The importance of the evolutionary heritage of locomotion on flat ground in small mammals for the development of arboreality

The earliest representatives of the mammalian stem line were small. Recent small mammals preserving their morphology possess rather similar kinematic and dynamic locomotor patterns, even if they are not closely related. For a small animal, the mechanics of locomotion on a large branch is comparable to locomotion on flat ground. Combining these informations, it seems sensible to start a discussion on the origins of arboreality with a detailed analysis of the locomotion of small mammals on flat ground. For this purpose, the kinematics of twelve species of mammals were observed using cineradiography, a "general limb" of small mammals was derived as a principle, and its interactions with the trunk were analyzed. These data form the basis for a theoretical upscaling of the motion patterns in arboreal animals, revealing that the transfer of torques between animal and branch becomes unavoidable, thus making the use of prehensile hands advantageous, which by their tendency of distal concentration of muscle masses force the need to change the basic kinematic patterns.     

Population balance approach to modeling hairy root growth

Though numerous models have been developed to describe the growth of microbial cell cultures, far fewer models are available to describe the growth of hairy root cultures. Here a population balance model is proposed to simulate the growth of hairy roots. The model accounts for the increase in biomass due to elongation of a branch by cell division as well as the formation of new branches. The model incorporates the fact that although the likelihood of the formation of a new lateral branch is a maximum at a specific age of the parent branch, lateral branches can form over a distribution of ages of the parent branch. Model parameters are estimated using the genetic algorithm based on experimental data for batch and continuous bioreactors. The model proposed here may provide a better understanding of the increase in biomass of hairy root cultures.     

Individual-based and continuum models of growing cell populations: a comparison

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical agent-based and a continuum mechanical model that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress. The biophysical agent-based model introduced earlier (Drasdo and Hoehme in Phys Biol 2:133-147, 2005) approximates each cell as an isotropic, homogeneous, elastic, spherical object parameterised by measurable biophysical and cell-biological quantities and has been shown by comparison to experimental findings to explain the growth patterns of dense monolayers and multicellular spheroids. Both models exhibit the same growth kinetics, with initial exponential growth of the population size and aggregate diameter followed by linear growth of the diameter and power-law growth of the cell population size. Very sparse monolayers can be explained by a very small or absent cell-cell adhesion and large random cell migration. In this case the expansion speed is not controlled by mechanical stress but by random cell migration and can be modelled by the Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) reaction-diffusion equation. The growth kinetics differs from that of densely packed aggregates in that the initial spread, as quantified by the radius of gyration, is diffusive. Since simulations of the lattice-free agent-based model in the case of very large random migration are too long to be practical, lattice-based cellular automaton (CA) models have to be used for a quantitative analysis of sparse monolayers. Analysis of these dense monolayers leads to the identification of a critical parameter of the CA model so that eventually a hierarchy of three model types (a detailed biophysical lattice-free model, a rule-based cellular automaton and a continuum approach) emerge which yield the same growth pattern for dense and sparse cell aggregates.     

Growth mechanisms and growth kinetics of filamentous microorganisms

Filamentous microorganisms are of major biotechnological importance, being responsible for production of the majority of secondary metabolites, particularly antibiotics. Two main groups are involved, filamentous fungi and filamentous actinomycetes, particularly the streptomycetes. In terms of cellular growth mechanisms, these groups differ greatly. Eukaryotic fungi possess subcellular organelles and cytoskeletal structures directing growth while prokaryotic streptomycetes have no such cellular organization. Despite these fundamental differences, both groups exhibit similar morphologies, growth patterns, growth forms, and hyphal and mycelial growth kinetics on solid media and in liquid culture both grow as dispersed mycelia and pellets. The article therefore discusses the relationship between cellular growth mechanisms and vegetative growth in both filamentous fungi and actinomycetes, the conceptual and theoretical models applicable to both groups, and the significance of such models in industrial fermentation processes.     

Models for mineralization kinetics with the variables of substrate concentration and population density.

The rates of mineralization of [14C]benzoate by an induced population of Pseudomonas sp. were measured at initial substrate concentrations ranging from 10 ng/ml to 100 micrograms/ml. Plots of the radioactivity remaining in the culture were fit by nonlinear regression to six kinetic models derived from the Monod equation. These models incorporate only the variables of substrate concentration and cell density. Plots of the mineralization kinetics in cultures containing low, intermediate, and high initial substrate concentrations were well fit by first-order, integrated Monod, and logarithmic kinetics, respectively. Parameters such as maximum specific growth rate, half-saturation constant, and initial population density divided by yield agreed between cultures to within a factor of 3.4. Benzoate mineralization by microorganisms in acclimated sewage was shown to fit logistic (sigmoidal), Monod, and logarithmic kinetics when the compound was added at initial concentrations of 0.1, 1.0, and 10 micrograms/ml, respectively. The mineralization of 10 micrograms of benzoate per ml in sewage also followed logarithmic kinetics in the absence of protozoa. It is concluded that much of the diversity in shapes of mineralization curves is a result of the interactions of substrate concentration and population density. Nonlinear regression with models incorporating these variables is a valuable means for analysis of microbial mineralization kinetics.     

Time-course analysis of cyanobacterium transcriptome: detecting oscillatory genes

The microarray technique allows the simultaneous measurements of the expression levels of thousands of mRNAs. By mining these data one can identify the dynamics of the gene expression time series. The detection of genes that are periodically expressed is an important step that allows us to study the regulatory mechanisms associated with the circadian cycle. The problem of finding periodicity in biological time series poses many challenges. Such challenge occurs due to the fact that the observed time series usually exhibit non-idealities, such as noise, short length, outliers and unevenly sampled time points. Consequently, the method for finding periodicity should preferably be robust against such anomalies in the data. In this paper, we propose a general and robust procedure for identifying genes with a periodic signature at a given significance level. This identification method is based on autoregressive models and the information theory. By using simulated data we show that the suggested method is capable of identifying rhythmic profiles even in the presence of noise and when the number of data points is small. By recourse of our analysis, we uncover the circadian rhythmic patterns underlying the gene expression profiles from Cyanobacterium Synechocystis.     

The cellular basis of cell sorting kinetics

Cell sorting is a dynamical cooperative phenomenon that is fundamental for tissue morphogenesis and tissue homeostasis. According to Steinberg's differential adhesion hypothesis, the structure of sorted cell aggregates is determined by physical characteristics of the respective tissues, the tissue surface tensions. Steinberg postulated that tissue surface tensions result from quantitative differences in intercellular adhesion. Several experiments in cell cultures as well as in developing organisms support this hypothesis.The question of how tissue surface tension might result from differential adhesion was addressed in some theoretical models. These models describe the cellular interdependence structure once the temporal evolution has stabilized. In general, these models are capable of reproducing sorted patterns. However, the model dynamics at the cellular scale are defined implicitly and are not well-justified. The precise mechanism describing how differential adhesion generates the observed sorting kinetics at the tissue level is still unclear.It is necessary to formulate the concepts of cell level kinetics explicitly. Only then it is possible to understand the temporal development at the cellular and tissue scales. Here we argue that individual cell mobility is reduced the more the cells stick to their neighbors. We translate this assumption into a precise mathematical model which belongs to the class of stochastic interacting particle systems. Analyzing this model, we are able to predict the emergent sorting behavior at the population level. We describe qualitatively the geometry of cell segregation depending on the intercellular adhesion parameters. Furthermore, we derive a functional relationship between intercellular adhesion and surface tension and highlight the role of cell mobility in the process of sorting. We show that the interaction between the cells and the boundary of a confining vessel has a major impact on the sorting geometry.     

Global analysis of proteins synthesized by Mycobacterium smegmatis provides direct evidence for physiological heterogeneity in stationary-phase cultures

We have characterized the induction kinetics of approximately 1,700 proteins during entry into and survival in carbon-starved stationary phase by Mycobacterium smegmatis. Strikingly, among the patterns of expression observed were a group of proteins that were expressed in exponential-phase cultures and severely repressed in 48-h stationary-phase cultures (Spr or stationary-phase-repressed proteins) but were synthesized again at high levels in > or =128-day stationary-phase cultures (Spr(128) proteins). A number of Spr(128) proteins were identified, and they included the heat shock protein DnaK, the tricarboxylic acid cycle enzyme succinyl coenzyme A synthase, a FixA-like flavoprotein, a single-stranded DNA binding protein, and elongation factor Tu (EF-Tu). The identification of EF-Tu as an Spr(128) protein is significant, as ribosomal components are known to be expressed in a growth rate-dependent way. We interpreted these data in terms of a model whereby stationary-phase mycobacteria comprise populations of cells that differ in both their growth status and gene expression patterns. To investigate this further, we constructed gene fusions between the rpsL gene promoter (which heads the Mycobacterium smegmatis operon encoding the tuf gene encoding EF-Tu) or the rrnA promoter gene and an unstable variant of green fluorescent protein. While the majority of cells in old stationary-phase cultures had low levels of fluorescence and so rpsL expression, a small but consistently observed population of approximately 1 in 1,000 cells was highly fluorescent. This indicates that a small fraction of the cells was expressing rpsL at high levels, and we argue that this represents the growing subpopulation of cells in stationary-phase cultures.     

Real-time analysis of ureteric bud branching morphogenesis in vitro

While it is clear that the normal branching morphogenesis of the ureteric bud (UB) is critical for development of the metanephric kidney, the specific patterns of branching and growth have heretofore only been inferred from static images. Here, we present a systematic time-lapse analysis of UB branching morphogenesis during the early development of the mouse kidney in organ culture. Metanephric primordia from Hoxb7/GFP transgenic embryos were cultured for 3-4 days, and GFP images of the UB taken every 30 min were assembled into movies. Analysis of these movies (available as )revealed that the UB is a highly plastic structure, which can branch in a variety of complex patterns, including terminal bifid, terminal trifid, and lateral branching. To examine kinetic parameters of branching and elongation, skeletal representations of the UB were used to measure the number of segments and branch points and the length of each segment as a function of time and of branch generation. These measurements provide a baseline for future studies on mutant kidneys with defects in renal development. To illustrate how these quantitative methods can be applied to the analysis of abnormal kidney development, we examined the effects of the MEK1 inhibitor PD98059 on renal organ cultures and confirmed a previous report that the drug has a specific inhibitory effect on UB branching as opposed to elongation.     

Oscillating growth patterns of multicellular tumour spheroids

The growth kinetics of 9L (rat glioblastoma cell line) and U118 (human glioblastoma cell line) multicellular tumour spheroids (MTS) have been investigated by non-linear least square fitting of individual growth curves with the Gompertz growth equation and power spectrum analysis of residuals. Residuals were not randomly distributed around calculated growth trajectories. At least one main frequency was found for all analysed MTS growth curves, demonstrating the existence of time-dependent periodic fluctuations of MTS volume dimensions. Similar periodic oscillations of MTS volume dimensions were also observed for MTS generated using cloned 9L cells. However, we found significant differences in the growth kinetics of MTS obtained with cloned cells if compared to the growth kinetics of MTS obtained with polyclonal cells. Our findings demonstrate that the growth patterns of three-dimensional tumour cell cultures are more complex than has been previously predicted using traditional continuous growth models.     

The Min system as a general cell geometry detection mechanism: branch lengths in Y-shaped Escherichia coli cells affect Min oscillation patterns and division dynamics

In Escherichia coli, division site placement is regulated by the dynamic behavior of the MinCDE proteins, which oscillate from pole to pole and confine septation to the centers of normal rod-shaped cells. Some current mathematical models explain these oscillations by considering interactions among the Min proteins without recourse to additional localization signals. So far, such models have been applied only to regularly shaped bacteria, but here we test these models further by employing aberrantly shaped E. coli cells as miniature reactors. The locations of MinCDE proteins fused to derivatives of green fluorescent protein were monitored in branched cells with at least three conspicuous poles. MinCDE most often moved from one branch to another in an invariant order, following a nonreversing clockwise or counterclockwise direction over the time periods observed. In cells with two short branches or nubs, the proteins oscillated symmetrically from one end to the other. The locations of FtsZ rings were consistent with a broad MinC-free zone near the branch junctions, and Min rings exhibited the surprising behavior of moving quickly from one possible position to another. Using a reaction-diffusion model that reproduces the observed MinCD oscillations in rod-shaped and round E. coli, we predict that the oscillation patterns in branched cells are a natural response of Min behavior in cellular geometries having different relative branch lengths. The results provide further evidence that Min protein oscillations act as a general cell geometry detection mechanism that can locate poles even in branched cells.     

Neural modeling of intrinsic and spike-discharge properties of cochlear nucleus neurons

The purpose of this study was to develop neurobiologically plausible models to account for the response properties of several types of cochlear nucleus neurons. Three cell types--the bushy cells, stellate cells, and fusiform cells--were selected because useful data from intracellular recordings were available for these cell types, and because these three cell types exhibit distinct contrasts in their neuronal signal coding strategies. Stellate cells have primarily linear current-voltage (I-V) characteristics, but both bushy and fusiform cells have highly non-linear I-V characteristics. In light of this, we hypothesize that some of these cells have non-linear voltage-dependent conductances which alter their response properties. We modeled the bushy cell membrane conductance as an exponentially increasing function of membrane voltage, that of the fusiform cell as an exponentially decreasing function of the voltage, and that of the stellate cell as being voltage-independent. We have combined the voltage-dependent non-linear conductances of the cell membrane with a simple R-C circuit type of neuron model. These models reproduced the salient features of the experimentally observed I-V characteristics of the cells. In addition, we found that the models reproduced the spike discharge behavior to intracellularly injected current steps. Moreover, a more detailed study of stellate cell 'chopper'-type response patterns yielded hypotheses regarding the nature of the current that must exist at the soma during a pure-tone stimulus in order for the cells to exhibit various chopper subtype patterns, such as chop-S, chop-T, and Oc. The chop-S pattern requires a steady average current level with a relatively small variability during the tone-burst stimulus. The chop-T pattern, in contrast, requires that the current become more irregular during the tone-burst stimulus. The Oc pattern arises, however, when the input is similar to the chop-T case but the intrinsic properties of the cell model have been changed to increase the accommodation of the threshold. The implications of these findings for circuitry in the cochlear nucleus are discussed. Our analysis of these models revealed that this approach can be used to simulate neuronal cell types where I-V characteristics are known but more detailed ion channel data are not known.     

Role of substrate inhibition kinetics in enzymatic chemical oscillations.

Two chemical kinetic models are investigated using standard nonlinear dynamics techniques to determine the conditions under which substrate inhibition kinetics can lead to oscillations. The first model is a classical substrate inhibition scheme based on Michaelis-Menten kinetics and involves a single substrate. Only when this reaction takes place in a flow reactor (i.e., both substrate and product are taken to follow reversible flow terms) are oscillations observed; however, the range of parameter values over which such oscillations occur is so narrow it is experimentally unobservable. A second model based on a general mechanism applied to the kinetics of many pH-dependent enzymes is also studied. This second model includes both substrate inhibition kinetics as well as autocatalysis through the activation of the enzyme by hydrogen ion. We find that it is the autocatalysis that is always responsible for oscillatory behavior in this scheme. The substrate inhibition terms affect the steady-state behavior but do not lead to oscillations unless product inhibition or multiple substrates are present; this is a general conclusion we can draw from our studies of both the classical substrate inhibition scheme and the pH-dependent enzyme mechanism. Finally, an analysis of the nullclines for these two models allows us to prove that the nullcline slopes must have a negative value for oscillatory behavior to exist; this proof can explain our results. From our analysis, we conclude with a brief discussion of other enzymes that might be expected to produce oscillatory behavior based on a pH-dependent substrate inhibition mechanism.     

Labyrinthine versus straight-striped patterns generated by two-dimensional Turing systems

Striped patterns are often observed on fish skin. Such patterns have been accounted for by reaction-diffusion (RD) Turing-type models, in which two substances can spontaneously form a spatially heterogeneous pattern in a homogeneous field. Among the striped patterns generated by Turing-type models, some are "straight-striped patterns," with many stripes running in parallel, while others are "labyrinthine patterns," in which the stripes often change direction, merge with each other, and frequently branch out. RD models differ in terms of their tendency to generate either labyrinthine or straight-striped patterns. Here, we studied the conditions under which either a labyrinthine or straight-striped pattern would emerge. First, we defined an index for stripe clearness, Sh. Straight-striped patterns (large Sh) are formed if only a narrow range of spatial periods corresponds to an unstable mode. Labyrinthine patterns (small Sh) are formed when a wide range of spatial periods is unstable. More specifically, labyrinthine patterns are formed when the maximum spatial period of unstable modes is more than twice that of the minimum spatial period of unstable modes; otherwise, straight-striped patterns are formed. We then examined RD models with nonlinear reaction terms, including both activator-inhibitor and substrate-depletion models, and we demonstrated that the same conclusions hold with respect to the conditions required for labyrinthine versus straight-striped patterns.     

Differential localisation of BPIFA1 (SPLUNC1) and BPIFB1 (LPLUNC1) in the nasal and oral cavities of mice

Despite being initially identified in mice, little is known about the sites of production of members of the BPI fold (BPIF) containing (PLUNC) family of putative innate defence proteins in this species. These proteins have largely been considered to be specificaly expressed in the respiratory tract, and we have recently shown that they exhibit differential expression in the epithelium of the proximal airways. In this study, we have used species-specific antibodies to systematically localize two members of this protein family; BPIFA1 (PLUNC/SPLUNC1) and BPIFB1 (LPLUNC1) in adult mice. In general, these proteins exhibit distinct and only partially overlapping localization. BPIFA1 is highly expressed in the respiratory epithelium and Bowman??s glands of the nasal passages, whereas BPIFB1 is present in small subset of goblet cells in the nasal passage and pharynx. BPIFB1 is also present in the serous glands in the proximal tongue where is co-localised with the salivary gland specific family member, BPIFA2E (parotid secretory protein) and also in glands of the soft palate. Both proteins exhibit limited expression outside of these regions. These results are consistent with the localization of the proteins seen in man. Knowledge of the complex expression patterns of BPIF proteins in these regions will allow the use of tractable mouse models of disease to dissect their function.     

Static and dynamic behavior of a class of unstructured models of continuous bioreactors with growth associated product

The static and dynamic behavior of a class of unstructured models of continuous bioprocesses, for which the product is growth associated, are analyzed using elementary concepts of singularity theory and continuation techniques. The class consists of models for which both the rates of utilization of limiting substrate and product formation are linearly proportional to the specific cell growth rate. The kinetic expressions are allowed to assume general forms of substrate and nonbiomass product. The steady-state analysis allows the derivation of analytical results and the construction of a useful picture in the models' parameter space delineating the different static behavior these models can predict, including unique steady states and bistability. The analysis of the dynamic behavior allows the derivation of general analytical conditions for the occurrence of periodic behavior in the models. It is also shown that the subclass of these models for which the specific cell growth rate expression is monotonic with respect to the nonbiomass product is unable to predict a stable oscillatory behavior regardless of the expression of the growth rate. These results illustrate the fundamental weakness of this class of unstructured models in predicting transient behavior in continuous cultures. The effect of kinetic and operating parameters on the stability characteristics of these models is also investigated.     

Spontaneous coordinated activity in cultured networks: Analysis of multiple ignition sites,primary circuits,and burst phase delay distributions

All higher order central nervous systems exhibit spontaneous neural activity, though the purpose and mechanistic origin of such activity remains poorly understood. We quantitatively analyzed the ignition and spread of collective spontaneous electrophysiological activity in networks of cultured cortical neurons growing on microelectrode arrays. Leader neurons, which form a mono-synaptically connected primary circuit, and initiate a majority of network bursts were found to be a small subset of recorded neurons. Leader/follower firing delay times formed temporally stable positively skewed distributions. Blocking inhibitory synapses usually resulted in shorter delay times with reduced variance. These distributions are characterizations of general aspects of internal network dynamics and provide estimates of pair-wise synaptic distances. The resulting analysis produced specific quantitative constraints and insights into the activation patterns of collective neuronal activity in self-organized cortical networks, which may prove useful for models emulating spontaneously active systems.