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Bayesian network to predict breast cancer risk of mammographic microcalcifications and reduce number of benign biopsy results: initial experience.

PURPOSE: To retrospectively determine whether a Bayesian network (BN) computer model can accurately predict the probability of breast cancer on the basis of risk factors and mammographic appearance of microcalcifications, to improve the positive predictive value (PPV) of biopsy, with pathologic examination and follow-up as reference standards. MATERIALS AND METHODS: The institutional review board approved this HIPAA-compliant study; informed consent was not required. Results of 111 consecutive image-guided breast biopsies performed for microcalcifications deemed suspicious by radiologists were analyzed. Mammograms obtained before biopsy were analyzed in a blinded manner by a breast imager who recorded Breast Imaging Reporting and Data System (BI-RADS) descriptors and provided a probability of malignancy. The BN uses probabilistic relationships between breast disease and mammography findings to estimate the risk of malignancy. Probability estimates from the radiologist and the BN were used to create receiver operating characteristic (ROC) curves, and area under the ROC curve (A(z)) values were compared. PPV of biopsy was also evaluated on the basis of these probability estimates. RESULTS: The BN and the radiologist achieved A(z) values of 0.919 and 0.916, respectively, which were not significantly different. If the 34 patients estimated by the BN to have less than a 10% probability of malignancy had not undergone biopsy, the PPV of biopsy would have increased from 21.6% to 31.2% without missing a breast cancer (P < .001). At this level, the radiologist's probability estimation improved the PPV to 30.0% (P < .001). CONCLUSION: A probabilistic model that includes BI-RADS descriptors for microcalcifications can distinguish between benign and malignant abnormalities at mammography as well as a breast imaging specialist can and may be able to improve the PPV of image-guided breast biopsy.

Adult↗

On the use of the Price equation.

This paper distinguishes two categories of questions that the Price equation can help us answer. The two different types of questions require two different disciplines that are related, but nonetheless move in opposite directions. These disciplines are probability theory on the one hand and statistical inference on the other. In the literature on the Price equation this distinction is not made. As a result of this, questions that require a probability model are regularly approached with statistical tools. In this paper, we examine the possibilities of the Price equation for answering questions of either type. By spending extra attention on mathematical formalities, we avoid the two disciplines to get mixed up. After that, we look at some examples, both from kin selection and from group selection, that show how the inappropriate use of statistical terminology can put us on the wrong track. Statements that are 'derived' with the help of the Price equation are, therefore, in many cases not the answers they seem to be. Going through the derivations in reverse can, however, be helpful as a guide how to build proper (probabilistic) models that do give answers.

Animals↗

Efficient detection of unusual words.

Words that are, by some measure, over- or underrepresented in the context of larger sequences have been variously implicated in biological functions and mechanisms. In most approaches to such anomaly detections, the words (up to a certain length) are enumerated more or less exhaustively and are individually checked in terms of observed and expected frequencies, variances, and scores of discrepancy and significance thereof. Here we take the global approach of annotating the suffix tree of a sequence with some such values and scores, having in mind to use it as a collective detector of all unexpected behaviors, or perhaps just as a preliminary filter for words suspicious enough to undergo a more accurate scrutiny. We consider in depth the simple probabilistic model in which sequences are produced by a random source emitting symbols from a known alphabet independently and according to a given distribution. Our main result consists of showing that, within this model, full tree annotations can be carried out in a time-and-space optimal fashion for the mean, variance and some of the adopted measures of significance. This result is achieved by an ad hoc embedding in statistical expressions of the combinatorial structure of the periods of a string. Specifically, we show that the expected value and variance of all substrings in a given sequence of n symbols can be computed and stored in (optimal) O(n2) overall worst-case, O (n log n) expected time and space. The O (n2) time bound constitutes an improvement by a linear factor over direct methods. Moreover, we show that under several accepted measures of deviation from expected frequency, the candidates over- or underrepresented words are restricted to the O(n) words that end at internal nodes of a compact suffix tree, as opposed to the theta(n2) possible substrings. This surprising fact is a consequence of properties in the form that if a word that ends in the middle of an arc is, say, overrepresented, then its extension to the nearest node of the tree is even more so. Based on this, we design global detectors of favored and unfavored words for our probabilistic framework in overall linear time and space, discuss related software implementations and display the results of preliminary experiments.

Algorithms↗

A stochastic model of trunk muscle coactivation during trunk bending.

Biomechanical models of the spine have traditionally assumed that workplace lifting conditions (weight, posture, motion, etc.) precisely dictate the magnitude of individual muscle forces necessary to maintain a biomechanical balance within the trunk. However, because there are a large number of muscle groups within the trunk there is also an infinite number of possible combinations of muscle forces that can satisfy this biomechanical balance requirement for a given condition. Currently there are no methods available to predict this possible variability in muscle activity. Such variability in a multiple muscle system can result in variations in spinal loading. To quantitatively capture this trunk muscle variability during bending motions, such as those involved in lifting, a stochastic (probabilistic) model of trunk muscle activation was developed. The model was based on a simulation of experimentally derived data and predicted the possible combinations of time-dependent trunk muscle coactivations that could be expected given a set of trunk bending conditions. These simulated muscle activities were then used as input to an electromyographically assisted biomechanical model so that the magnitude and variability of the spine reaction forces could be estimated. This procedure allows one to assess the range of spinal loads that would be expected with a particular task. Significant variability in muscle activities was observed for each specific lifting condition and explained biomechanically. The results indicated that the variability in trunk muscle force had a small effect on spinal compression variability (+/- 7% of the mean compression), but greatly influenced both lateral (+/- 90% of mean) and anteroposterior shear forces (+/- 40% of mean). A validation study confirmed that the model predictions were reasonable estimates of muscle activity variability under previously untested conditions. This work could help explain how some repetitive lifting motions could increase the risk of acquiring a low back disorder and the simulation model could help drive electromyographically assisted models without the need for recording actual electromyographic activity.

Adult↗

CMfinder--a covariance model based RNA motif finding algorithm.

MOTIVATION: The recent discoveries of large numbers of non-coding RNAs and computational advances in genome-scale RNA search create a need for tools for automatic, high quality identification and characterization of conserved RNA motifs that can be readily used for database search. Previous tools fall short of this goal. RESULTS: CMfinder is a new tool to predict RNA motifs in unaligned sequences. It is an expectation maximization algorithm using covariance models for motif description, featuring novel integration of multiple techniques for effective search of motif space, and a Bayesian framework that blends mutual information-based and folding energy-based approaches to predict structure in a principled way. Extensive tests show that our method works well on datasets with either low or high sequence similarity, is robust to inclusion of lengthy extraneous flanking sequence and/or completely unrelated sequences, and is reasonably fast and scalable. In testing on 19 known ncRNA families, including some difficult cases with poor sequence conservation and large indels, our method demonstrates excellent average per-base-pair accuracy--79% compared with at most 60% for alternative methods. More importantly, the resulting probabilistic model can be directly used for homology search, allowing iterative refinement of structural models based on additional homologs. We have used this approach to obtain highly accurate covariance models of known RNA motifs based on small numbers of related sequences, which identified homologs in deeply-diverged species.

Algorithms↗

Model of complications of NIDDM. I. Model construction and assumptions.

OBJECTIVE: To develop a model of NIDDM for analyzing prevention strategies for NIDDM. RESEARCH DESIGN AND METHODS: A Markov type model with Monte Carlo techniques was used. Age, sex, and ethnicity of cohort was based on U.S. data. Incidence rates of complications were also based on community and population studies. RESULTS: Nonproliferative retinopathy, proliferative retinopathy, and macular edema are predicted in 79, 19, and 52%, respectively, of people with NIDDM; 19% are predicted to develop legal blindness. Microalbuminuria, gross proteinuria, and end-stage renal disease related to diabetes are predicted in 53, 40, and 17%, respectively. Symptomatic sensorimotor neuropathy and lower-extremity amputation are predicted in 31 and 17%, respectively. Cardiovascular disease is predicted in 39%. Higher rates of complications (1.1-3.0x) are predicted in minority populations. Predicted average life expectancy is 17 years after diagnosis. CONCLUSIONS: A probabilistic model of NIDDM predicts the vascular complications of NIDDM in a cohort representative of the incident cases of diabetes in the U.S. before age 75 years. Predictions of complications and mortality are consistent with the known epidemiology of NIDDM. The model is suitable for evaluating the effect of preventive interventions on the natural history of NIDDM.

Adult↗

Modelling sequential protein folding under kinetic control.

MOTIVATION: This study presents a novel investigation of the effect of kinetic control on cotranslational protein folding. We demonstrate the effect using simple HP lattice models and show that the cotranslational folding of proteins under kinetic control has a significant impact on the final conformation. Differences arise if nature is not capable of pushing a partially folded protein back over a large energy barrier. For this reason we argue that such constraints should be incorporated into structure prediction techniques. We introduce a finite surmountable energy barrier which allows partially formed chains to partly unfold, and permits us to enumerate exhaustively all energy pathways. RESULTS: We compare the ground states obtained sequentially with the global ground states of designing sequences (those with a unique global ground state). We find that the sequential ground states become less numerous and more compact as the surmountable energy barrier increases. We also introduce a probabilistic model to describe the distribution of final folds and allow partial settling to the Boltzmann distribution of states at each stage. As a result, conformations with the highest probability of final occurrence are not necessarily the ones of lowest energy. AVAILABILITY: Software available on request.

Amino Acid Sequence↗

Independence of evolutionary and mutational rates after transmission of avian influenza viruses to swine.

In 1979, an H1N1 avian influenza virus crossed the species barrier, establishing a new lineage in European swine. Because there is no direct or serologic evidence of previous H1N1 strains in these pigs, these isolates provide a model for studying early evolution of influenza viruses. The evolutionary rates of both the coding and noncoding changes of the H1N1 swine strains are higher than those of human and classic swine influenza A viruses. In addition, early H1N1 swine isolates show a marked plaque heterogeneity that consistently appears after a few passages. The presence of a mutator mutation was postulated (C. Scholtissek, S. Ludwig, and W. M. Fitch, Arch. Virol. 131:237-250, 1993) to account for these observations and the successful establishment of an avian H1N1 strain in swine. To address this question, we calculated the mutation rates of A/Mallard/New York/6750/78 (H2N2) and A/Swine/Germany/2/81 (H1N1) by using the frequency of amantadine-resistant mutants. To account for the inherent variability of estimated mutation rates, we used a probabilistic model for the statistical analysis. The resulting estimated mutation rates of the two strains were not significantly different. Therefore, an increased mutation rate due to the presence of a mutator mutation is unlikely to have led to the successful introduction of avian H1N1 viruses in European swine.

Animals↗

Gene prediction in eukaryotes with a generalized hidden Markov model that uses hints from external sources.

BACKGROUND: In order to improve gene prediction, extrinsic evidence on the gene structure can be collected from various sources of information such as genome-genome comparisons and EST and protein alignments. However, such evidence is often incomplete and usually uncertain. The extrinsic evidence is usually not sufficient to recover the complete gene structure of all genes completely and the available evidence is often unreliable. Therefore extrinsic evidence is most valuable when it is balanced with sequence-intrinsic evidence. RESULTS: We present a fairly general method for integration of external information. Our method is based on the evaluation of hints to potentially protein-coding regions by means of a Generalized Hidden Markov Model (GHMM) that takes both intrinsic and extrinsic information into account. We used this method to extend the ab initio gene prediction program AUGUSTUS to a versatile tool that we call AUGUSTUS+. In this study, we focus on hints derived from matches to an EST or protein database, but our approach can be used to include arbitrary user-defined hints. Our method is only moderately effected by the length of a database match. Further, it exploits the information that can be derived from the absence of such matches. As a special case, AUGUSTUS+ can predict genes under user-defined constraints, e.g. if the positions of certain exons are known. With hints from EST and protein databases, our new approach was able to predict 89% of the exons in human chromosome 22 correctly. CONCLUSION: Sensitive probabilistic modeling of extrinsic evidence such as sequence database matches can increase gene prediction accuracy. When a match of a sequence interval to an EST or protein sequence is used it should be treated as compound information rather than as information about individual positions.

Algorithms↗

A sequence alignment-independent method for protein classification.

Annotation of the rapidly accumulating body of sequence data relies heavily on the detection of remote homologues and functional motifs in protein families. The most popular methods rely on sequence alignment. These include programs that use a scoring matrix to compare the probability of a potential alignment with random chance and programs that use curated multiple alignments to train profile hidden Markov models (HMMs). Related approaches depend on bootstrapping multiple alignments from a single sequence. However, alignment-based programs have limitations. They make the assumption that contiguity is conserved between homologous segments, which may not be true in genetic recombination or horizontal transfer. Alignments also become ambiguous when sequence similarity drops below 40%. This has kindled interest in classification methods that do not rely on alignment. An approach to classification without alignment based on the distribution of contiguous sequences of four amino acids (4-grams) was developed. Interest in 4-grams stemmed from the observation that almost all theoretically possible 4-grams (20(4)) occur in natural sequences and the majority of 4-grams are uniformly distributed. This implies that the probability of finding identical 4-grams by random chance in unrelated sequences is low. A Bayesian probabilistic model was developed to test this hypothesis. For each protein family in Pfam-A and PIR-PSD, a feature vector called a probe was constructed from the set of 4-grams that best characterised the family. In rigorous jackknife tests, unknown sequences from Pfam-A and PIR-PSD were compared with the probes for each family. A classification result was deemed a true positive if the probe match with the highest probability was in first place in a rank-ordered list. This was achieved in 70% of cases. Analysis of false positives suggested that the precision might approach 85% if selected families were clustered into subsets. Case studies indicated that the 4-grams in common between an unknown and the best matching probe correlated with functional motifs from PRINTS. The results showed that remote homologues and functional motifs could be identified from an analysis of 4-gram patterns.

Algorithms↗

A free energy principle for the brain.

By formulating Helmholtz's ideas about perception, in terms of modern-day theories, one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts: using constructs from statistical physics, the problems of inferring the causes of sensory input and learning the causal structure of their generation can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory input is caused. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of cortical organisation and responses. In this paper, we show these perceptual processes are just one aspect of emergent behaviours of systems that conform to a free energy principle. The free energy considered here measures the difference between the probability distribution of environmental quantities that act on the system and an arbitrary distribution encoded by its configuration. The system can minimise free energy by changing its configuration to affect the way it samples the environment or change the distribution it encodes. These changes correspond to action and perception respectively and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment assumes that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at the models entailed by the brain and how minimisation of its free energy can explain its dynamics and structure.

Afferent Pathways↗

[The use of the probability model for an estimation of a infection rate of White Sea mussels (MYtilus edulis) by Metacercariae Himasthla elongata (Trematoda: Echinostomidae) ].

A comparison of simple probability analytic model of infection rate depending on host's age with natural infection rate of mussels (Bivalvia: Mythilidae) with metacercariae Himasthla elongata (Trematoda: Echinostomidae) was carried out. Data on the natural rate of infection were accumulated during 3 years; 1152 individuals M. edulis were collected in two horizons within fucoid zone of the Kruglaya inlet and the Chupa inlet of the Kandalaksha bay (White Sea). A size of shell and number of H. elongata metacercariae were defined for each mussel using compressive dissection technique. The infection of mussels per year within our model is considers as independent evens: Pn = 1 - (1 - p)n, where n is the age of mussels, Pn is the theoretical part of infected n-year mussels, p is the probability of infection within one year. The probability of infection within year is assumed equal for every age of host. The estimate of probability of infection per year on the basis of sample of n-year's mussels was calculated as Pn = 1 - n square root of 1 - I(n), where n is the age of mussels, I(n) is the part of infected n-year mussels. The retransformed weighted average value of aresine-transformed p'n was used as p in our model (p = 0.3476). Statistically significant differences between empirical and theoretical (calculated from our models on the basis this value) infection rates were not found (P > > 0.05 chi 2-test). Moreover, statistical significant differences were absent (P > 0.05 Fisher exact test) in pairwise comparisons between empirical and theoretical infection rates for each age of mussels. The model does not take into consideration an effect of such factors as host's resistance, host's migration and increase of mortality in infected hosts. The absence of significant differences between the empirical and theoretical infection rates allows to suggest, that mentioned factors under the conditions of the Kruglaya inlet do not influence essentially onto infection of mussels with metacercariae H. elongata. This conclusions is in certain inconsistency with essential differences in such characteristic as an individual resistance of mussels to the infection with metacercariae H. elongata, detected in experiments in vitro (Gorbushin, Levakin, unpublished data). Analysis of intensity of the invasion of metacercariae H. elongata into mussels allows to suggest the existence of differential death rate of the hosts, which is exhibited in individuals over 7 years old. Studied example of mussels infected with metacercariae H. elongata under conditions of the Kruglaya inlet shows that the simple probabilistic model of the natural infection rate is usable for this kind of investigation. Our study also allows to conclude that in this case the infection rate of hosts is mainly determined by stochastic reasons. However, in some cases the probability of infection rate may not depend on the age and size of the host. The study of infection rate can not be used for analyses of individual differences of hosts in a resistance to parasites and an infection ability of the parasite.

Age Factors↗

Automated seeded lesion segmentation on digital mammograms.

Segmenting lesions is a vital step in many computerized mass-detection schemes for digital (or digitized) mammograms. We have developed two novel lesion segmentation techniques-one based on a single feature called the radial gradient index (RGI) and one based on simple probabilistic models to segment mass lesions, or other similar nodular structures, from surrounding background. In both methods a series of image partitions is created using gray-level information as well as prior knowledge of the shape of typical mass lesions. With the former method the partition that maximizes the RGI is selected. In the latter method, probability distributions for gray-levels inside and outside the partitions are estimated, and subsequently used to determine the probability that the image occurred for each given partition. The partition that maximizes this probability is selected as the final lesion partition (contour). We tested these methods against a conventional region growing algorithm using a database of biopsy-proven, malignant lesions and found that the new lesion segmentation algorithms more closely match radiologists' outlines of these lesions. At an overlap threshold of 0.30, gray level region growing correctly delineates 62% of the lesions in our database while the RGI and probabilistic segmentation algorithms correctly segment 92% and 96% of the lesions, respectively.

Algorithms↗

An approach to forecasting health expenditures, with application to the U.S. Medicare system.

OBJECTIVE: To quantify uncertainty in forecasts of health expenditures. STUDY DESIGN: Stochastic time series models are estimated for historical variations in fertility, mortality, and health spending per capita in the United States, and used to generate stochastic simulations of the growth of Medicare expenditures. Individual health spending is modeled to depend on the number of years until death. DATA SOURCES/STUDY SETTING: A simple accounting model is developed for forecasting health expenditures, using the U.S. Medicare system as an example. PRINCIPAL FINDINGS: Medicare expenditures are projected to rise from 2.2 percent of GDP (gross domestic product) to about 8 percent of GDP by 2075. This increase is due in equal measure to increasing health spending per beneficiary and to population aging. The traditional projection method constructs high, medium, and low scenarios to assess uncertainty, an approach that has many problems. Using stochastic forecasting, we find a 95 percent probability that Medicare spending in 2075 will fall between 4 percent and 18 percent of GDP, indicating a wide band of uncertainty. Although there is substantial uncertainty about future mortality decline, it contributed little to uncertainty about future Medicare spending, since lower mortality both raises the number of elderly, tending to raise spending, and is associated with improved health of the elderly, tending to reduce spending. Uncertainty about fertility, by contrast, leads to great uncertainty about the future size of the labor force, and therefore adds importantly to uncertainty about the health-share of GDP. In the shorter term, the major source of uncertainty is health spending per capita. CONCLUSIONS: History is a valuable guide for quantifying our uncertainty about future health expenditures. The probabilistic model we present has several advantages over the high-low scenario approach to forecasting. It indicates great uncertainty about future Medicare expenditures relative to GDP.

Accounting↗

Connexin diversity and gap junction regulation by pHi.

The molecular mechanisms controlling pH-sensitivity of gap junctions formed of two different connexins are yet to be determined. We used a proton-sensitive fluorophore and electrophysiological techniques to correlate changes in intracellular pH (pHi) with electrical coupling between connexin-expressing Xenopus oocytes. The pH sensitivities of alpha 3 (connexin46), alpha 2 (connexin38), and alpha 1 (connexin43) were studied when these proteins were expressed as: 1) nonjunctional hemichannels (for alpha 3 and alpha 2), 2) homotypic gap junctions, and 3) heterotypic gap junctions. We found that alpha 3 hemichannels are sensitive to changes in pHi within a physiological range (pKa = 7.13 +/- 0.03; Hill coefficient = 3.25 +/- 1.73; n = 8; mean +/- SEM); an even more alkaline pKa was obtained for alpha 2 hemichannels (pKa = 7.50 +/- 0.03; Hill coefficient = 3.22 +/- 0.66; n = 13). The pH sensitivity curves of alpha 2 and alpha 3 homotypic junctions were indistinguishable from those recorded from hemichannels of the same connexin. Based on a comparison of pKa values, both alpha 3 and alpha 2 gap junctions were more pHi-dependent than alpha 1. The pH sensitivity of alpha 2-containing heterotypic junctions could not be predicted from the behavior of the two connexons in the pair. When alpha 2 was paired with alpha 3, the pH sensitivity curve was similar to that obtained from alpha 2 homotypic pairs. Yet, pairing alpha 2 with alpha 1 shifted the curve similar to homotypic alpha 1 channels. Pairing alpha 2 with a less pH sensitive mutant of alpha 1 (M257) yielded the same curve as when alpha 1 was used. However, the pH sensitivity curve of alpha 3/alpha 1 channels was similar to alpha 3/alpha 3, while alpha 3/M257 was indistinguishable from alpha 3/alpha 1. Our results could not be consistently predicted by a probabilistic model of two independent gates in series. The data show that dissimilarities in the pH regulation of gap junctions are due to differences in the primary sequence of connexins. Moreover, we found that pH regulation is an intrinsic property of the hemichannels, but pH sensitivity is modified by the interactions between connexons. These interactions should provide a higher level of functional diversity to gap junctions that are formed by more than one connexin.

Animals↗

ProbID: a probabilistic algorithm to identify peptides through sequence database searching using tandem mass spectral data.

With the recent quick expansion of DNA and protein sequence databases, intensive efforts are underway to interpret the linear genetic information of DNA in terms of function, structure, and control of biological processes. The systematic identification and quantification of expressed proteins has proven particularly powerful in this regard. Large-scale protein identification is usually achieved by automated liquid chromatography-tandem mass spectrometry of complex peptide mixtures and sequence database searching of the resulting spectra [Aebersold and Goodlett, Chem. Rev. 2001, 101, 269-295]. As generating large numbers of sequence-specific mass spectra (collision-induced dissociation/CID) spectra has become a routine operation, research has shifted from the generation of sequence database search results to their validation. Here we describe in detail a novel probabilistic model and score function that ranks the quality of the match between tandem mass spectral data and a peptide sequence in a database. We document the performance of the algorithm on a reference data set and in comparison with another sequence database search tool. The software is publicly available for use and evaluation at http://www.systemsbiology.org/research/software/proteomics/ProbID.

Algorithms↗

C-fiber (Remak) bundles contain both isolectin B4-binding and calcitonin gene-related peptide-positive axons.

Unmyelinated nerve fibers (Remak bundles) in the rodent sciatic nerve typically contain multiple axons. This study asked whether C-fiber bundles contain axons arising from more than one type of neuron. Most small neurons of the lumbar dorsal root ganglion (DRG) are either glial cell line-derived neurotrophic factor dependent or nerve growth factor dependent, binding either isolectin B4 (IB4) or antibodies to calcitonin gene-related peptide (CGRP), respectively. Injection of IB4-conjugated horseradish peroxidase into a lumbar DRG resulted in intense labeling of IB4 axons, with very low background. Visualized by confocal fluorescence, IB4-binding and CGRP-positive nerve fibers originating from different DRG neurons came together and remained closely parallel over long distances, suggesting that these two types of axon occupy the same Remak bundle. With double-labeling immunogold electron microscopy (EM), we confirmed that IB4 and CGRP axons were distinct and were found together in single Remak bundles. Previous studies indicate that some DRG neurons express both CGRP and IB4 binding. To ensure that our immunogold results were not a consequence of coexpression, we studied large populations of unmyelinated axons by using quantitative single-label EM. Tetramethylbenzidine, a chromogen with strong intrinsic signal amplification of IB4-horseradish peroxidase, labeled as many as 52% of unmyelinated axons in the dorsal root. Concomitantly, 97% of the Remak bundles with more than one axon contained at least one IB4-labeled axon. Probabilistic modeling using binomial distribution functions rejected the hypothesis that IB4 axons segregate into IB4-specific bundles (P < 0.00001). We conclude that most Remak bundle Schwann cells simultaneously support diverse axon types with different growth factor dependences.

Animals↗

Sequence-dependent bending propensity of DNA as revealed by DNase I: parameters for trinucleotides.

Structural parameters characterizing the bending propensity of trinucleotides were deduced from DNase I digestion data using simple probabilistic models. In contrast to dinucleotide-based models of DNA bending and/or bendability, the trinucleotide parameters are in good agreement with X-ray crystallographic data on bent DNA. This improvement may be due to the fact that the trinucleotide model incorporates more sequence context information than do dinucleotide-based descriptions.

Base Sequence↗