A stochastic model of neuronal growth cone guidance regulated by multiple sensors

Neuronal growth cones migrate directionally under the control of axon guidance molecules, thereby forming synapses in the developing brain. The signal transduction system by which a growth cone detects surrounding guidance molecules, analyzes the detected signals, and then determines the overall behavior remains undetermined. In this study, we describe a novel stochastic model of this behavior that utilizes multiple sensors on filopodia to respond to guidance molecules. Overall growth cone behavior is determined by using only the concentration gradients of guidance molecules in the immediate vicinity of each sensor. The detected signal at each sensor, which is treated as a vector quantity, is sent to the growth cone center and then integrated to determine axonal growth in the next step by means of a simple vector operation. We compared the results of computer simulations of axonal growth with observations of actual axonal growth from co-culture experiments using olfactory bulb and septum. The probabilistic distributions of axonal growth generated by the computer simulation were consistent with those obtained from the culture experiments, indicating that our model accurately simulates growth cone behavior. We believe that this model will be useful for elucidating the as yet unknown mechanisms responsible for axonal growth in vivo.     

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.     

Coevolution of foraging behavior with intrinsic growth rate: risk-taking in naturally and artificially selected growth genotypes of <Emphasis Type="Italic">Menidia menidia</Emphasis>

Although there is accumulating evidence of growth-rate optimization by natural selection, the coevolution of growth rate and risk-taking behavior has not been sufficiently documented. The Atlantic silverside fish, Menidia menidia, displays countergradient variation in growth across a latitudinal gradient: genotypes from Nova Scotia (NS), for example, grow in length twofold faster than those from South Carolina (SC). Past work has established that fast growth is adaptive in northern climates, but the trade-off is poorer swimming performance and higher susceptibility to predators. We compared escape behavior and willingness to forage under threat of predation among growth genotypes reared and tested under common-garden conditions. When chased with a predator model, NS fish occupied shelter more quickly than SC fish. When food was supplied after a chase, NS fish reemerged from the shelter much more quickly than SC fish and immediately commenced feeding, whereas many SC fish displayed timid behavior and did not feed. When food was absent following a chase, however, NS fish remained in the shelter longer than did SC fish and both displayed timid behavior. Hence, the fast-growing NS genotype was bolder than SC fish in the presence of food, but shyer in the absence of food. These behaviors are adaptive given the physiological constraints intrinsic to each genotype. Experiments on captive populations of silversides that had been artificially selected for fast or slow growth confirmed that foraging behavior is genetically correlated with intrinsic growth rate, although in these trials the fast-growth genotype was always more bold, regardless of food availability, as would be expected in the absence of predators. We conclude that risk-taking foraging behavior coevolves adaptively with intrinsic growth rate in M. menidia.     

Propagation of surface fatigue cracks in human cortical bone

An understanding of how fatigue cracks grow in bone is of importance as fatigue is thought to be the main cause of clinical stress fractures. This study presents new results on the fatigue-crack growth behavior of small surface cracks (approximately 75-1000 microm in size) in human cortical bone, and compares their growth rates with data from other published studies on the behavior of both surface cracks and many millimeter, through-thickness large cracks. Results are obtained with a cyclically loaded cantilever-beam geometry using optical microscopy to examine for crack growth after every 100-500 cycles. Based on the current and previous results, small fatigue cracks appear to become more resistant to fatigue-crack growth with crack extension, analogous to the way the fracture resistance of cortical bone increases with crack growth. Mechanistically, a theory attributing such behavior to the development of bridges in the wake of the crack with crack growth is presented. The existence of such bridges is directly confirmed using optical microscopy.     

Pursuing a ‘turning point’ in growth cone research

Growth cones are highly motile structures found at the leading edge of developing and regenerating nerve processes. Their role in axonal pathfinding has been well established and many guidance cues that influence growth cone behavior have now been identified. Many studies are now providing insights into the transduction and integration of signals in the growth cone, though a full understanding of growth cone behavior still eludes us. This review focuses on recent studies adding to the growing body of literature on growth cone behavior, focusing particularly on the level of autonomy the growth cone possesses and the role of local protein synthesis.     

Comparison of growth and exploratory behavior in mice fed an exclusively milk formula diet and mice fed a food-pellet diet post weaning

An exclusively milk formula diet stunted the growth of mice immediately following weaning. Milk-fed mice displayed a low-frequency profile of exploratory behavior, while pellet-fed mice showed high-frequency exploration. In contrast to exploratory behavior, feeding behavior did not differ significantly between milk- and pellet-fed mice. Despite showing low-frequency exploratory behavior, mice on an exclusively milk formula diet showed no difference in behavioral activities analyzed by an automatic hole-board apparatus compared to pellet-fed mice. These results suggest that the growth stunt caused by an exclusively milk formula diet retards the acquisition of active exploratory behavior without affecting the emotional state of mice.     

Analysis of kinetic uptake phenomena of monosaccharide and disaccharide by suspension TBY-2 cells using an FT-IR/ATR method

The influence of sugars in culture media on the kinetics of the mono- and disaccharide uptake and cell growth behavior was studied by mid-infrared spectroscopy using a Fourier transform infrared spectrometer (FT-IR) equipped with an attenuate total reflection accessory (ATR). We performed the plant cell cultivation with Nicotiana tabacum cv. Bright Yellow No.2 (TBY-2) cells in the culture media, which contained glucose, fructose, mannose, galactose, sucrose, trehalose, maltose or lactose. Consequently, the differences of the kinetic sugar uptake and cell growth behavior among all the cultivations were confirmed. In particular, a very long lag time before the galactose uptake was observed, and the spectral-pattern of the maltose medium presented almost the same as the initial one during the cultivation. Furthermore, base on the non-dimensional cultivation time for cell growth behavior, it was suggested that the TBY-2 cells consumed sugar before cell growth and produced the ethanol just after cell growth.     

Biodegradation of chlorophenol mixtures by Pseudomonas putida

The dynamic growth behavior of Pseudomonas putida has been studied when resting calls were inoculated into a growth medium containing inhibitory concentrations of mixtures of phenol and monochlorophenols. Resting cells inoculated into single carbon substrate media did not demonstrate enhanced cell lysis by any of the phenol substrates. The apprarent death rate was reduced as the concentrations of phenol or chlorophenols were increased. This behavior was modeled by employing a constant specific death rate (k(d) = 0.0075 h(-1)) and assuming all organic species result in a lag-phase, specific growth rate which may be larger or smaller than k(d).Logarithmic biomass growth on pure monochlorophenols did not occur within 2 weeks after inoculation. Logarithmic growth phases were only observed when the monochlorophenols were cometabolized with phenol. The delay time over which the lag phase exists increased exponentially with phenol concentration and linearly with monochlorophenol concentration. The log growth yield coefficient decreased linearly with monochlorophenol concentration.The lag-phase, specific growth rate was found to decrease exponentially with the concentration of monochlorophenols. This resulted in a 50% lag growth rate inhibition for both 3- and 4-chlorophenol of 9 ppm and for 2-chlorophenol of only 2 ppm. The new, empirical correlations are shown to closely model the complete lag and log growth behavior ot P. putida on phenol and chlorophenol mixtures. (c) 1992 John Wiley & Sons, Inc.     

Developmental timing of a sensory-mediated larval surfacing behavior correlates with cessation of feeding and determination of final adult size

Controlled organismal growth to an appropriate adult size requires a regulated balance between nutrient resources, feeding behavior and growth rate. Defects can result in decreased survival and/or reproductive capability. Since Drosophila adults do not grow larger after eclosion, timing of feeding cessation during the third and final larval instar is critical to final size. We demonstrate that larval food exit is preceded by a period of increased larval surfacing behavior termed the Intermediate Surfacing Transition (IST) that correlates with the end of larval feeding. This behavioral transition occurred during the larval Terminal Growth Period (TGP), a period of constant feeding and exponential growth of the animal. IST behavior was dependent upon function of a subset of peripheral sensory neurons expressing the Degenerin/Epithelial sodium channel (DEG/ENaC) subunit, Pickpocket1(PPK1). PPK1 neuron inactivation or loss of PPK1 function caused an absence of IST behavior. Transgenic PPK1 neuron hyperactivation caused premature IST behavior with no significant change in timing of larval food exit resulting in decreased final adult size. These results suggest a peripheral sensory mechanism functioning to alter the relationship between the animal and its environment thereby contributing to the length of the larval TGP and determination of final adult size.     

Photophobic behavior of maize roots

Primary roots of young maize seedlings showed peculiar growth behavior when challenged by placing them on a slope, or if whole seedlings were turned upside down. Importantly, this behavior was dependent on the light conditions. If roots were placed on slopes in the dark, they performed “crawling” behavior and advanced rapidly up the slope. However, as soon as these roots were illuminated, their crawling movements along their horizontal paths slowed down, and instead tried to grow downwards along the gravity vector. A similar light-induced switch in the root behavior was observed when roots were inverted, by placing them in thin glass capillaries. As long as they were kept in the darkness, they showed rapid growth against the gravity vector. If illuminated, these inverted roots rapidly accomplished U-turns and grew down along the gravity vector, eventually escaping from the capillaries upon reaching their open ends. De-capped roots, although growing vigorously, did not display these light-induced photophobic growth responses. We can conclude that intact root cap is essential for the photophobic root behavior in maize.     

Continuous culture of Methanococcus maripaludis under defined nutrient conditions

To study global regulation in the methanogenic archaeon Methanococcus maripaludis, we devised a system for steady-state growth in chemostats. New Brunswick Bioflo 110 bioreactors were equipped with controlled delivery of hydrogen, nitrogen, carbon dioxide, hydrogen sulfide, and anaerobic medium. We determined conditions and media compositions for growth with three different limiting nutrients, hydrogen, phosphate, and leucine. To investigate leucine limitation we constructed and characterized a mutant in the leuA gene for 2-isopropylmalate synthase, demonstrating for the first time the function of this gene in the Archaea. Steady state specific growth rates in these studies ranged from 0.042 to 0.24 h(-1). Plots of culture density vs. growth rate for each condition showed the behavior predicted by growth modeling. The results show that growth behavior is normal and reproducible and validate the use of the chemostat system for metabolic and global regulation studies in M. maripaludis.     

Cybernetic modeling of microbial growth on multiple substrates

The internal regulatory processes, which underlie a variety of behavior in microbial growth on multiple substrates, are viewed as a manifestation of an invariant strategy to optimize some goal of the cells. A goal-seeking or cybernetic model is proposed here, with the optimization obased on a short-term perspective of response to the environment. The model parameters are determined from the growth data on single substrates. The model predicts the entire range of microbial growth behavior on multiple substrates from simultaneous utilization of all sugars to sequential utilization with pronounced diauxic lags. It is shown to predict the many variations of the diauxic phenomenon in different growth conditions. The transients in continuous culture growth on mixed substrates caused by varying the feed strategies are easily simulated by this model. The framework of this model can be applied to batch or continuous culture growth of many bacteria on different combinations of substrates.     

Rheological,Mass Transfer,and Mixing Characterization of Cellulase-Producing Trichoderma reesei Suspensions

Steady and dynamic shear measurements are utilized to characterize the rheological behavior of Trichoderma reesei RUT-C30 fungal suspensions during batch growth on xylose (soluble substrate) or cellulose (particulate solid substrate) at three different fermentor impeller speeds (250, 400, and 550 rpm). Biomass concentrations versus time were unimodal on xylose and bimodal on cellulose. This behavior is consistent with relatively rapid, early growth on easily metabolized growth medium components (yeast extract), followed by a second, slower growth phase due to hydrolysis of recalcitrant cellulose by increasing cellulase concentrations. Critical dissolved oxygen (DO) concentration for T. reesei growth on cellulose was found to be 0.073 mmol/L. The DO was kept above this level by supplementing the air feed with pure oxygen, implying that mass transfer limitations were not the cause of bimodal cell growth. Steady shear rheological data showed shear thinning behavior and a yield stress for all broth samples regardless of substrate. Casson and Herschel−Bulkley constitutive equations fit steady shear data well. Dynamic shear measurements on broth suspensions indicated “gel-like” behavior at low strains, with microstructural breakdown at larger displacements. Time variations of the Casson model parameters (yield stress and Casson viscosity) and dynamic moduli (elastic and viscous modulus) followed both cell mass and morphology: a single maximum in all rheological variables resulted when cells were grown on xylose or on cellulose at impeller speeds of 400 or 550 rpm, and dual maxima were observed for cellulose-grown cells at 250 rpm.     

Short- and Long-Term Exposure of Lumbriculus variegatus (Oligochaete) to Metal Lead: Ecotoxicological and Behavioral Effects

Metals are naturally occurring constituents of the environment and although many are essential nutrients for living organisms, at higher concentrations they can be toxic. Some aquatic species can help understand and even predict the impact of those contaminants. Lumbriculus variegatus is a recommended species for use in sediment toxicity tests and is known to have a remarkable ability of segmental regeneration. Short- (10-day) and long-term (28-day) toxicity tests were used to test the effects of a metal on the survival, growth, and behavior of L. variegatus. This work aims to investigate and validate the use of behavior as a new parameter in standard toxicity tests. Worms were exposed to sediments contaminated with different levels of lead and the results indicated a positive relation between lead concentrations and mortality and growth: higher lead concentrations resulted in higher mortalities and strong inhibition of growth. An inhibition of behavior was observed and results suggested that although behavior could not be used in sediment toxicity tests, it proved useful as an addition to short-term tests and helps select sediments. Thus, exposure to sediments contaminated with lead affects the presence of this species in nature, because it interferes with growth and survival.     

In vivo directed enzyme evolution in nanoliter reactors with antimetabolite selection

Scoring changes in enzyme or pathway performance by their effect on growth behavior is a widely applied strategy for identifying improved biocatalysts. While in directed evolution this strategy is powerful in removing non-functional catalysts in selections, measuring subtle differences in growth behavior remains difficult at high throughput, as it is difficult to focus metabolic control on only one or a few enzymatic steps over the entire process of growth-based discrimination. Here, we demonstrate successful miniaturization of a growth-based directed enzyme evolution process. For cultivation of library clones we employed optically clear gel-like microcarriers of nanoliter volume (NLRs) as reaction vessels and used fluorescence-assisted particle sorting to estimate the growth behavior of each of the gel-embedded clones in a highly parallelized fashion. We demonstrate that the growth behavior correlates with the desired improvements in enzyme performance and that we can fine-tune selection stringency by including an antimetabolite in the assay. As a model enzyme reaction, we improve the racemization of ornithine, a possible starting block for the large-scale synthesis of sulphostin, by a broad-spectrum amino acid racemase and confirm the discriminatory power by showing that even moderately improved enzyme variants can be readily identified.     

Social and developmental biology of the myxobacteria.

Myxobacteria are soil bacteria whose unusually social behavior distinguishes them from other groups of procaryotes. Perhaps the most remarkable aspect of their social behavior occurs during development, when tens of thousands of cells aggregate and form a colorful fruiting body. Inside the fruiting body the vegetative cells convert into dormant, resistant myxospores. However, myxobacterial social behavior is not restricted to the developmental cycle, and three other social behaviors have been described. Vegetative cells have a multigene social motility system in which cell-cell contact is essential for gliding in multicellular swarms. Cell growth on protein is cooperative in that the growth rate increases with the cell density. Rippling is a periodic behavior in which the cells align themselves in ridges and move in waves. These social behaviors indicate that myxobacterial colonies are not merely collections of individual cells but are societies in which cell behavior is synchronized by cell-cell interactions. The molecular basis of these social behaviors is becoming clear through the use of a combination of behavioral, biochemical, and genetic experimental approaches.     

Roles of actin filaments and three second-messenger systems in short-term regulation of chick dorsal root ganglion neurite outgrowth.

In a previous study (J. Cell Biol. 109: 1229-1243, 1989), we reported that conditions which increased growth cone calcium levels and induced neurite retraction in cultured chick DRG neurons also resulted in an apparent loss of actin filaments in the growth cone periphery. We further showed that the actin-stabilizing drug phalloidin could block or reverse calcium-ionophore-induced neurite retraction, indicating that the behavioral changes were mediated, at least in part, by changes in actin filament stability. In this study, we have further characterized the calcium sensitivity of growth cone behavior to identify which features of calcium-induced behavioral effects can be attributed to effects on actin filaments alone, and to assess whether two other second-messenger systems, cAMP and protein kinase C, might influence neurite outgrowth by altering calcium levels or actin stability. The results indicated that growth cone behavior was highly sensitive to small changes in calcium concentrations. Neurite outgrowth was only observed in calcium-permeabilized cells when extracellular calcium concentrations were between 200 and 300 nM, and changes as small as 50 nM commonly produced detectable changes in behavior. Furthermore, low doses of cytochalasins mimicked all of the grossly observable features of growth cone responses to elevation of intracellular calcium, including the apparent preferential destruction of lamellipodial actin filaments and sparing of filopodial actin, suggesting that the behavioral effects of calcium elevation could be explained by loss of actin filaments alone. The effects of cAMP elevation and protein kinase C activation on growth cone behavior, ultrastructure, and fura2-AM-measured calcium levels indicated that the effects of cAMP manipulations could be partially explained by a cAMP-induced lowering of growth cone calcium levels and concomitant increased stabilization of actin filaments, but protein kinase C appeared to act through an independent mechanism.     

Growth velocities of branched actin networks

The growth of an actin network against an obstacle that stimulates branching locally is studied using several variants of a kinetic rate model based on the orientation-dependent number density of filaments. The model emphasizes the effects of branching and capping on the density of free filament ends. The variants differ in their treatment of side versus end branching and dimensionality, and assume that new branches are generated by existing branches (autocatalytic behavior) or independently of existing branches (nucleation behavior). In autocatalytic models, the network growth velocity is rigorously independent of the opposing force exerted by the obstacle, and the network density is proportional to the force. The dependence of the growth velocity on the branching and capping rates is evaluated by a numerical solution of the rate equations. In side-branching models, the growth velocity drops gradually to zero with decreasing branching rate, while in end-branching models the drop is abrupt. As the capping rate goes to zero, it is found that the behavior of the velocity is sensitive to the thickness of the branching region. Experiments are proposed for using these results to shed light on the nature of the branching process.     

Local calcium changes regulate the length of growth cone filopodia

Previous studies have demonstrated that the free intracellular calcium concentration ([Ca(2+)](i)) in growth cones can act as an important regulator of growth cone behavior. Here we investigated whether there is a spatial and temporal correlation between [Ca(2+)](i) and one particular aspect of growth cone behavior, namely the regulation of growth cone filopodia. Calcium was released from the caged compound NP-EGTA (o-nitrophenyl EGTA tetrapotassium salt) to simulate a signaling event in the form of a transient increase in [Ca(2+)](i). In three different experimental paradigms, we released calcium either globally (within an entire growth cone), regionally (within a small area of the lamellipodium), or locally (within a single filopodium). We demonstrate that global photolysis of NP-EGTA in growth cones caused a transient increase in [Ca(2+)](i) throughout the growth cone and elicited subsequent filopodial elongation that was restricted to the stimulated growth cone. Pharmacological blockage of either calmodulin or the Ca(2+)-dependent phosphatase, calcineurin, inhibited the effect of uncaging calcium, suggesting that these enzymes are acting downstream of calcium. Regional uncaging of calcium in the lamellipodium caused a regional increase in [Ca(2+)](i), but induced filopodial elongation on the entire growth cone. Elevation of [Ca(2+)](i) locally within an individual filopodium resulted in the elongation of only the stimulated filopodium. These findings suggest that the effect of an elevation of [Ca(2+)](i) on filopodial behavior depends on the spatial distribution of the calcium signal. In particular, calcium signals within filopodia can cause filopodial length changes that are likely a first step towards directed filopodial steering events seen during pathfinding in vivo.