Diffusion theory, the cell and the synapse

Models for Nociception Stimulation and Memory Effects in Awake and Aware Healthy Individuals

OBJECTIVE

This paper introduces a primer in the health care practice, namely a mathematical model and methodology for detecting and analysing nociceptor stimulation followed by related tissue memory effects.

METHODS

Noninvasive nociceptor stimulus protocol and prototype device for measuring bioimpedance is provided. Various time instants, sensor location, and stimulus train have been analysed.

RESULTS

The method and model indicate that nociceptor stimulation perceived as pain in awake healthy volunteers is noninvasively detected. The existence of a memory effect is proven from data. Sensor location had minimal effect on detection level, while day-to-day variability was observed without being significant.

CONCLUSION

Following the experimental study, the model enables a comprehensive management of chronic pain patients, and possibly other analgesia, or pain related regulatory loops.

SIGNIFICANCE

A device and methodology for noninvasive for detecting nociception stimulation have been developed. The proposed method and models have been validated on healthy volunteers.

Traveling Slow Oscillations During Sleep: A Marker of Brain Connectivity in Childhood

Slow oscillations, a defining characteristic of the nonrapid eye movement sleep electroencephalogram (EEG), proliferate across the scalp in highly reproducible patterns. In adults, the propagation of slow oscillations is a recognized fingerprint of brain connectivity and excitability. In this study, we (1) describe for the first time maturational features of sleep slow oscillation propagation in children (n = 23; 2-13 years) using high-density (hd) EEG and (2) examine associations between sleep slow oscillatory propagation characteristics (ie, distance, traveling speed, cortical involvement) and white matter myelin microstructure as measured with multicomponent Driven Equilibrium Single Pulse Observation of T1 and T2-magnetic resonance imaging (mcDESPOT-MRI). Results showed that with increasing age, slow oscillations propagated across longer distances (average growth of 0.2 cm per year; R(21) = 0.50, p < .05), while traveling speed and cortical involvement (ie, slow oscillation expanse) remained unchanged across childhood. Cortical involvement (R(20) = 0.44) and slow oscillation speed (R(20) = -0.47; both p < .05, corrected for age) were associated with myelin content in the superior longitudinal fascicle, the largest anterior-posterior, intrahemispheric white matter connectivity tract. Furthermore, slow oscillation distance was moderately associated with whole-brain (R(21) = 0.46, p < .05) and interhemispheric myelin content, the latter represented by callosal myelin water fraction (R(21) = 0.54, p < .01, uncorrected). Thus, we demonstrate age-related changes in slow oscillation propagation distance, as well as regional associations between brain activity during sleep and the anatomical connectivity of white matter microstructure. Our findings make an important contribution to knowledge of the brain connectome using a noninvasive and novel analytic approach. These data also have implications for understanding the emergence of neurodevelopmental disorders and the role of sleep in brain maturation trajectories.

Combustion, respiration and intermittent exercise: a theoretical perspective on oxygen uptake and energy expenditure

While no doubt thought about for thousands of years, it was Antoine Lavoisier in the late 18th century who is largely credited with the first “modern” investigations of biological energy exchanges. From Lavoisier’s work with combustion and respiration a scientific trend emerges that extends to the present day: the world gains a credible working hypothesis but validity goes missing, often for some time, until later confirmed using proper measures. This theme is applied to glucose/glycogen metabolism where energy exchanges are depicted as conversion from one form to another and, transfer from one place to another made by both the anaerobic and aerobic biochemical pathways within working skeletal muscle, and the hypothetical quantification of these components as part of an oxygen (O₂) uptake measurement. The anaerobic and aerobic energy exchange components of metabolism are represented by two different interpretations of O₂ uptake: one that contains a glycolytic component (1 L O₂ = 21.1 kJ) and one that does not (1 L O₂ = 19.6 kJ). When energy exchange transfer and oxygen-related expenditures are applied separately to exercise and recovery periods, an increased energy cost for intermittent as compared to continuous exercise is hypothesized to be a direct result.

A methodological combined framework for roadmapping biosensor research: a fault tree analysis approach within a strategic technology evaluation frame

Biosensor technology began in the 1960s to revolutionize instrumentation and measurement. Despite the glucose sensor market success that revolutionized medical diagnostics, and artificial pancreas promise currently the approval stage, the industry is reluctant to capitalize on other relevant university-produced knowledge and innovation. On the other hand, the scientific literature is extensive and persisting, while the number of university-hosted biosensor groups is growing. Considering the limited marketability of biosensors compared to the available research output, the biosensor field has been used by the present authors as a suitable paradigm for developing a methodological combined framework for "roadmapping" university research output in this discipline. This framework adopts the basic principles of the Analytic Hierarchy Process (AHP), replacing the lower level of technology alternatives with internal barriers (drawbacks, limitations, disadvantages), modeled through fault tree analysis (FTA) relying on fuzzy reasoning to count for uncertainty. The proposed methodology is validated retrospectively using ion selective field effect transistor (ISFET) - based biosensors as a case example, and then implemented prospectively membrane biosensors, putting an emphasis on the manufacturability issues. The analysis performed the trajectory of membrane platforms differently than the available market roadmaps that, considering the vast industrial experience in tailoring and handling crystallic forms, suggest the technology path of biomimetic and synthetic materials. The results presented herein indicate that future trajectories lie along with nanotechnology, and especially nanofabrication and nano-bioinformatics, and focused, more on the science-path, that is, on controlling the natural process of self-assembly and the thermodynamics of bioelement-lipid interaction. This retained the nature-derived sensitivity of the biosensor platform, pointing out the differences between the scope of academic research and the market viewpoint.

A molecular diffusion based utility model for Drosophila larval phototaxis

Background

Generally, utility based decision making models focus on experimental outcomes. In this paper we propose a utility model based on molecular diffusion to simulate the choice behavior of Drosophila larvae exposed to different light conditions.

Methods

In this paper, light/dark choice-based Drosophila larval phototaxis is analyzed with our molecular diffusion based model. An ISCEM algorithm is developed to estimate the model parameters.

Results

By applying this behavioral utility model to light intensity and phototaxis data, we show that this model fits the experimental data very well.

Conclusions

Our model provides new insights into decision making mechanisms in general. From an engineering viewpoint, we propose that the model could be applied to a wider range of decision making practices.

Philosophical basis and some historical aspects of systems biology: from Hegel to Noble - applications for bioenergetic research

We live in times of paradigmatic changes for the biological sciences. Reductionism, that for the last six decades has been the philosophical basis of biochemistry and molecular biology, is being displaced by Systems Biology, which favors the study of integrated systems. Historically, Systems Biology - defined as the higher level analysis of complex biological systems - was pioneered by Claude Bernard in physiology, Norbert Wiener with the development of cybernetics, and Erwin Schrödinger in his thermodynamic approach to the living. Systems Biology applies methods inspired by cybernetics, network analysis, and non-equilibrium dynamics of open systems. These developments follow very precisely the dialectical principles of development from thesis to antithesis to synthesis discovered by Hegel. Systems Biology opens new perspectives for studies of the integrated processes of energy metabolism in different cells. These integrated systems acquire new, system-level properties due to interaction of cellular components, such as metabolic compartmentation, channeling and functional coupling mechanisms, which are central for regulation of the energy fluxes. State of the art of these studies in the new area of Molecular System Bioenergetics is analyzed.

Metabolic compartmentation - a system level property of muscle cells: real problems of diffusion in living cells

Problems of quantitative investigation of intracellular diffusion and compartmentation of metabolites are analyzed. Principal controversies in recently published analyses of these problems for the living cells are discussed. It is shown that the formal theoretical analysis of diffusion of metabolites based on Fick's equation and using fixed diffusion coefficients for diluted homogenous aqueous solutions, but applied for biological systems in vivo without any comparison with experimental results, may lead to misleading conclusions, which are contradictory to most biological observations. However, if the same theoretical methods are used for analysis of actual experimental data, the apparent diffusion constants obtained are orders of magnitude lower than those in diluted aqueous solutions. Thus, it can be concluded that local restrictions of diffusion of metabolites in a cell are a system-level properties caused by complex structural organization of the cells, macromolecular crowding, cytoskeletal networks and organization of metabolic pathways into multienzyme complexes and metabolons. This results in microcompartmentation of metabolites, their channeling between enzymes and in modular organization of cellular metabolic networks. The perspectives of further studies of these complex intracellular interactions in the framework of Systems Biology are discussed.

Isoflurane strongly affects the diffusion of intracellular metabolites, as shown by 1H nuclear magnetic resonance spectroscopy of the monkey brain

Isoflurane is a volatile anesthetic commonly used for animal studies. In particular, diffusion nuclear magnetic resonance (NMR) spectroscopy is frequently performed under isoflurane anesthesia. However, isoflurane is known to affect the phase transition of lipid bilayer, possibly resulting in increased permeability to metabolites. Resulting decreased restriction may affect metabolite apparent diffusion coefficient (ADC). In the present work, the effect of isoflurane dose on metabolite ADC is evaluated using diffusion tensor spectroscopy in the monkey brain. For the five detected intracellular metabolites, the ADC exhibits a significant increase when isoflurane dose varies from 1% to 2%: 13%+/-8% for myo-inositol, 14%+/-13% for total N-acetyl-aspartate, 20%+/-18% for glutamate, 27%+/-7% for total creatine and 53%+/-17% for total choline. Detailed analysis of ADC changes experienced by the five different metabolites argues in favor of facilitated metabolite exchange between subcellular structures at high isoflurane dose. This work strongly supports the idea of metabolite diffusion in vivo being significantly restricted in subcellular structures at long diffusion time, and provides new insights for interpreting ADC values as measured by diffusion NMR spectroscopy.

Development of nanostructured biomedical micro-drug testing device based on in situ cellular activity monitoring

Integration of micro and nanofabrication techniques with biotechnology has resulted in the development of in vitro analytical and diagnostic tools for biomedical applications. The focus of such technology has primarily been on therapeutic and sensing applications. The long-term integration of cells with inorganic materials provides the basis for novel sensing platforms. This paper describes the creation of, nanoporous, biocompatible, alumina membranes as a platform for incorporation into a cell based device targeted for in situ recording of cellular electrical activity variations due to the changes associated with the surrounding microenvironments more specifically due to the effect of therapeutic drugs. Studies described herein focus on the interaction of nanoporous alumina substrates embedded in silicon, patterned with cells of interest. The cells that have been used to develop the in vitro test platform are primary hippocampal neurons. Demonstrated here, is the fidelity of such a system in terms of determination of cell viability, proliferation, and functionality. The response of the cells to the "drug" molecules is electro-optically characterized in an in situ manner. The capability of such, micro fabricated nanoporous membranes as in vitro drug testing platforms, is first theoretically estimated using two dimensional finite element modeling of the diffusion of the molecules of interest through the nanoporous substrate using CFDRC. It is then experimentally established, using glucose and immunoglobulin G (IgG).

Modeling the signaling endosome hypothesis: why a drive to the nucleus is better than a (random) walk

Background

Information transfer from the plasma membrane to the nucleus is a universal cell biological property. Such information is generally encoded in the form of post-translationally modified protein messengers. Textbook signaling models typically depend upon the diffusion of molecular signals from the site of initiation at the plasma membrane to the site of effector function within the nucleus. However, such models fail to consider several critical constraints placed upon diffusion by the cellular milieu, including the likelihood of signal termination by dephosphorylation. In contrast, signaling associated with retrogradely transported membrane-bounded organelles such as endosomes provides a dephosphorylation-resistant mechanism for the vectorial transmission of molecular signals. We explore the relative efficiencies of signal diffusion versus retrograde transport of signaling endosomes.

Results

Using large-scale Monte Carlo simulations of diffusing STAT-3 molecules coupled with probabilistic modeling of dephosphorylation kinetics we found that predicted theoretical measures of STAT-3 diffusion likely overestimate the effective range of this signal. Compared to the inherently nucleus-directed movement of retrogradely transported signaling endosomes, diffusion of STAT-3 becomes less efficient at information transfer in spatial domains greater than 200 nanometers from the plasma membrane.

Conclusion

Our model suggests that cells might utilize two distinct information transmission paradigms: 1) fast local signaling via diffusion over spatial domains on the order of less than 200 nanometers; 2) long-distance signaling via information packets associated with the cytoskeletal transport apparatus. Our model supports previous observations suggesting that the signaling endosome hypothesis is a subset of a more general hypothesis that the most efficient mechanism for intracellular signaling-at-a-distance involves the association of signaling molecules with molecular motors that move along the cytoskeleton. Importantly, however, cytoskeletal association of membrane-bounded complexes containing ligand-occupied transmembrane receptors and downstream effector molecules provides the ability to regenerate signals at any point along the transmission path. We conclude that signaling endosomes provide unique information transmission properties relevant to all cell architectures, and we propose that the majority of relevant information transmitted from the plasma membrane to the nucleus will be found in association with organelles of endocytic origin.

Diffusion, perfusion and the exclusion principles in the structural and functional organization of the living cell: reappraisal of the properties of the 'ground substance'

The thesis is presented that only within very small microdomains of the cell internum might diffusion operate in the sorting of molecular affinities. Much of cell metabolism is guided and controlled in rate by the speed with which molecules that have to interact encounter one another. What is clear, however, is that the cell does not have a single 'modus operandi' but has the choice of many different strategies, each of which can contribute in different proportion to the rate of ongoing activity. It is probably our own desire to simplify things and use the most (or more) probable strategy that confines our appreciation of the overall robustness of the cell as a 'survival machine'. The main operative process at any given time (perfusion, diffusion or whatever) has always to be considered very carefully in relation to the organisational structure of the cell, which can be transient and fickle but nevertheless has been seen as involving an extensive cytomatrix, a ground substance, within an aqueous environment in which the degree of water structuring is even more fickle.

Presynaptic quantal plasticity: Katz's original hypothesis revisited

Changes in the amplitudes of signals conveyed at synaptic contacts between neurons underlie many brain functions and pathologies. Here we review the possible determinants of the amplitude and plasticity of the elementary postsynaptic signal, the miniature. In the absence of a definite understanding of the molecular mechanism releasing transmitters, we investigated a possible alternative interpretation. Classically, both the quantal theory and the vesicle theory predict that the amount of transmitter producing a miniature is determined presynaptically prior to release and that rapid changes in miniature amplitude reflect essentially postsynaptic alterations. However, recent data indicates that short-term and long-lasting changes in miniature amplitude are in large part due to changes in the amount of transmitter in individual released packets that show no evidence of preformation. Current representations of transmitter release derive from basic properties of neuromuscular transmission and endocrine secretion. Reexamination of overlooked properties of these two systems indicate that the amplitude of miniatures may depend as much, if not more, on the Ca(2+) signals in the presynaptic terminal than on the number of postsynaptic receptors available or on vesicle's contents. Rapid recycling of transmitter and its possible adsorption at plasma and vesicle lumenal membrane surfaces suggest that exocytosis may reflect membrane traffic rather than actual transmitter release. This led us to reconsider the disregarded hypothesis introduced by Fatt and Katz (1952; J Physiol 117:109-128) that the excitability of the release site may account for the "quantal effect" in fast synaptic transmission. In this case, changes in excitability of release sites would contribute to the presynaptic quantal plasticity that is often recorded.

Diffusion NMR spectroscopy

MR offers unique tools for measuring molecular diffusion. This review focuses on the use of diffusion-weighted MR spectroscopy (DW-MRS) to non-invasively quantitate the translational displacement of endogenous metabolites in intact mammalian tissues. Most of the metabolites that are observed by in vivo MRS are predominantly located in the intracellular compartment. DW-MRS is of fundamental interest because it enables one to probe the in situ status of the intracellular space from the diffusion characteristics of the metabolites, while at the same time providing information on the intrinsic diffusion properties of the metabolites themselves. Alternative techniques require the introduction of exogenous probe molecules, which involves invasive procedures, and are also unable to measure molecular diffusion in and throughout intact tissues. The length scale of the process(es) probed by MR is in the micrometer range which is of the same order as the dimensions of many intracellular entities. DW-MRS has been used to estimate the dimensions of the cellular elements that restrict intracellular metabolite diffusion in muscle and nerve tissue. In addition, it has been shown that DW-MRS can provide novel information on the cellular response to pathophysiological changes in relation to a range of disorders, including ischemia and excitotoxicity of the brain and cancer.

Oxygen, homeostasis, and metabolic regulation

Even a cursory review of the literature today indicates that two views dominate experimental approaches to metabolic regulation. Model I assumes that cell behavior is quite similar to that expected for a bag of enzymes. Model II assumes that 3-D order and structure constrain metabolite behavior and that metabolic regulation theory has to incorporate structure to ever come close to describing reality. The phosphagen system may be used to illustrate that both approaches lead to very productive experimentation and significant advances are being made within both theoretical frameworks. However, communication between the two approaches or the two 'groups' is essentially nonexistent and in many cases (our own for example) some experiments are done in one framework and some in the other (implying some potential schizophrenia in the field). In our view, the primary paradox and problem which no one has solved so far is that essentially all metabolite concentrations are remarkably stable (are homeostatic) over large changes in pathway fluxes. For muscle cells O2 is one of the most perfectly homeostatic of all even though O2 delivery and metabolic rate usually correlate in a 1:1 fashion. Four explanations for this behavior are given by traditional metabolic regulation models. Additionally, there is some evidence for universal O2 sensors which could help to get us out of the paradox. In contrast, proponents of an ultrastructurally dominated view of the cell assume intracellular perfusion or convection as the main means for accelerating enzyme-substrate encounter and as a way to account for the data which have been most perplexing so far: the striking lack of correlation between changes in pathway reaction rates and changes in concentrations of pathway substrates and intermediates, including oxygen. The polarization illustrated by these two views of living cells extends throughout the metabolic regulation field (and has caused the field to progress along two surprisingly independent paths with minimal communication between them). The time may have come when cross talk between the two fields may be useful.

In vivo (31)P-NMR diffusion spectroscopy of ATP and phosphocreatine in rat skeletal muscle

The aim of this study was to measure the diffusion of ATP and phosphocreatine (PCr) in intact rat skeletal muscle, using (31)P-NMR. The acquisition of the diffusion-sensitized spectra was optimized in terms of the signal-to-noise ratio for ATP by using a frequency-selective stimulated echo sequence in combination with adiabatic radio-frequency pulses and surface coil signal excitation and reception. Diffusion restriction was studied by measuring the apparent diffusion coefficients of ATP and PCr as a function of the diffusion time. Orientation effects were eliminated by determining the trace of the diffusion tensor. The data were fitted to a cylindrical restriction model to estimate the unbounded diffusion coefficient and the radial dimensions of the restricting compartment. The unbounded diffusion coefficients of ATP and PCr were approximately 90% of their in vitro values at 37 degrees C. The diameters of the cylindrical restriction compartment were approximately 16 and approximately 22 microm for ATP and PCr, respectively. The diameters of rat skeletal muscle fibers are known to range from 60 to 80 microm. The modelling therefore suggests that the in vivo restriction of ATP and PCr diffusion is not imposed by the sarcolemma but by other, intracellular structures with an overall cylindrical orientation.

Cross-species studies of glycolytic function

Researchers probing the functional properties of glycogen (glucose) fermentation to lactate typically work within either one of two theoretical frameworks or models. The first assumes that the cell is analogous to a watery bag of enzymes, while the second assumes that three dimensional order and structure constrain the behaviors of glycolytic intermediates, of glycolytic enzymes, and of integrated glycolytic pathway functions per se. The former approach has been quite successful in accounting for many glycolytic functions but has not been able to satisfactorily explain a hallmark property of the pathway: namely, that large scale change in pathway flux is reflected in only modest changes in concentrations of pathway intermediates. Despite being composed of very different kinds of enzymes, the pathway is remarkably homeostatic by criterion of stability of concentrations of its intermediates in different metabolic states. The view of the cell as a system in which enzyme, substrate, and modulator mobilities are constrained by intracellular structures, the second framework above, posits intracellular perfusion or convection as a means for increasing rates of enzyme-substrate encounter and as an explanation for how high glycolytic pathway fluxes and homeostasis of pathway intermediates can be sustained simultaneously.

Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intracellular surface area

Classical biochemistry is founded on several assumptions valid in dilute aqueous solutions that are often extended without question to the interior milieu of intact cells. In the first section of this chapter, we present these assumptions and briefly examine the ways in which the cell interior may depart from the conditions of an ideal solution. In the second section, we summarize experimental evidence regarding the physical properties of the cell cytoplasm and their effect on the diffusion and binding of macromolecules and vesicles. While many details remain to be worked out, it is clear that the aqueous phase of the cytoplasm is crowded rather than dilute, and that the diffusion and partitioning of macromolecules and vesicles in cytoplasm is highly restricted by steric hindrance as well as by unexpected binding interactions. Furthermore, the enzymes of several metabolic pathways are now known to be organized into structural and functional units with specific localizations in the solid phase, and as much as half the cellular protein content may also be in the solid phase.

The metabolic implications of intracellular circulation

Two views currently dominate research into cell function and regulation. Model I assumes that cell behavior is quite similar to that expected for a watery bag of enzymes and ligands. Model II assumes that three-dimensional order and structure constrain and determine metabolite behavior. A major problem in cell metabolism is determining why essentially all metabolite concentrations are remarkably stable (are homeostatic) over large changes in pathway fluxes-for convenience, this is termed the [s] stability paradox. For muscle cells, ATP and O(2) are the most perfectly homeostatic, even though O(2) delivery and metabolic rate correlate in a 1:1 fashion. In total, more than 60 metabolites are known to be remarkably homeostatic in differing metabolic states. Several explanations of [s] stability are usually given by traditional model I studies-none of which apply to all enzymes in a pathway, and all of which require diffusion as the means for changing enzyme-substrate encounter rates. In contrast, recent developments in our understanding of intracellular myosin, kinesin, and dyenin motors running on actin and tubulin tracks or cables supply a mechanistic basis for regulated intracellular circulation systems with cytoplasmic streaming rates varying over an approximately 80-fold range (from 1 to >80 micrometer x sec(-1)). These new studies raise a model II hypothesis of intracellular perfusion or convection as a primary means for bringing enzymes and substrates together under variable metabolic conditions. In this view, change in intracellular perfusion rates cause change in enzyme-substrate encounter rates and thus change in pathway fluxes with no requirement for large simultaneous changes in substrate concentrations. The ease with which this hypothesis explains the [s] stability paradox is one of its most compelling features.

Two research paths for probing the roles of oxygen in metabolic regulation

Tissues such as skeletal and cardiac muscles must sustain very large-scale changes in ATP turnover rate during equally large changes in work. In many skeletal muscles these changes can exceed 100-fold. Examination of a number of cell and whole-organism level systems identifies ATP concentration as a key parameter of the interior milieu that is nearly universally 'homeostatic'; it is common to observe no change in ATP concentration even while change in its turnover rate can increase or decrease by two orders of magnitude or more. A large number of other intermediates of cellular metabolism are also regulated within narrow concentration ranges, but none seemingly as precisely as is [ATP]. In fact, the only other metabolite in aerobic energy metabolism that is seemingly as 'homeostatic' is oxygen--at least in working muscles where myoglobin serves to buffer oxygen concentrations at stable and constant values at work rates up to the aerobic maximum. In contrast to intracellular oxygen concentration, a 1:1 relationship between oxygen delivery and metabolic rate is observed over biologically realistic and large-magnitude changes in work. The central regulatory question is how the oxygen delivery signal is transmitted to the intracellular metabolic machinery. Traditional explanations assume diffusion as the dominant mechanism, while proponents of an ultrastructurally dominated view of the cell assume an intracellular perfusion system to account for the data which have been most perplexing to metabolic biochemistry so far: the striking lack of correlation between changes in pathway reaction rates and changes in concentrations of pathway substrates, including oxygen and pathway intermediates.