From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

Neuromuscular junction morphology, fiber-type proportions, and satellite-cell proliferation rates are altered in MyoD(-/-) mice

Gene compensation by members of the myogenic regulatory factor (MRF) family has been proposed to explain the apparent normal adult phenotype of MyoD(-/-) mice. Nerve and field stimulation were used to investigate contraction properties of muscle from MyoD(-/-) mice, and molecular approaches were used to investigate satellite-cell behavior. We demonstrate that MyoD deletion results in major alterations in the organization of the neuromuscular junction, which have a dramatic influence on the physiological contractile properties of skeletal muscle. Second, we show that the lineage progression of satellite cells (especially initial proliferation) in the absence of MyoD is abnormal and linked to perturbations in the nuclear localization of beta-catenin, a key readout of canonical Wnt signaling. These results show that MyoD has unique functions in both developing and adult skeletal muscle that are not carried out by other members of the MRF family.

Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

High-affinity small molecule-phospholipid complex formation: Binding of siramesine to phosphatidic acid

Siramesine (SRM) is a sigma-2 receptor agonist which has been recently shown to inhibit growth of cancer cells. Fluorescence spectroscopy experiments revealed two distinct binding sites for this drug in phospholipid membranes. More specifically, acidic phospholipids retain siramesine on the bilayer surface due to a high-affinity interaction, reaching saturation at an apparent 1:1 drug-acidic phospholipid stoichiometry, where after the drug penetrates into the hydrocarbon core of the membrane. This behavior was confirmed using Langmuir films. Of the anionic phospholipids, the highest affinity, comparable to the affinities for the binding of small molecule ligands to proteins, was measured for phosphatidic acid (PA, mole fraction Of X-PA = 0.2 in phosphatidylcholine vesicles), yielding a molecular partition coefficient of 240 +/- 80 x 10(6). An MD simulation on the siramesine:PA interaction was in agreement with the above data. Taking into account the key role of PA as a signaling molecule promoting cell growth our results suggest a new paradigm for the development of anticancer drugs, viz. design of small molecules specifically scavenging phospholipids involved in the signaling cascades controlling cell behavior.

New self-assembling multifunctional templates for the biofabrication and controlled self-release of cultured tissue

The need to source live human tissues for research and clinical applications has been a major driving force for the development of new biomaterials. Ideally, these should elicit the formation of scaffold-free tissues with native-like structure and composition. In this study, we describe a biologically interactive coating that combines the fabrication and subsequent self-release of live purposeful tissues using template–cell–environment feedback. This smart coating was formed from a self-assembling peptide amphiphile comprising a proteasecleavable sequence contiguous with a cell attachment and signaling motif. This multifunctional material was subsequently used not only to instruct human corneal or skin fibroblasts to adhere and deposit discreet multiple layers of native extracellular matrix but also to govern their own self-directed release from the template solely through the action of endogenous metalloproteases. Tissues recovered through this physiologically relevant process were carrier-free and structurally and phenotypically equivalent to their natural counterparts. This technology contributes to a new paradigm in regenerative medicine, whereby materials are able to actively direct and respond to cell behavior. The novel application of such materials as a coating capable of directing the formation and detachment of complex tissues solely under physiological conditions can have broad use for fundamental research and in future cell and tissue therapies.

CLEC-2 and Syk in the megakaryocytic/platelet lineage are essential for development

The C-type lectin receptor CLEC-2 signals through a pathway that is critically dependent on the tyrosine kinase Syk. We show that homozygous loss of either protein results in defects in brain vascular and lymphatic development, lung inflation, and perinatal lethality. Furthermore, we find that conditional deletion of Syk in the hematopoietic lineage, or conditional deletion of CLEC-2 or Syk in the megakaryocyte/platelet lineage, also causes defects in brain vascular and lymphatic development, although the mice are viable. In contrast, conditional deletion of Syk in other hematopoietic lineages had no effect on viability or brain vasculature and lymphatic development. We show that platelets, but not platelet releasate, modulate the migration and intercellular adhesion of lymphatic endothelial cells through a pathway that depends on CLEC-2 and Syk. These studies found that megakaryocyte/platelet expression of CLEC-2 and Syk is required for normal brain vasculature and lymphatic development and that platelet CLEC-2 and Syk directly modulate lymphatic endothelial cell behavior in vitro.

Dynamic behavior of Arabidopsis eif4a-iii, putative core protein of exon junction complex: fast relocation to nucleolus and splicing speckles under hypoxia

Here, we identify the Arabidopsis thaliana ortholog of the mammalian DEAD box helicase, eIF4A-III, the putative anchor protein of exon junction complex (EJC) on mRNA. Arabidopsis eIF4A-III interacts with an ortholog of the core EJC component, ALY/Ref, and colocalizes with other EJC components, such as Mago, Y14, and RNPS1, suggesting a similar function in EJC assembly to animal eIF4A-III. A green fluorescent protein (GFP)-eIF4A-III fusion protein showed localization to several subnuclear domains: to the nucleoplasm during normal growth and to the nucleolus and splicing speckles in response to hypoxia. Treatment with the respiratory inhibitor sodium azide produced an identical response to the hypoxia stress. Treatment with the proteasome inhibitor MG132 led to accumulation of GFP-eIF4A-III mainly in the nucleolus, suggesting that transition of eIF4A-III between subnuclear domains and/or accumulation in nuclear speckles is controlled by proteolysis-labile factors. As revealed by fluorescence recovery after photobleaching analysis, the nucleoplasmic fraction was highly mobile, while the speckles were the least mobile fractions, and the nucleolar fraction had an intermediate mobility. Sequestration of eIF4A-III into nuclear pools with different mobility is likely to reflect the transcriptional and mRNA processing state of the cell.

Effects of dendritic morphology on CA3 pyramidal cell electrophysiology: a simulation study

We investigated the effect of morphological differences on neuronal firing behavior within the hippocampal CA3 pyramidal cell family by using three-dimensional reconstructions of dendritic morphology in computational simulations of electrophysiology. In this paper, we report for the first time that differences in dendritic structure within the same morphological class can have a dramatic influence on the firing rate and firing mode (spiking versus bursting and type of bursting). Our method consisted of converting morphological measurements from three-dimensional neuroanatomical data of CA3 pyramidal cells into a computational simulator format. In the simulation, active channels were distributed evenly across the cells so that the electrophysiological differences observed in the neurons would only be due to morphological differences. We found that differences in the size of the dendritic tree of CA3 pyramidal cells had a significant qualitative and quantitative effect on the electrophysiological response. Cells with larger dendritic trees: (1) had a lower burst rate, but a higher spike rate within a burst, (2) had higher thresholds for transitions from quiescent to bursting and from bursting to regular spiking and (3) tended to burst with a plateau. Dendritic tree size alone did not account for all the differences in electrophysiological responses. Differences in apical branching, such as the distribution of branch points and terminations per branch order, appear to effect the duration of a burst. These results highlight the importance of considering the contribution of morphology in electrophysiological and simulation studies.

Unit-cell approximation for diblock−copolymer brushes grafted to spherical particles

This paper examines the equilibrium phase behavior of thin diblock-copolymer films tethered to a spherical core, using numerical self-consistent field theory (SCFT). The computational cost of the calculation is greatly reduced by implementing the unit-cell approximation (UCA) routinely used in the study of bulk systems. This provides a tremendous reduction in computational time, permitting us to map out the phase behavior more extensively and allowing us to consider far larger particles. The main consequence of the UCA is that it omits packing frustration, but evidently the effect is minor for large particles. On the other hand, when the particles are small, the UCA calculation can be readily followed up with the full SCFT, the comparison to which conveniently allows one to quantitatively assess the effect of packing frustration.

Assisted remote viewing of a teleoperation work cell

Intelligent viewing systems are required if efficient and productive teleoperation is to be applied to dynamic manufacturing environments. These systems must automatically provide remote views to an operator which assist in the completion of the task. This assistance increases the productivity of the teleoperation task if the robot controller is responsive to the unpredictable dynamic evolution of the workcell. Behavioral controllers can be utilized to give reactive 'intelligence.' The inherent complex structure of current systems, however, places considerable time overheads on any redesign of the emergent behavior. In industry, where the remote environment and task frequently change, this continual redesign process becomes inefficient. We introduce a novel behavioral controller, based on an 'ego-behavior' architecture, to command an active camera (a camera mounted on a robot) within a remote workcell. Using this ego-behavioral architecture the responses from individual behaviors are rapidly combined to produce an 'intelligent' responsive viewing system. The architecture is single-layered, each behavior being autonomous with no explicit knowledge of the number, description or activity of other behaviors present (if any). This lack of imposed structure decreases the development time as it allows each behavior to be designed and tested independently before insertion into the architecture. The fusion mechanism for the behaviors provides the ability for each behavior to compete and/or co-operate with other behaviors for full or partial control of the viewing active camera. Each behavior continually reassesses this degree of competition or co-operation by measuring its own success in controlling the active camera against pre-defined constraints. The ego-behavioral architecture is demonstrated through simulation and experimentation.

Adaptation-induced collective dynamics of a single-cell protozoan

We investigate the behavior of a single-cell protozoan in a narrow tubular ring. This environment forces them to swim under a one-dimensional periodic boundary condition. Above a critical density, single-cell protozoa aggregate spontaneously without external stimulation. The high-density zone of swimming cells exhibits a characteristic collective dynamics including translation and boundary fluctuation. We analyzed the velocity distribution and turn rate of swimming cells and found that the regulation of the turing rate leads to a stable aggregation and that acceleration of velocity triggers instability of aggregation. These two opposing effects may help to explain the spontaneous dynamics of collective behavior. We also propose a stochastic model for the mechanism underlying the collective behavior of swimming cells.

Classification and fault detection methods for fuel cell monitoring and quality control

In this paper, various types of fault detection methods for fuel cells are compared. For example, those that use a model based approach or a data driven approach or a combination of the two. The potential advantages and drawbacks of each method are discussed and comparisons between methods are made. In particular, classification algorithms are investigated, which separate a data set into classes or clusters based on some prior knowledge or measure of similarity. In particular, the application of classification methods to vectors of reconstructed currents by magnetic tomography or to vectors of magnetic field measurements directly is explored. Bases are simulated using the finite integration technique (FIT) and regularization techniques are employed to overcome ill-posedness. Fisher's linear discriminant is used to illustrate these concepts. Numerical experiments show that the ill-posedness of the magnetic tomography problem is a part of the classification problem on magnetic field measurements as well. This is independent of the particular working mode of the cell but influenced by the type of faulty behavior that is studied. The numerical results demonstrate the ill-posedness by the exponential decay behavior of the singular values for three examples of fault classes.

Estrogens, brain and behavior: studies in fundamental neurobiology and observations related to women's health

Mechanisms and consequences of the effects of estrogen on the brain have been studied both at the fundamental level and with therapeutic applications in mind. Estrogenic hormones binding in particular neurons in a limbic-hypothalamic system and their effects on the electrophysiology and molecular biology of medial hypothalamic neurons were central in establishing the first circuit for a mammalian behavior, the female-typical mating behavior, lordosis. Notably, the ability of estradiol to facilitate transcription from six genes whose products are important for lordosis behavior proved that hormones can turn on genes in specific neurons at specific times, with sensible behavioral consequences. The use of a gene knockout for estrogen receptor alpha (ERalpha) revealed that homozygous mutant females simply would not do lordosis behavior and instead were extremely aggressive, thus identifying a specific gene as essential for a mammalian social behavior. In dramatic contrast, ERbeta knockout females can exhibit normal lordosis behavior. With the understanding, in considerable mechanistic detail, of how the behavior is produced, now we are also studying brain mechanisms for the biologically adaptive influences which constrain reproductive behavior. With respect to cold temperatures and other environmental or metabolic circumstances which are not consistent with successful reproduction, we are interested in thyroid hormone effects in the brain. Competitive relations between two types of transcription factors - thyroid hormone receptors and estrogen receptors have the potential of subserving the blocking effects of inappropriate environmental circumstances on female reproductive behaviors. TRs can compete with ERalpha both for DNA binding to consensus and physiological EREs and for nuclear coactivators. In the presence of both TRs and ERs, in transfection studies, thyroid hormone coadministration can reduce estrogen-stimulated transcription. These competitive relations apparently have behavioral consequences, as thyroid hormones will reduce lordosis, and a TRbeta gene knockout will increase it. In sum, we not only know several genes that participate in the selective control of this sex behavior, but also, for two genes, we know the causal routes. Estrogenic hormones are also the foci of widespread attention for their potential therapeutic effects improving, for example, certain aspects of mood and cognition. The former has an efficient animal analog, demonstrated by the positive effects of estrogen in the Porsolt forced swim test. The latter almost certainly depends upon trophic actions of estrogen on several fundamental features of nerve cell survival and growth. The hypothesis is raised that the synaptic effects of estrogens are secondary to the trophic actions of this type of hormone in the nucleus and nerve cell body.