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.     

Stochasticity and functionality of neural systems: mathematical modelling of axon growth in the spinal cord of tadpole

In this paper we study a simple mathematical model of axon growth in the spinal cord of tadpole. Axon development is described by a system of three difference equations (the dorso-ventral and longitudinal coordinates of the growth cone and the growth angle) with stochastic components. We find optimal parameter values by fitting the model to experimentally measured characteristics of the axon and using the quadratic cost function. The fitted model generates axons for different neuron types in both ascending and descending directions which are similar to the experimentally measured axons. Studying the model of axon growth we have found the analytical solution for dynamics of the variance of the dorso-ventral coordinate and the variance of the growth angle. Formulas provide conditions for the case when the increase of the variance is limited and the analytical expression for the saturation level. It is remarkable that optimal parameters always satisfy the condition of limited variance increase. Taking into account experimental data on distribution of neuronal cell bodies along the spinal cord and dorso-ventral distribution of dendrites we generate a biologically realistic architecture of the whole tadpole spinal cord. Preliminary study of the electrophysiological properties of the model with Morris-Lecar neurons shows that the model can generate electrical activity corresponding to the experimentally observed swimming pattern activity of the tadpole in a broad range of parameter values.     

Spread of information through a population with socio-structural bias: I. Assumption of transitivity

A previously derived iteration formula for a random net was applied to some data on the spread of information through a population. It was found that if the axon density (the only free parameter in the formula) is determined by the first pair of experimental values, the predicted spread is much more rapid than the observed one. If the successive values of the “apparent axon density” are calculated from the successive experimental values, it is noticed that this quantity at first suffers a sharp drop from an initial high value to its lowest value and then gradually “recovers”. An attempt is made to account for this behavior of the apparent axon density in terms of the “assumption of transitivity”, based on a certain socio-structural bias, namely, that the likely contacts of two individuals who themselves have been in contact are expected to be strongly overlapping. The assumption of transitivity leads to a drop in the apparent axon density from an arbitrary initial value to the vicinity of unity (if the actual axon density is not too small). However, the “recovery” is not accounted for, and thus the predicted spread turns out to beslower than the observed.     

Contribution to the theory of random and biased nets

The probabilistic theory of random and biased nets is further developed by the “tracing” method treated previously. A number of biases expected to be operating in nets, particularly in sociograms, is described. Distribution of closed chain lengths is derived for random nets and for nets with a simple “reflexive” bias. The “island model” bias is treated for the case of two islands and a single axon tracing, resulting in a pair of linear difference equations with two indices. The reflexive bias is extended to multiple-axon tracing by an approximate method resulting in a modification of the random net recursion formula. Results previously obtained are compared with empirical findings and attempts are made to account for observed discrepancies.     

Rheumatic fever susceptibility in four ascertainments: regressive segregation on a geometric ascertainment pattern

On resolving the ascertainment biases of the observed data in the geometric continuum vaffected-1 x P(sibship), where 0 less than v----infinity, four published ascertainments of rheumatic fever show excellent conformation with Mendelian recessive segregation, even in multiplex sibships. In two surveys in which ascertainment bias is near or a little above random sampling (v = 1), this conclusion is further corroborated by classical segregation analysis. The other two surveys have bias trends declining (v less than 1) very much below random sampling. Such levels of ascertainment bias, if defined through the ascertainment probability parameter pi, would be out of range because the range is from single ascertainment, where pi----0 to random sampling where pi = 1 and probability cannot exceed unity. Highly successful antimicrobial measures that would reduce the number of diseased sibs independent of the distribution of susceptible sibs could produce a dissociation of the gene-to-"rheumatic" relationship and thus explains the declining ascertainment bias.     

Multi-modality of pI distribution in whole proteome

Multi-modality of pI distribution is a common feature in different whole proteomes. Some researchers considered it relate to the proteins with different subcellular locations, indicating the result of natural selection. We explored the pI distribution of predicted proteomes (including animals, plants, bacterium, archaeans) and random proteome [random protein sequences constructed according to the special amino acid composition and molecular weight (MW) distribution of human predicted proteome]. Our results suggest that the multi-modality is the result of discrete pK(R) values for different amino acids. Amino acid composition and MW distribution of a proteome also contributes to the specific pI distribution. Although protein subcellular location was related to pI value, our analyses revealed that comparing with the random proteome, neither the multi-modality phenomenon nor the distribution bias of pI values is caused by subcellular location. It seems that the multi-modality distribution is just a mathematical fun. The blank region near the neutral pI was caused by the absence of amino acids with neutral pK(R), and suggests that the selection of amino acids with ionizable side chain might be restricted by the requirement for a special pH environment during the origin of life. From this point of view, the special distribution was the result of natural selection.     

A stochastic model for adhesion-mediated cell random motility and haptotaxis

The active migration of blood and tissue cells is important in a number of physiological processes including inflammation, wound healing, embryogenesis, and tumor cell metastasis. These cells move by transmitting cytoplasmic force through membrane receptors which are bound specifically to adhesion ligands in the surrounding substratum. Recently, much research has focused on the influence of the composition of extracellular matrix and the distribution of its components on the speed and direction of cell migration. It is commonly believed that the magnitude of the adhesion influences cell speed and/or random turning behavior, whereas a gradient of adhesion may bias the net direction of the cell movement, a phenomenon known as haptotaxis. The mechanisms underlying these responses are presently not understood.A stochastic model is presented to provide a mechanistic understanding of how the magnitude and distribution of adhesion ligands in the substratum influence cell movement. The receptor-mediated cell migration is modeled as an interrelation of random processes on distinct time scales. Adhesion receptors undergo rapid binding and transport, resulting in a stochastic spatial distribution of bound receptors fluctuating about some mean distribution. This results in a fluctuating spatio-temporal pattern of forces on the cell, which in turn affects the speed and turning behavior on a longer time scale. The model equations are a system of nonlinear stochastic differential equations (SDE's) which govern the time evolution of the spatial distribution of bound and free receptors, and the orientation and position of the cell. These SDE's are integrated numerically to simulate the behavior of the model cell on both a uniform substratum, and on a gradient of adhesion ligand concentration.Furthermore, analysis of the governing SDE system and corresponding Fokker-Planck equation (FPE) yields analytical expressions for indices which characterize cell movement on multiple time scales in terms of cell cytomechanical, morphological, and receptor binding and transport parameters. For a uniform adhesion ligand concentration, this analysis provides expressions for traditional cell movement indices such as mean speed, directional persistence time, and random motility coefficient. In a small gradient of adhesion, a perturbation analysis of the FPE yields a constitutive cell flux expression which includes a drift term for haptotactic directional cell migration. The haptotactic drift contains terms identified as contributions from directional orientation bias (taxis).     

Action potentials of isolated single muscle fibers recorded by potential-sensitive dyes

Light transmission changes upon massive stimulation of single muscle fibers of Xenopus were studied with the potential-sensitive nonpermeant dyes, merocyanine rhodanine (WW375) and merocyanine oxazolone (NK2367). Upon stimulation an absorption change (wave a) occurred, which probably represents the sum of action potentials in the transverse tubules and surface membrane. In WW375-stained fibers wave a is a decrease in transmission over the range of 630 to 730 nm (with NK2367, over the range of 590 to 700 nm) but becomes an increase outside this range, thus showing a triphasic spectral pattern. This spectrum differs from that of the squid axon, in which depolarization produces only an increase in transmission over the whole range of wavelengths (Ross et al. 1977. J. Membr. Biol. 33:141-183). When wave a was measured at the edge of the fiber to obtain more signal from the surface membrane, the spectrum did not seem to differ markedly from that obtained from the entire width of the fiber. Thus, the difference in the spectrum between the squid axon and the vertebrate muscle cannot be attributed to the presence of the tubular system.     

Quantifying allosteric effects in proteins

In allosteric regulation, protein activity is altered when ligand binding causes changes in the protein conformational distribution. Little is known about which aspects of protein design lead to effective allosteric regulation, however. To increase understanding of the relation between protein structure and allosteric effects, we have developed theoretical tools to quantify the influence of protein-ligand interactions on probability distributions of reaction rates and protein conformations. We define the rate divergence, Dk, and the allosteric potential, Dx, as the Kullback-Leibler divergence between either the reaction-rate distributions or protein conformational distributions with and without the ligand bound. We then define Dx as the change in the conformational distribution of the combined protein/ligand system, derive Dx in the harmonic approximation, and identify contributions from 3 separate terms: the first term, D[stackxomega], results from changes in the eigenvalue spectrum; the second term, D[stackxDeltax], results from changes in the mean conformation; and the third term, Dxv, corresponds to changes in the eigenvectors. Using normal modes analysis, we have calculated these terms for a natural interaction between lysozyme and the ligand tri-N-acetyl-D-glucosamine, and compared them with calculations for a large number of simulated random interactions. The comparison shows that interactions in the known binding-site are associated with large values of Dxv. The results motivate using allosteric potential calculations to predict functional binding sites on proteins, and suggest the possibility that, in Nature, effective ligand interactions occur at intrinsic control points at which binding induces a relatively large change in the protein conformational distribution.     

Simulation study on effects of channel noise on differential conduction at an axon branch.

Effects of membrane channel noise (random opening and closing of ion channels) are studied on spike conduction at a branching point on an axon. Computer simulation is done on the basis of a stochastic version of the Hodgkin-Huxley cable model, into which the channel noise is incorporated. It is shown that the channel noise makes conduction of spikes into daughter branches random; spikes randomly succeed or fail in conduction into daughter branches. The conduction is then randomly differential even though the forms and properties of daughter branches are the same. The randomness is considerable when the radius of an axon is small (approximately 1 microns).     

Respiratory and heart rate patterns in infants destined to be victims of sudden infant death syndrome: average rates and their variability measured over 24 hours.

From a prospective study in which 24 hour recordings of the electrocardiogram and respiratory activity (abdominal wall movement) were made on a population of full term infants, 22 recordings were obtained from 16 infants who later were victims of the sudden infant death syndrome. The average heart rate, average heart rate variability, average breath to breath interval, and average breath to breath interval variability over the whole of each recording for the 22 recordings were compared with those from a control group of 324 infants selected at random from the rest of the population. No significance was found in the number of recordings from those infants who suffered the sudden infant death syndrome which lay outside the 5th-95th percentile range of the control group for the four variables studied. In a group comparison no difference was found between the sudden infant death syndrome group and the controls either in terms of the respiratory variables studied or in terms of the average heart rate variability. The results did, however, suggest that there may be a group difference in terms of the average instantaneous heart rate.     

A new method for RAPD primers selection based on primer bias in nucleotide sequence data

Sequence analysis has proved that decamer nucleotides, used as primers of RAPD (random amplified polymorphic DNA), differ with each other greatly in number of annealing sites in the Arabidopsis thaliana genome. It is called the 'primer bias' by the authors. The biased primers produce a highly variable number of amplicons by polymerase chain reaction (PCR). The number of amplicons is proved to correlate with the number of annealing sites. Therefore, a statistical method is proposed for selecting efficient primers based on the primer bias in the genomic sequence. The method was tested by experiment in A. thaliana genome, and the results demonstrate that the method outperforms routine methods and can substantially increase the efficiency of RAPD methodologies. We also proved that the expressed sequence tags (ESTs) show a highly coincident bias pattern with that of the whole genomic sequence, and can therefore be used to assess efficiencies of primers for species whose genomic sequence data are currently unknown.     

Stochastic constancy,variability and adaptation of spike generation: Performance of a giant neuron in the visual system of the fly

The stochastic structure of the spike activity generated by a movement processing wide-field element in the visual system of the fly has been studied over the whole performance area of the neuron. The structure of this discharge is described in terms of an Adaptive Integrate-to-Threshold model for a wide variety of spatio-temporal stimuli as well as steady-state stimuli. In order to reproduce the experimental results it is shown that the source of randomness in the model (e.g. the threshold) behaves like a random variable which is distributed according to a two-state Markov renewal process. In the case of stationary discharges generated by moving sinewave patterns the shape of the interspike interval distribution (which, in the Integrate-to-Threshold model, reflects the shape of the threshold distribution) changes continuously from a two-state distribution at low firing rates to a one-state distribution at high firing rates. In dynamic conditions of the discharge, generated by temporal dynamic stimuli, the experimental results show that the shape of the (demodulated) interval distribution of the discharge is determined by the highest instantaneous firing rate with an adaptation time constant of a few seconds. The physioligical origin of this intriguing behaviour remains — up till now — out of the picture.     

Territorial dynamics and stable home range formation for central place foragers

Uncovering the mechanisms behind territory formation is a fundamental problem in behavioural ecology. The broad nature of the underlying conspecific avoidance processes are well documented across a wide range of taxa. Scent marking in particular is common to a large range of terrestrial mammals and is known to be fundamental for communication. However, despite its importance, exact quantification of the time-scales over which scent cues and messages persist remains elusive. Recent work by the present authors has begun to shed light on this problem by modelling animals as random walkers with scent-mediated interaction processes. Territories emerge as dynamic objects that continually change shape and slowly move without settling to a fixed location. As a consequence, the utilisation distribution of such an animal results in a slowly increasing home range, as shown for urban foxes (Vulpes vulpes). For certain other species, however, home ranges reach a stable state. The present work shows that stable home ranges arise when, in addition to scent-mediated conspecific avoidance, each animal moves as a central place forager. That is, the animal's movement has a random aspect but is also biased towards a fixed location, such as a den or nest site. Dynamic territories emerge but the probability distribution of the territory border locations reaches a steady state, causing stable home ranges to emerge from the territorial dynamics. Approximate analytic expressions for the animal's probability density function are derived. A programme is given for using these expressions to quantify both the strength of the animal's movement bias towards the central place and the time-scale over which scent messages persist. Comparisons are made with previous theoretical work modelling central place foragers with conspecific avoidance. Some insights into the mechanisms behind allometric scaling laws of animal space use are also given.     

Statistical analysis of binary data generated from multilocus dominant DNA markers

The use of methodologies such as RAPD and AFLP for studying genetic variation in natural populations is widespread in the ecology community. Because data generated using these methods exhibit dominance, their statistical treatment is less straightforward. Several estimators have been proposed for estimating population genetic parameters, assuming simple random sampling and the Hardy-Weinberg (HW) law. The merits of these estimators remain unclear because no comparative studies of their theoretical properties have been carried out. Furthermore, ascertainment bias has not been explicitly modelled. Here, we present a comparison of a set of candidate estimators of null allele frequency (q), locus-specific heterozygosity (h) and average heterozygosity () in terms of their bias, standard error, and root mean square error (RMSE). For estimating q and h, we show that none of the estimators considered has the least RMSE over the parameter space. Our proposed zero-correction procedure, however, generally leads to estimators with improved RMSE. Assuming a beta model for the distribution of null homozygote proportions, we show how correction for ascertainment bias can be carried out using a linear transform of the sample average of h and the truncated beta-binomial likelihood. Simulation results indicate that the maximum likelihood and empirical Bayes estimator of have negligible bias and similar RMSE. Ascertainment bias in estimators of is most pronounced when the beta distribution is J-shaped and negligible when the latter is inverse J-shaped. The validity of the current findings depends importantly on the HW assumption-a point that we illustrate using data from two published studies.     

A zero‐augmented generalized gamma regression calibration to adjust for covariate measurement error: A case of an episodically consumed dietary intake

Measurement error in exposure variables is a serious impediment in epidemiological studies that relate exposures to health outcomes. In nutritional studies, interest could be in the association between long‐term dietary intake and disease occurrence. Long‐term intake is usually assessed with food frequency questionnaire (FFQ), which is prone to recall bias. Measurement error in FFQ‐reported intakes leads to bias in parameter estimate that quantifies the association. To adjust for bias in the association, a calibration study is required to obtain unbiased intake measurements using a short‐term instrument such as 24‐hour recall (24HR). The 24HR intakes are used as response in regression calibration to adjust for bias in the association. For foods not consumed daily, 24HR‐reported intakes are usually characterized by excess zeroes, right skewness, and heteroscedasticity posing serious challenge in regression calibration modeling. We proposed a zero‐augmented calibration model to adjust for measurement error in reported intake, while handling excess zeroes, skewness, and heteroscedasticity simultaneously without transforming 24HR intake values. We compared the proposed calibration method with the standard method and with methods that ignore measurement error by estimating long‐term intake with 24HR and FFQ‐reported intakes. The comparison was done in real and simulated datasets. With the 24HR, the mean increase in mercury level per ounce fish intake was about 0.4; with the FFQ intake, the increase was about 1.2. With both calibration methods, the mean increase was about 2.0. Similar trend was observed in the simulation study. In conclusion, the proposed calibration method performs at least as good as the standard method.     

A coupled model of fast axonal transport of organelles and slow axonal transport of tau protein

We have developed a model that accounts for the effect of a non-uniform distribution of tau protein along the axon length on fast axonal transport of intracellular organelles. The tau distribution is simulated by using a slow axonal transport model; the numerically predicted tau distributions along the axon length were validated by comparing them with experimentally measured tau distributions reported in the literature. We then developed a fast axonal transport model for organelles that accounts for the reduction of kinesin attachment rate to microtubules by tau. We investigated organelle transport for two situations: (1) a uniform tau distribution and (2) a non-uniform tau distribution predicted by the slow axonal transport model. We found that non-uniform tau distributions observed in healthy axons (an increase in tau concentration towards the axon tip) result in a significant enhancement of organelle transport towards the synapse compared with the uniform tau distribution with the same average amount of tau. This suggests that tau may play the role of being an enhancer of organelle transport.     

A bayesian random-effects markov model for tumor progression in women with a family history of breast cancer

SUMMARY: It makes intuitive sense to model the natural history of breast cancer, tumor progression from preclinical screen-detectable phase (PCDP) to clinical disease, as a multistate process, but the multilevel structure of the available data, which generally comes from cluster (family)-based service screening programs, makes the required parameter estimation intractable because there is a correlation between screening rounds in the same individual, and between subjects within clusters (families). There is also residual heterogeneity after adjusting for covariates. We therefore proposed a Bayesian hierarchical multistate Markov model with fixed and random effects and applied it to data from a high-risk group (women with a family history of breast cancer) participating in a family-based screening program for breast cancer. A total of 4867 women attended (representing 4464 families) and by the end of 2002, a total of 130 breast cancer cases were identified. Parameter estimation was carried out using Markov chain Monte Carlo (MCMC) simulation and the Bayesian software package WinBUGS. Models with and without random effects were considered. Our preferred model included a random-effect term for the transition rate from preclinical to clinical disease (sigma(2)(2f)), which was estimated to be 0.50 (95% credible interval = 0.22-1.49). Failure to account for this random effect was shown to lead to bias. The incorporation of covariates into multistate models with random effect not only reduced residual heterogeneity but also improved the convergence of stationary distribution. Our proposed Bayesian hierarchical multistate model is a valuable tool for estimating the rate of transitions between disease states in the natural history of breast cancer (and possibly other conditions). Unlike existing models, it can cope with the correlation structure of multilevel screening data, covariates, and residual (unexplained) variation.     

Effect of mycoplasma contamination of a human cervical carcinoma cell line M HeLa clone 11 on karyotypic variability

The karyotypic variability has been investigated for an immortalized human epithelioid cervix carcinoma cell line M HeLa clone 11, cultivated for 15-60 days after contamination with Acholeplasma laidlawii A, strain PG-8, and for 30 days after contamination with Mycoplasma arginini R-16. The character of cell distribution for chromosome number changes in contaminated cells significantly, as compared to the control. So, the frequency of cells with the modal number of chromosomes being equal to 50 decreases significantly, and the range of variability in the number of chromosomes increases. With the prolongation of the term of cultivation in control variants up to 60 days the character of cell distribution for chromosomal number changes, as compared to the preceding terms (15 and 30 days), which is expressed in the extended range of variability in the chromosomal number at the expense of decreased frequency of cells with submodal number of chromosomes equal to 49. But the degree of these changes is significantly smaller than in contaminated variants. The frequency of polyploid cells did not differ in all investigated variants. The number of chromosomal aberrations in cultures contaminated with A. laidlawii (for 15-60 days) and M. arginini (for 30 days) does not differ from that in the corresponding controls. The absence of dicentrics (telomeric association) at a long-term contamination of the human epithelioid cervix carcinoma cell line M HeLa clone 11 having marker chromosomes in karyotype and a comparison of these results with the earlier obtained data on other "marker" and "markerless" cell lines seems to confirm the point of view that dicentrics appear a characteristic feature of karyotypic variability of "markerless" cell lines, mainly with a long-term contamination in different conditions.     

Spectral analysis of inert gas elimination data: resolution limits

A new method of analyzing inert gas data for recovery of the pulmonary ventilation-perfusion ration (VA/Q) distribution is proposed. It is shown that the conventional inert gas elimination equation takes the form of a convolution integral, and the relationship between VA/Q distribution and inert gas elimination resembles that of a noncausal low-pass filter with infinite zero-frequency gain. With the use of this formulation, characteristic features of VA/Q distribution may be represented in the frequency domain in terms of the corresponding energy spectrum. It is shown that the lack of resolution associated with finite data samples and measurement error is caused by distortions in the high-frequency contents of the resulting VA/Q distribution. With six inert gases, the technique cannot resolve a log SD less than 0.21 decade and a modal separation less than 0.87 decade. In the presence of measurement error, the degree of resolution is even less. It is suggested that for maximum resolution the number of discrete and duplicate data samples should be chosen so that the resulting noise and sampling cutoff frequencies are approximately equal.