Signaling in small subcellular volumes. I. Stochastic and diffusion effects on individual pathways

Many cellular signaling events occur in small subcellular volumes and involve low-abundance molecular species. This context introduces two major differences from mass-action analyses of nondiffusive signaling. First, reactions involving small numbers of molecules occur in a probabilistic manner which introduces scatter in chemical activities. Second, the timescale of diffusion of molecules between subcellular compartments and the rest of the cell is comparable to the timescale of many chemical reactions, altering the dynamics and outcomes of signaling reactions. This study examines both these effects on information flow through four protein kinase regulatory pathways. The analysis uses Monte Carlo simulations in a subcellular volume diffusively coupled to a bulk cellular volume. Diffusion constants and the volume of the subcellular compartment are systematically varied to account for a range of cellular conditions. Each pathway is characterized in terms of the probabilistic scatter in active kinase levels as a measure of "noise" on the pathway output. Under the conditions reported here, most signaling outcomes in a volume below one femtoliter are severely degraded. Diffusion and subcellular compartmentalization influence the signaling chemistry to give a diversity of signaling outcomes. These outcomes may include washout of the signal, reinforcement of signals, and conversion of steady responses to transients.     

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker–Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).     

A versatile shear cell for diffusion measurements on small sample volumes allowing analytical recording of multicomponent transport: II. Applications

A diffusion cell described in the preceding paper has been used to determine mutual and intradiffusion coefficients for various compounds in the range 2–2000 × 10^?12 m² s^?1. The results are in good agreement with previously reported values. The standard deviation in a series of 13 runs on serum albumin performed in four different instruments was 6%.     

Synapsin is a novel Rab3 effector protein on small synaptic vesicles. II. Functional effects of the Rab3A-synapsin I interaction

Synapsins, a family of neuron-specific phosphoproteins that play an important role in the regulation of synaptic vesicle trafficking and neurotransmitter release, were recently demonstrated to interact with the synaptic vesicle-associated small G protein Rab3A within nerve terminals (Giovedi, S., Vaccaro, P., Valtorta, F., Darchen, F., Greengard, P., Cesareni, G., and Benfenati, F. (2004) J. Biol. Chem. 279, 43760-43768). We have analyzed the functional consequences of this interaction on the biological activities of both proteins and on their subcellular distribution within nerve terminals. The presence of synapsin I stimulated GTP binding and GTPase activity of both purified and endogenous synaptic vesicle-associated Rab3A. Conversely, Rab3A inhibited synapsin I binding to F-actin, as well as synapsin-induced actin bundling and vesicle clustering. Moreover, the amount of Rab3A associated with synaptic vesicles was decreased in synapsin knockout mice, and the presence of synapsin I prevented RabGDI-induced Rab3A dissociation from synaptic vesicles. The results indicate that an interaction between synapsin I and Rab3A exists on synaptic vesicles that modulates the functional properties of both proteins. Given the well recognized importance of both synapsins and Rab3A in synaptic vesicles exocytosis, this interaction is likely to play a major role in the modulation of neurotransmitter release.     

Adenylate gradients and Ar:O2 effects on legume nodules. II. Changes in the subcellular adenylate pools

Central infected zone tissue of soybean (Glycine max L. Merr.) nodules was fractionated into separate subcellular compartments using density gradient centrifugation in nonaqueous solvents to better understand how exposure to Ar:O(2) (80:20%, v/v) atmosphere affects C and N metabolism, and to explore a potential role for adenylates in regulating O(2) diffusion. When nodules were switched from air to Ar:O(2), adenylate energy charge (AEC) in the plant cytosol rose from 0.63 +/- 0.02 to 0.73 +/- 0.02 within 7 min and to 0.80 +/- 0.01 by 60 min. In contrast, AEC of the mitochondrial compartment of this central zone tissue remained high (0.80 +/- 0.02 to 0.81 +/- 0.02) following Ar treatment while that of the bacteroid compartment was unchanged, at 0.73 +/- 0.02, after 7 min, but declined to 0.57 +/- 0.03 after 60 min. These results were consistent with a simulation model that predicted Ar:O(2) exposure would first reduce ATP demand for ammonia assimilation and rapidly increase cytosolic AEC, before the Ar:O(2)-induced decline mediated by a decrease in nodule O(2) permeability reduces bacteroid AEC. The possibility that adenylates play a key, integrating role in regulating nodule permeability to oxygen diffusion is discussed.     

Stochastic effects in LMC models.

LMC (local mate competition) was first introduced by W. D. Hamilton to explain extraordinary female-biased sex ratios observed in a variety of insects and mites. In the original model, the population is subdivided into an infinite number of colonies founded by a fixed number of inseminated females producing the same very large number of offspring. The male offspring compete within the colonies to inseminate the female offspring and then these disperse at random to found new colonies. An unbeatable sex ratio strategy is found to be female-biased. In this paper, the effects of having colonies of random size and foundresses producing a random finite number of offspring are considered. The exact evolutionarily stable strategy (ESS) sex ratio is deduced and comparisons with previous approximate or numerical results are made. As the mean or the variance of brood size increases, the ESS sex ratio becomes more female-biased. An increase in the variance of colony size increases the ESS proportion of males when the mean brood size and colony size are both small, but decreases this proportion when the mean brood size or the mean colony size is large.     

Signaling between glia and neurons: focus on synaptic plasticity

Glial cells are now emerging from the shadows cast by their more excitable CNS counterparts. Within the developing nervous system, astrocytes and Schwann cells actively help to promote synapse formation and function, and have even been implicated in synapse elimination. In the adult brain, astrocytes respond to synaptic activity by releasing transmitters that modulate synaptic activity. Thus, glia are active participants in brain function. Many questions remain about the identity of glial-neuronal signals and their significance.     

Modeling Hermissenda: II. Effects of variations in type-B cell excitability, synaptic strength, and network architecture

Because the Hermissenda eye is relatively simple and its cells well characterized, it provides an attractive preparation for detailed computational analysis. To examine the neural mechanisms of learning in this system, we developed multicompartmental models of the type-A and type-B photoreceptors, simulated the eye, and asked three questions: First, how do conductance changes affect cells in a network as compared with those in isolation; second, what are the relative contributions of increases in B-cell excitability and synaptic strength to network output; and third, how do these contributions vary as a function of network architecture? We found that reductions in the type-B cells of two K⁺ currents, I _A and I _C, differentially affected the type-B cells themselves, with I _C reductions increasing firing rate (excitability) in response to light, and I _A reductions increasing quantal output (synaptic strength) onto postsynaptic targets. Increases in either type-B cell excitability or synaptic strength, induced directly or indirectly, each suppressed A-cell photoresponses, and the combined effect of both changes occurring together was greater than either alone. To examine the effects of network architecture, we compared the full network with a simple feedforward B-A pair and intermediate configurations. Compared with a feedforward pair, the complete network exhibited greater A-cell sensitivity to B-cell changes. This was due to many factors, including an increased number of B-cells (which increased B-cell impact on A-cells), A-B feedback inhibition (which slowed both cell types and altered spike timing relationships), and B-B lateral inhibition (which reduced B-cell sensitivity to intrinsic biophysical modifications). These results suggest that an emergent property of the network is an increase both in the rate of information acquisition (“learning”) and in the amount of information that can be stored (“memory”).     

The subcellular localizations of atypical synaptotagmins III and VI. Synaptotagmin III is enriched in synapses and synaptic plasma membranes but not in synaptic vesicles.

Multiple synaptotagmins are expressed in brain, but only synaptotagmins I and II have known functions in fast, synchronous Ca2+-triggered neurotransmitter release. Synaptotagmin III was proposed to regulate other aspects of synaptic vesicle exocytosis, particularly its slow component. Such a function predicts that synaptotagmin III should be an obligatory synaptic vesicle protein, as would also be anticipated from its high homology to synaptotagmins I and II. To test this hypothesis, we studied the distribution, developmental expression, and localization of synaptotagmin III and its closest homolog, synaptotagmin VI. We find that synaptotagmins III and VI are present in all brain regions in heterogeneous distributions and that their levels increase during development in parallel with synaptogenesis. Furthermore, we show by immunocytochemistry that synaptotagmin III is concentrated in synapses, as expected. Surprisingly, however, we observed that synaptotagmin III is highly enriched in synaptic plasma membranes but not in synaptic vesicles. Synaptotagmin VI was also found to be relatively excluded from synaptic vesicles. Our data suggest that synaptotagmins III and VI perform roles in neurons that are not linked to synaptic vesicle exocytosis but to other Ca2+-related nerve terminal events, indicating that the functions of synaptotagmins are more diverse than originally thought.     

Studies on intestinal adenosine triphosphatases. II. Stabilitiies in different rat subcellular fractions.

Subcellular fraction (brush border, mitochondria, microsomes and plasma membranes) are isolated from the rat intestinal epithelial cells. A comparison was made between the effect of cold storage, freeze-thawing, heating and of some chemicals (DMSO, DTT, glycerol, sucrose) on the stability of Mg2+ and (Na+-K+) dependent ATPases in these fractions in order to determine possible difference linked to the localization in the enterocyte. Enzymatic activities were found more stable at -20 degrees C than at +4 degrees C. Microsomal (Na+-K+)-ATPase increased in activity until the 8th day, then declined. Brush border (Na+-K+)-ATPase was the least resistant of all fractions. For Mg2+-ATPase, that from mitochondria was that had lost much more activity (84%) in 15 days at +4 degrees C. With freeze-thawing there was a comparable decrease in all activities (20-35%). by heating between 35 and 60 degrees C, Mg2+-ATPase was shown to be more heat resistant than (Na+-K+)-ATPase. The addition of some stabilizing chemicals (DMSO, glycerol, sucrose) improved the heat stability of the two enzymes: better results were obtained with glycerol for Mg2+-ATPase and sucrose for (Na+-K+)-ATPase. These differences might be due to the compositon in membraine lipids or to the nature of the enzymes studied.     

Stochastic selection in large and small populations

We describe two models of stochastic variation in selection intensity. In both models the arithmetic mean fitness of all genotypes is equal; in both models the geometric mean fitness of the heterozygous genotype is greater than that of both homozygous genotypes. In one model the correlation between the fitnesses of the homozygous genotypes is +1; in the other it is −1. We show that the expected time to absorption of an allele in a finite population is significantly retarded for all initial gene frequencies in the former model. The expected time to absorption of an allele in the latter model is retarded only at extreme initial gene frequencies; at intermediate initial gene frequencies the expected time to absorption is accelerated. We conclude that the criterion for polymorphism based on the geometric mean of the heterozygote being greater than that of both homozygotes provides only limited information about the fate of gene frequency.     

Synapsin II. Mapping of a domain in the NH2-terminal region which binds to small synaptic vesicles

The synapsins are a family of neuron-specific phosphoproteins that selectively bind to small synaptic vesicles in the presynaptic nerve terminal. Using the cDNA encoding rat synapsin IIb, we employed an Escherichia coli expression system to synthesize a variety of fusion proteins containing a truncated protein A linked to different portions of the NH2-terminal region of synapsin II. The recombinant proteins were purified by IgG-Sepharose chromatography and tested in vitro for their ability to bind to purified synaptic vesicles. These experiments identified a region between amino acids 43 and 121 of the amino-terminal portion of synapsin II which binds to synaptic vesicles. Mild trypsinization of synaptic vesicles reduces binding of recombinant proteins to synaptic vesicles, suggesting that the interaction between synapsin II and the vesicles is in part mediated by a synaptic vesicle protein. The 42 NH2-terminal amino acids of synapsin II are not necessary for binding to synaptic vesicles, although this domain contains the phosphorylation site for cAMP-dependent protein kinase.     

Effect of a small molecule on diffusion and swelling properties of selected polysaccharide gel beads

The effect of a small molecule (e.g., sodium fluorescein, SF) on the swelling properties of and diffusion from calcium polysaccharide (alginate or pectin) gel beads was investigated. The gel beads were prepared by ionotropic gelation, soaked in different concentrations of SF solution, and then dried. The swelling behavior and release of SF from the dried beads were investigated. After soaking in SF, the beads swelled to sizes that depended on the initial concentration of SF. However, the size of the dried beads was independent of the SF concentration. The swelling of the beads occurred quite rapidly and reached a maximum within 2 h. Although most beads swelled to a size which was less than their original size of wet beads, some of them swelled much more than their original wet size. Higher concentration of SF and lower concentration of sodium alginate provided a greater increase in weight. The release profile of SF from dried gel beads in water consists of a burst or a very rapid release phase during the first 60 min followed by a much slower release phase. The similarity of the relative weight increase and release profiles of SF, suggests that swelling might contribute to release of SF, particularly during the burst phase.