SAX-3 (Robo) and UNC-40 (DCC) Regulate a Directional Bias for Axon Guidance in Response to Multiple Extracellular Cues

Axons in Caenorhabditis elegans are guided by multiple extracellular cues, including UNC-6 (netrin), EGL-20 (wnt), UNC-52 (perlecan), and SLT-1 (slit). How multiple extracellular cues determine the direction of axon guidance is not well understood. We have proposed that an axon''s response to guidance cues can be modeled as a random walk, i.e., a succession of randomly directed movement. Guidance cues dictate the probability of axon outgrowth activity occurring in each direction, which over time creates a directional bias. Here we provide further evidence for this model. We describe the effects that the UNC-40 (DCC) and SAX-3 (Robo) receptors and the UNC-6, EGL-20, UNC-52, and SLT-1 extracellular cues have on the directional bias of the axon outgrowth activity for the HSN and AVM neurons. We find that the directional bias created by the cues depend on UNC-40 or SAX-3. UNC-6 and EGL-20 affect the directional bias for both neurons, whereas UNC-52 and SLT-1 only affect the directional bias for HSN and AVM, respectively. The direction of the bias created by the loss of a cue can vary and the direction depends on the other cues. The random walk model predicts this combinatorial regulation. In a random walk a probability is assigned for each direction of outgrowth, thus creating a probability distribution. The probability distribution for each neuron is determined by the collective effect of all the cues. Since the sum of the probabilities must equal one, each cue affects the probability of outgrowth in multiple directions.     

Mutation-biased adaptation in a protein NK model

Evolutionary trends responsible for systematic differences in genome and proteome composition have been attributed to GC:AT mutation bias in the context of neutral evolution or to selection acting on genome composition. A possibility that has been ignored, presumably because it is part of neither the Modern Synthesis nor the Neutral Theory, is that mutation may impose a directional bias on adaptation. This possibility is explored here with simulations of the effect of a GC:AT bias on amino acid composition during adaptive walks on an abstract protein fitness landscape called an "NK" model. The results indicate that adaptation does not preclude mutation-biased evolution. In the complete absence of neutral evolution, a modest GC:AT bias of realistic magnitude can displace the trajectory of adaptation in a mutationally favored direction, to such a degree that amino acid composition is biased substantially and persistently. Thus, mutational explanations for evolved patterns need not presuppose neutral evolution.     

Directional penalties for optimal matching in observational studies

Multivariate matching in observational studies tends to view covariate differences symmetrically: a difference in age of 10 years is thought equally problematic whether the treated subject is older or younger than the matched control. If matching is correcting an imbalance in age, such that treated subjects are typically older than controls, then the situation in need of correction is asymmetric: a matched pair with a difference in age of 10 years is much more likely to have an older treated subject and a younger control than the opposite. Correcting the bias may be easier if matching tries to avoid the typical case that creates the bias. We describe several easily used, asymmetric, directional penalties and illustrate how they can improve covariate balance in a matched sample. The investigator starts with a matched sample built in a conventional way, then diagnoses residual covariate imbalances in need of reduction, and achieves the needed reduction by slightly altering the distance matrix with directional penalties, creating a new matched sample. Unlike penalties commonly used in matching, a directional penalty can go too far, reversing the direction of the bias rather than reducing the bias, so the magnitude of the directional penalty matters and may need adjustment. Our experience is that two or three adjustments, guided by balance diagnostics, can substantially improve covariate balance, perhaps requiring fifteen minutes effort sitting at the computer. We also explore the connection between directional penalties and a widely used technique in integer programming, namely Lagrangian relaxation of problematic linear side constraints in a minimum cost flow problem. In effect, many directional penalties are Lagrange multipliers, pushing a matched sample in the direction of satisfying a linear constraint that would not be satisfied without penalization. The method and example are in an R package DiPs at CRAN .     

Mathematical analysis of cell-target encounter rates in two dimensions. The effect of chemotaxis.

The process by which cells encounter their targets is the first step of a number of cell functions involved in the immune response, such as cell-mediated cytotoxicity and phagocytic ingestion of foreign material. In many instances, this encounter may be rate-limiting, and therefore it is important to understand what factors influence the encounter rate. One key aspect of cell-target encounter is the motility behavior of the cell in the vicinity of a target. This movement may be entirely random, or there may be a directed, or chemotactic, component to it. In this paper we focus on the effects of cell motility properties, and particularly the chemotactic directional bias, on the rate of cell-target encounter. Specifically, we derive an expression for the mean encounter time of cells that meet targets in two dimensions as a function of the cells' directional orientation bias. We show that a modest degree of bias can reduce the mean encounter time by orders of magnitude, while nearly perfect directional bias offers little additional benefit. We illustrate the application of these results to a particular example system: alveolar macrophages removing inhaled particles and bacteria from the lung surface.     

Effect of strong directional selection on weakly selected mutations at linked sites: implication for synonymous codon usage

The fixation of weakly selected mutations can be greatly influenced by strong directional selection at linked loci. Here, I investigate a two-locus model in which weakly selected, reversible mutations occur at one locus and recurrent strong directional selection occurs at the other locus. This model is analogous to selection on codon usage at synonymous sites linked to nonsynonymous sites under strong directional selection. Two approximations obtained here describe the expected frequency of the weakly selected preferred alleles at equilibrium. These approximations, as well as simulation results, show that the level of codon bias declines with an increasing rate of substitution at the strongly selected locus, as expected from the well-understood theory that selection at one locus reduces the efficacy of selection at linked loci. These solutions are used to examine whether the negative correlation between codon bias and nonsynonymous substitution rates recently observed in Drosophila can be explained by this hitchhiking effect. It is shown that this observation can be reasonably well accounted for if a large fraction of the nonsynonymous substitutions on genes in the data set are driven by strong directional selection.     

A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations

Two central features of polymorphonuclear leukocyte chemosensory movement behavior demand fundamental theoretical understanding. In uniform concentrations of chemoattractant, these cells exhibit a persistent random walk, with a characteristic "persistence time" between significant changes in direction. In chemoattractant concentration gradients, they demonstrate a biased random walk, with an "orientation bias" characterizing the fraction of cells moving up the gradient. A coherent picture of cell movement responses to chemoattractant requires that both the persistence time and the orientation bias be explained within a unifying framework. In this paper, we offer the possibility that "noise" in the cellular signal perception/response mechanism can simultaneously account for these two key phenomena. In particular, we develop a stochastic mathematical model for cell locomotion based on kinetic fluctuations in chemoattractant/receptor binding. This model can simulate cell paths similar to those observed experimentally, under conditions of uniform chemoattractant concentrations as well as chemoattractant concentration gradients. Furthermore, this model can quantitatively predict both cell persistence time and dependence of orientation bias on gradient size. Thus, the concept of signal "noise" can quantitatively unify the major characteristics of leukocyte random motility and chemotaxis. The same level of noise large enough to account for the observed frequency of turning in uniform environments is simultaneously small enough to allow for the observed degree of directional bias in gradients.     

Apparent directional selection by biased pleiotropic mutation

Pleiotropic effects of deleterious mutations are considered to be among the factors responsible for genetic constraints on evolution by long-term directional selection acting on a quantitative trait. If pleiotropic phenotypic effects are biased in a particular direction, mutations generate apparent directional selection, which refers to the covariance between fitness and the trait owing to a linear association between the number of mutations possessed by individuals and the genotypic values of the trait. The present analysis has shown how the equilibrium mean value of the trait is determined by a balance between directional selection and biased pleiotropic mutations. Assuming that genes act additively both on the trait and on fitness, the total variance-standardized directional selection gradient was decomposed into apparent and true components. Experimental data on mutation bias from the bristle traits of Drosophila and life history traits of Daphnia suggest that apparent selection explains a small but significant fraction of directional selection pressure that is observed in nature; the data suggest that changes induced in a trait by biased pleiotropic mutation (i.e., by apparent directional selection) are easily compensated for by (true) directional selection.     

How much can we know about the causes of evolutionary trends?

One of the first questions that paleontologists ask when they identify a large-scale trend in the fossil record (e.g., size increase, complexity increase) is whether it is passive or driven. In this article, I explore two questions about driven trends: (1) what is the underlying cause or source of the directional bias? and (2) has the strength of the directional bias changed over time? I identify two underdetermination problems that prevent scientists from giving complete answers to these two questions.     

Articular constraint, handedness, and directional asymmetry in the human second metacarpal

The hypothesis that functional adaptation of joint surfaces to mechanical loading occurs primarily through change in mass, density, and structure of subarticular trabeculae (the "articular constraint" model) is investigated through an analysis of directional asymmetry among three separate bone compartments in the human second metacarpal. Measures of midshaft cross-sectional geometry, osteometry of the distal epiphysis, and subarticular trabecular microarchitecture of the distal epiphysis (assessed by high-resolution microcomputed tomography) were determined for 29 paired male and female metacarpals from a well-preserved nineteenth-century Euro-Canadian historic cemetery sample. For each measure, asymmetry was quantified using both mean-difference and confidence-interval methods. Both methods found a significant right-hand bias for measures of structural strength in midshaft geometry, as has been previously noted for this sample. Articular size, however, exhibits a right-hand bias only with regard to mediolateral, and not dorsopalmar, dimensions, a result that may reflect directional asymmetry in hand breadth at the distal palmar arch. The most striking asymmetries occur for subarticular trabecular microarchitecture. The right metacarpal head exhibits greater bone volume fraction, bone surface density, trabecular number, connectivity, and a more platelike rather than rodlike structure. These outcomes confer greater resistance to both axial compressive and shear strains for the metacarpal head at the metacarpophalangeal arthrosis. In all, these results confirm and extend previous research documenting structural asymmetries and limb dominance and are consistent with the concept of articular constraint. They also suggest a morphological signal through which functional asymmetry associated with handedness in fossil hominins may be investigated.     

Treadmill experience alters treadmill effects on perceived visual motion

Information on ongoing body movements can affect the perception of ambiguous visual motion. Previous studies on "treadmill capture" have shown that treadmill walking biases the perception of ambiguous apparent motion in backward direction in accordance with the optic flow during normal walking, and that long-term treadmill experience changes the effect of treadmill capture. To understand the underlying mechanisms for these phenomena, we conducted Experiment 1 with non-treadmill runners and Experiment 2 with treadmill runners. The participants judged the motion direction of the apparent motion stimuli of horizontal gratings in front of their feet under three conditions: walking on a treadmill, standing on a treadmill, and standing on the floor. The non-treadmill runners showed the presence of downward bias only under the walking condition, indicating that ongoing treadmill walking but not the awareness of being on a treadmill biased the visual directional discrimination. In contrast, the treadmill runners showed no downward bias under any of the conditions, indicating that neither ongoing activity nor the awareness of spatial context produced perception bias. This suggests that the long-term repetitive experience of treadmill walking without optic flow induced the formation of a treadmill-specific locomotor-visual linkage to perceive the complex relationship between self and the environment.     

The C. elegans Male Exercises Directional Control during Mating through Cholinergic Regulation of Sex-Shared Command Interneurons

Background

Mating behaviors in simple invertebrate model organisms represent tractable paradigms for understanding the neural bases of sex-specific behaviors, decision-making and sensorimotor integration. However, there are few examples where such neural circuits have been defined at high resolution or interrogated.

Methodology/Principal Findings

Here we exploit the simplicity of the nematode Caenorhabditis elegans to define the neural circuits underlying the male’s decision to initiate mating in response to contact with a mate. Mate contact is sensed by male-specific sensilla of the tail, the rays, which subsequently induce and guide a contact-based search of the hermaphrodite’s surface for the vulva (the vulva search). Atypically, search locomotion has a backward directional bias so its implementation requires overcoming an intrinsic bias for forward movement, set by activity of the sex-shared locomotory system. Using optogenetics, cell-specific ablation- and mutant behavioral analyses, we show that the male makes this shift by manipulating the activity of command cells within this sex-shared locomotory system. The rays control the command interneurons through the male-specific, decision-making interneuron PVY and its auxiliary cell PVX. Unlike many sex-shared pathways, PVY/PVX regulate the command cells via cholinergic, rather than glutamatergic transmission, a feature that likely contributes to response specificity and coordinates directional movement with other cholinergic-dependent motor behaviors of the mating sequence. PVY/PVX preferentially activate the backward, and not forward, command cells because of a bias in synaptic inputs and the distribution of key cholinergic receptors (encoded by the genes acr-18, acr-16 and unc-29) in favor of the backward command cells.

Conclusion/Significance

Our interrogation of male neural circuits reveals that a sex-specific response to the opposite sex is conferred by a male-specific pathway that renders subordinate, sex-shared motor programs responsive to mate cues. Circuit modifications of these types may make prominent contributions to natural variations in behavior that ultimately bring about speciation.     

Evidence for complex selection on four‐fold degenerate sites in Drosophila melanogaster

We considered genome‐wide four‐fold degenerate sites from an African Drosophila melanogaster population and compared them to short introns. To include divergence and to polarize the data, we used its close relatives Drosophila simulans, Drosophila sechellia, Drosophila erecta and Drosophila yakuba as outgroups. In D. melanogaster, the GC content at four‐fold degenerate sites is higher than in short introns; compared to its relatives, more AT than GC is fixed. The former has been explained by codon usage bias (CUB) favouring GC; the latter by decreased intensity of directional selection or by increased mutation bias towards AT. With a biallelic equilibrium model, evidence for directional selection comes mostly from the GC‐rich ancestral base composition. Together with a slight mutation bias, it leads to an asymmetry of the unpolarized allele frequency spectrum, from which directional selection is inferred. Using a quasi‐equilibrium model and polarized spectra, however, only purifying and no directional selection is detected. Furthermore, polarized spectra are proportional to those of the presumably unselected short introns. As we have no evidence for a decrease in effective population size, relaxed CUB must be due to a reduction in the selection coefficient. Going beyond the biallelic model and considering all four bases, signs of directional selection are stronger. In contrast to short introns, complementary bases show strand specificity and allele frequency spectra depend on mutation directions. Hence, the traditional biallelic model to describe the evolution of four‐fold degenerate sites should be replaced by more complex models assuming only quasi‐equilibrium and accounting for all four bases.     

FROM MORE TO FEWER? TESTING AN ALLEGEDLY PERVASIVE TREND IN THE EVOLUTION OF MORPHOLOGICAL STRUCTURE

While evolutionary trends have long received much attention and have been widely disputed, new methods are now allowing the testing of directional hypotheses with increased rigor. Here, we test a general hypothesis about the way many kinds of discrete characters are thought to evolve, termed oligomerization. This is the tendency for serial structures (such as arthropod body and appendage segments) or armature (such as spines) to evolve primarily through loss and fusion. Focusing on the Crustacea, we use maximum likelihood methods to test for directional evolution in a large sample (> 500) of discrete traits, analyzed against molecular-based phylogenies. We find evidence for a significant trend toward trait loss, in accordance with the reduction principle. However, this trend is far from ubiquitous, with many characters exhibiting a reconstructed bias toward gains. These results suggest that caution must be used before drawing conclusions about which taxa are "primitive" or about the directionality of morphological shifts in the absence of phylogenetic analysis. Nevertheless, oligomerization-as a trend rather than a law-may be an important process that influences evolutionary trajectories from both morphological and functional perspectives.     

Habitat structure and the dispersal of male and female bottlenose dolphins (Tursiops truncatus)

Bottlenose dolphins (Tursiops truncatus) are widely distributed and a high degree of morphometric and genetic differentiation has been found among both allopatric and parapatric populations. We analysed 145 samples along a contiguous distributional range from the Black Sea to the eastern North Atlantic for mitochondrial and nuclear genetic diversity, and found population structure with boundaries that coincided with transitions between habitat regions. These regions can be characterized by ocean floor topography, and oceanographic features such as surface salinity, productivity and temperature. At the extremes of this range there was evidence for the directional emigration of females. Bi-parentally inherited markers did not show this directional bias in migration, suggesting a different dispersal strategy for males and females at range margins. However, comparative assessment based on mitochondrial DNA and nuclear markers indicated that neither sex showed a strong bias for greater dispersal on average. These data imply a mechanism for the evolutionary structuring of populations based on local habitat dependence for both males and females.     

Effects of Surface Asymmetry on Neuronal Growth

Detailed knowledge of how the surface physical properties, such as mechanics, topography and texture influence axonal outgrowth and guidance is essential for understanding the processes that control neuron development, the formation of functional neuronal connections and nerve regeneration. Here we synthesize asymmetric surfaces with well-controlled topography and texture and perform a systematic experimental and theoretical investigation of axonal outgrowth on these substrates. We demonstrate unidirectional axonal bias imparted by the surface ratchet-based topography and quantify the topographical guidance cues that control neuronal growth. We describe the growth cone dynamics using a general stochastic model (Fokker-Planck formalism) and use this model to extract two key dynamical parameters: diffusion (cell motility) coefficient and asymmetric drift coefficient. The drift coefficient is identified with the torque caused by the asymmetric ratchet topography. We relate the observed directional bias in axonal outgrowth to cellular contact guidance behavior, which results in an increase in the cell-surface coupling with increased surface anisotropy. We also demonstrate that the disruption of cytoskeletal dynamics through application of Taxol (stabilizer of microtubules) and Blebbistatin (inhibitor of myosin II activity) greatly reduces the directional bias imparted by these asymmetric surfaces. These results provide new insight into the role played by topographical cues in neuronal growth and could lead to new methods for stimulating neuronal regeneration and the engineering of artificial neuronal tissue.     

Developmental biology: extending the limb and body with vectors and scalars

Outgrowth of the embryonic limb in vertebrates is driven by a proximodistal gradient of cell movement, with WNT and FGF activities controlling direction and velocity, respectively. A similar gradient, though without a directional bias, drives caudal body axis extension.     

A new genetic distance with application to constrained variation at microsatellite loci.

Genetic variation at microsatellite loci is supposed to be constrained within some range in allele size. In this case, the average-square distance (delta mu)2 between two diverged populations moves asymptotically around and underestimates the time since the populations had split. A distance based on the between-locus correlation in the mean repeat scores, DR, is introduced. Numerical simulations show that DR is a linear function of time if the constraints are approximated by a linear centripetal force, which might be due to mutation bias toward a definite range or be caused both by directional mutation bias toward larger allele size and by selection against the greater number of repeats.     

Adaptive threonine increase in transmembrane regions of mitochondrial proteins in higher primates

Background

The mitochondrial (mt) gene tree of placental mammals reveals a very strong acceleration of the amino acid (AA) replacement rate and a change in AA compositional bias in the lineage leading to the higher primates (simians), in contrast to the nuclear gene tree. Whether this acceleration and compositional bias were caused by adaptive evolution at the AA level or directional mutation pressure at the DNA level has been vigorously debated.

Methodology/Principal Findings

Our phylogenetic analysis indicates that the rate acceleration in the simian lineage is accompanied by a marked increase in threonine (Thr) residues in the transmembrane helix regions of mt DNA-encoded proteins. This Thr increase involved the replacement of hydrophobic AAs in the membrane interior. Even after accounting for lack of independence due to phylogeny, a regression analysis reveals a statistical significant positive correlation between Thr composition and longevity in primates.

Conclusion/Significance

Because crucial roles of Thr and Ser in membrane proteins have been proposed to be the formation of hydrogen bonds enhancing helix-helix interactions, the Thr increase detected in the higher primates might be adaptive by serving to reinforce stability of mt proteins in the inner membrane. The correlation between Thr composition in the membrane interior and the longevity of animals is striking, especially because some mt functions are thought to be involved in aging.     

Ants show a leftward turning bias when exploring unknown nest sites

Behavioural lateralization in invertebrates is an important field of study because it may provide insights into the early origins of lateralization seen in a diversity of organisms. Here, we present evidence for a leftward turning bias in Temnothorax albipennis ants exploring nest cavities and in branching mazes, where the bias is initially obscured by thigmotaxis (wall-following) behaviour. Forward travel with a consistent turning bias in either direction is an effective nest exploration method, and a simple decision-making heuristic to employ when faced with multiple directional choices. Replication of the same bias at the colony level would also reduce individual predation risk through aggregation effects, and may lead to a faster attainment of a quorum threshold for nest migration. We suggest the turning bias may be the result of an evolutionary interplay between vision, exploration and migration factors, promoted by the ants'' eusociality.