase of the translational mobility of water molecules at the surface of a rigid lysozyme molecule upon hydration is governed by the water-water interactions. Lysozyme dynamics strongly affect translational motions of water and this dynamic coupling is maximal at hydration levels, corresponding to the formation of a spanning water network. Anomalous diffusion of hydration water does not depend on hydration level up to monolayer coverage and reflects spatial disorder. Rotational dynamics of water molecules show stretched exponential decay at low hydrations. With increasing hydration, we observe appearance of weakly bound water molecules with bulklike rotational dynamics, whose fraction achieves 20-25% at the percolation threshold.     

Transient directed motions of GABA(A) receptors in growth cones detected by a speed correlation index

Single-molecule tracking of membrane proteins has become an important tool for investigating dynamic processes in live cells, such as cell signaling, membrane compartmentation or trafficking. The extraction of relevant parameters, such as interaction times between molecular partners or confinement-zone sizes, from the trajectories of single molecules requires appropriate statistical methods. Here we report a new tool, the speed correlation index, designed to detect transient periods of directed motion within trajectories of diffusing molecules. The ability to detect such events in a wide range of biologically relevant parameter values (speed, diffusion coefficient, and durations of the directed period) was first established on simulated data. The method was next applied to analyze the trajectories of quantum-dot-labeled GABA(A) receptors in nerve growth cones. The use of the speed correlation index revealed that the receptors had a "conveyor belt" type of motion due to temporary interactions ( approximately 4.0 s) between the receptors and the microtubules, leading to an average directed motion (velocity approximately 0.3 mum s(-1)) in the growth-cone membrane. Our observations point to the possibility of a cytoskeleton-dependent redistribution of the sensing molecules in the membrane, which could play a role in the modulation of the cell response to external signals.     

A common biomechanical model for the formation of stationary cell domains and propagating waves in the developing organisms

Many important morphogenetic processes that take place in the development of an animal start from the segregation of a homogeneous layer of cells into a different number of the domains of columnar and flattened cells. In many cases, waves of cell shape transformation travel throughout embryonic tissues. A biomechanical model is presented which embraces both kinds of event. The model is based on the idea of interplay between short- and long-range factors. While the former promote the spreading of a given cell state along a cell row in the recalculation direction, long-range factors are associated with self-generated tensions which, after exceeding a certain threshold, induce active cell extension and hence the rise of tangential pressure. Different kinds of biologically realistic stationary structures, as well as various kinds of the running waves, can be modelled under different parameter values. Moreover, the current model can be coupled with the previous one (Beloussov and Grabovsky, Comput. Methods Biomech. Biomed. Eng., 6: 53-63 (2003)) permitting a common causal chain to be created, moving from the state of an initial homogeneous cell layer towards the complicated shapes of embryonic rudiments.     

A common biomechanical model for the formation of stationary cell domains and propagating waves in the developing organisms

Many important morphogenetic processes that take place in the development of an animal start from the segregation of a homogeneous layer of cells into a different number of the domains of columnar and flattened cells. In many cases, waves of cell shape transformation travel throughout embryonic tissues. A biomechanical model is presented which embraces both kinds of event. The model is based on the idea of interplay between short- and long-range factors. While the former promote the spreading of a given cell state along a cell row in the recalculation direction, long-range factors are associated with self-generated tensions which, after exceeding a certain threshold, induce active cell extension and hence the rise of tangential pressure. Different kinds of biologically realistic stationary structures, as well as various kinds of the running waves, can be modelled under different parameter values. Moreover, the current model can be coupled with the previous one (Beloussov and Grabovsky, Comput. Methods Biomech. Biomed. Eng., 6: 53–63 (2003)) permitting a common causal chain to be created, moving from the state of an initial homogeneous cell layer towards the complicated shapes of embryonic rudiments.     

Cell adhesion molecules, signal transduction and cell growth

Signals from dynamic cellular interactions between the extracellular matrix and neighboring cells ultimately input into the cellular decision-making process. These interactions form the basis of anchorage-dependent growth. Recent advances have provided the mechanistic details behind the ability of integrins, and other cell adhesion molecules (CAMs), to regulate both early signal transduction events initiated by soluble factors and downstream events more proximally involved in cell cycle progression. These actions appear to depend on the ability of CAMs to initiate the formation of organized structures that permit the efficient flow of information.     

Fluorescence photobleaching recovery using total internal reflection interference fringes

Lateral diffusion measurements on cell membrane molecules, most commonly accomplished through fluorescence photobleaching recovery (FPR or FRAP), provide information on such molecules' size, environment, and participation in intermolecular interactions. However, difficulties arise in FPR measurements of lateral dynamics of materials, such as visible fluorescent protein (VFP) fusion proteins, where fluorescent intracellular species contribute to the fluorescence recovery signal and thus distort measurements intended to reflect surface molecules only. A new method helps eliminate these difficulties. In total internal reflection interference fringe FPR, interfering laser beams enter a 1.65-numercial aperture (NA) Olympus objective at the periphery of the back focal plane where the NA exceeds 1.38. This creates an extended interference pattern totally internally reflected at the coverslip-medium interface which excites fluorescence only from fluorescent molecules located where the cell contacts the coverslip. The large illuminated area interrogates many more membrane receptors than spot methods and hence obtains more diffusion information per measurement while rejecting virtually all interfering intracellular fluorescence. We report successful measurements of membrane dynamics of both VFP-containing and conventionally labeled molecules by this technique and compare them with results of other FPR methods.     

Two-Dimensional Continuum Percolation Threshold for Diffusing Particles of Nonzero Radius

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing obstructed diffusion is the percolation threshold. The thresholds are well known for point tracers, but for tracers of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. Here thresholds are obtained for circular obstacles on the continuum. Random obstacle configurations are generated by Brownian dynamics or Monte Carlo methods, the obstacles are immobilized, and the percolation threshold is obtained by solving a bond percolation problem on the Voronoi diagram of the obstacles. The percolation threshold is expressed as the diameter of the largest tracer that can cross a set of immobile obstacles at a prescribed number density. For random overlapping obstacles, the results agree with the known analytical solution quantitatively. When the obstacles are soft disks with a 1/r¹² repulsion, the percolating diameter is ∼20% lower than for overlapping obstacles. A percolation model predicts that the threshold is highly sensitive to the tracer radius. To our knowledge, such a strong dependence has so far not been reported for the plasma membrane, suggesting that percolation is not the factor controlling lateral diffusion. A definitive experiment is proposed.     

Lateral diffusion in an archipelago. The effect of mobile obstacles.

Lateral diffusion of mobile proteins and lipids (tracers) in a membrane is hindered by the presence of proteins (obstacles) in the membrane. If the obstacles are immobile, their effect may be described by percolation theory, which states that the long-range diffusion constant of the tracers goes to zero when the area fraction of obstacles is greater than the percolation threshold. If the obstacles are themselves mobile, the diffusion constant of the tracers depends on the area fraction of obstacles and the relative jump rate of tracers and obstacles. This paper presents Monte Carlo calculations of diffusion constants on square and triangular lattices as a function of the concentration of obstacles and the relative jump rate. The diffusion constant for particles of various sizes is also obtained. Calculated values of the concentration-dependent diffusion constant are compared with observed values for gramicidin and bacteriorhodopsin. The effect of the proteins as inert obstacles is significant, but other factors, such as protein-protein interactions and perturbation of lipid viscosity by proteins, are of comparable importance. Potential applications include the diffusion of proteins at high concentrations (such as rhodopsin in rod outer segments), the modulation of diffusion by release of membrane proteins from cytoskeletal attachment, and the diffusion of mobile redox carriers in mitochondria, chloroplasts, and endoplasmic reticulum.     

Diffusion and redistribution of lipid-like molecules between membranes in virus-cell and cell-cell fusion systems.

The kinetics of redistribution of lipid-like molecules between the membranes of two fused spherical vesicles is studied by solving the time-dependent diffusion equation of the system. The effects on the probe redistribution rate of pore size at the fusion junction and the relative sizes of the vesicles are examined. It is found that the redistribution rate constant decreases significantly, but not drastically, as the relative size of the pore to that of the vesicles decreases (the bottleneck effect). In general, the time scale of the probe redistribution rate is determined by the size of the vesicles that is loaded with the probe before the activation of the fusion. For a pore size 50 A in diameter and a typical diffusion coefficient of 10(-8) cm2/s for lipids, the mixing half times for typical virus-cell and cell-cell fusion systems are less than 30 ms and above 200 s, respectively. Thus, although the redistribution of lipid-like probes by diffusion is not rate limiting in virus-cell fusion, redistribution by diffusion is close to rate limiting in spike-protein mediated cell-cell fusion.     

Microhydrodynamics simulation of protein crystallization. I. Static calculations.

A computer simulation method is proposed to study the effects of hydrodynamic interactions on protein crystallization. It is a combination of Stokesian dynamics and continuum hydrodynamics and is referred to as "microhydrodynamics." The method is checked against analytical expressions for Stokes drag and diffusion coefficients for unit spheres. For a number of protein molecules the diffusion coefficients have been calculated and compared with experimental values. It is shown that the method works well for stationary calculations. Using dynamical calculations interacting protein molecules will be simulated to study the events in the early stages of protein crystallization.     

Morphomechanics: goals, basic experiments and models

Morphomechanics is a branch of developmental biology, studying the generation, space-time patterns and morphogenetic role of mechanical stresses (MS) which reside in embryonic tissues. All the morphogenetically active embryonic tissues studied in this respect have been shown to bear substantial mechanical stresses of tension or pressure. MS are indispensable for organized cell movements, expression of a number of developmentally important genes and the very viability of cells. Even a temporary relaxation of MS leads to an increase in the morphological variability and asymmetry of embryonic rudiments. Moreover, MS may be among the decisive links of morphogenetic feedback required for driving forth embryonic development and providing its regular space-time patterns. We hypothesize that one such feedback is based upon the tendency of cells and tissues to hyperrestore (restore with an overshoot) their MS values after any deviations, either artificial or produced by neighboring morphogenetically active tissues. This idea is supported by a number of observations and experiments performed on the tissue and individual cell levels. We describe also the models demonstrating that a number of biologically realistic stationary shapes and propagating waves can be generated by varying the parameters of the hyperrestoration feedback loop. Morphomechanics is an important and rapidly developing branch of developmental and cell biology, being complementary to other approaches.     

G protein threshold behavior in the human neutrophil oxidant response: measurement of G proteins available for signaling in responding and nonresponding subpopulations

Threshold behavior is an important aspect of signal transduction pathways that allows for responses to be turned on or off. Human neutrophil responses to N-formyl peptides, including oxidant production and release, exhibit threshold behavior with respect to the number of G proteins available for signaling; progressive treatment of neutrophils with pertussis toxin causes the conversion of responding cells to nonresponding cells. To quantify the threshold level of G proteins required for signaling of N-formyl peptide stimulated oxidant production in a neutrophil population, we used a plasma membrane associated G protein quantification assay in conjunction with a sorting flow cytometer and measured differences in the average number of G proteins available for signaling per cell in both the responding and the nonresponding subpopulations after pertussis toxin treatment. Although there appeared to be a threshold separating responding cells and nonresponding cells for a given sample, no discrete threshold was measured across multiple treatment conditions. A mathematical model of the early steps in signaling suggests that cell-to-cell variability in signal parameters, such as numbers of signal components and values of kinetic rate constants, obscures the measurement of a discrete threshold and leads to an apparent decrease in the threshold level of G proteins available for signaling as the total G proteins are decreased.