A Comprehensive Texture Segmentation Framework for Segmentation of Capillary Non-Perfusion Regions in Fundus Fluorescein Angiograms

Capillary non-perfusion (CNP) in the retina is a characteristic feature used in the management of a wide range of retinal diseases. There is no well-established computation tool for assessing the extent of CNP. We propose a novel texture segmentation framework to address this problem. This framework comprises three major steps: pre-processing, unsupervised total variation texture segmentation, and supervised segmentation. It employs a state-of-the-art multiphase total variation texture segmentation model which is enhanced by new kernel based region terms. The model can be applied to texture and intensity-based multiphase problems. A supervised segmentation step allows the framework to take expert knowledge into account, an AdaBoost classifier with weighted cost coefficient is chosen to tackle imbalanced data classification problems. To demonstrate its effectiveness, we applied this framework to 48 images from malarial retinopathy and 10 images from ischemic diabetic maculopathy. The performance of segmentation is satisfactory when compared to a reference standard of manual delineations: accuracy, sensitivity and specificity are 89.0%, 73.0%, and 90.8% respectively for the malarial retinopathy dataset and 80.8%, 70.6%, and 82.1% respectively for the diabetic maculopathy dataset. In terms of region-wise analysis, this method achieved an accuracy of 76.3% (45 out of 59 regions) for the malarial retinopathy dataset and 73.9% (17 out of 26 regions) for the diabetic maculopathy dataset. This comprehensive segmentation framework can quantify capillary non-perfusion in retinopathy from two distinct etiologies, and has the potential to be adopted for wider applications.     

Modeling non-homologous end joining

Non-homologous end joining (NHEJ) is an important DNA repair pathway for DNA double-strand breaks. Several proteins, including Ku, DNA-PKcs, Artemis, XRCC4/Ligase IV and XLF, are involved in the NHEJ for the DNA damage detection, DNA free end processing and ligation. The classical model of NHEJ is a sequential model in which DNA-PKcs is first recruited by the Ku bound DNA prior to any other repair proteins. Recent experimental study ( [McElhinny et al., 2000], [Costantini et al., 2007], [17] and [Yano and Chen, 2008]) suggested that the recruitment ordering is not crucial. In this work, by proposing a mathematical model in terms of biochemical reaction network and performing stability and related analysis, we demonstrate theoretically that if DSB repair pathway independent of DNA-PKcs exists, then the classical sequential model and new two-phase model are essentially indistinguishable in the sense that DSB can be repaired thoroughly in both models when the repair proteins are sufficient.     

The segmentation clock in mice: interaction between the Wnt and Notch signalling pathways

In the last few years, the efforts to elucidate the mechanisms underlying the segmentation clock in various vertebrate species have multiplied. Early evidence suggested that oscillations are caused by one of the genes under the Notch signalling pathway (like those of the her or Hes families). Recently, Aulehla et al. [Wnt3a plays a major role in the segmentation clock controlling somitogenesis. Dev. Cell 4, 395-406] discovered that Axin2 (a gene under the Wnt3a signalling pathway) also oscillates in the presomitic mesoderm (PSM) of mice embryos and proposed some mechanisms through which the Notch and Wnt3a pathways may interact. They further suggested that a decreasing concentration of Wnt3a along the PSM may be the gradient the segmentation clock interacts with to form somites. These results were reviewed by Rida et al. [A notch feeling of somite segmentation and beyond. Dev. Biol. 265, 2-22], who introduced a complex clockwork comprising genes Hes1, Lfng (under the Notch pathway), and Axin2, as well as their multiple interactions. In the present work we develop a mathematical model based on the Rida et al. review and use it to tackle some of the questions raided by the Aulehla et al. paper: can the Axin2 feedback loop constitute a clock? Could a decreasing Wnt3a signaling constitute the wavefront, where phase is recorded and the spatial pattern laid down? What is the master oscillator?     

The side-by-side model of two tRNA molecules allowing the alpha-helical conformation of the nascent polypeptide during the ribosomal transpeptidation.

Lim and Spirin [25] proposed a preferable conformation of the nascent peptide during the ribosomal transpeptidation. Spirin and Lim [26] excluded the possibilities of the side-by-side model proposed by Johnson et al [13] and the three-tRNA binding model (A, P and E sites) of Rheinberger and Nierhaus [3]. However, a slight conformational change at the 3' end regions of both A and P site tRNA molecules can enable the three different tRNA binding models to converge. With a modification of the angles of the ribose rings of both anticodon and mRNA this model can also be related to the model of Sundaralingam et al [19]. In this model of E coli rRNA the 3' end sequence ACCA76 or GCCA76 of P site tRNA is base-paired to UGGU810 of 23S rRNA, while the ACC75 or GCC75 of A site tRNA are base-paired to GGU1621 23S rRNA. The conformation of the A76 of A site tRNA is necessarily different from that of P site tRNA, at least during the course of the transpeptidation. The A76 of A site tRNA overlaps the binding region of puromycin. The C1400 of 16S rRNA in this model is located at a distance of 4 A from the 5' end of the anticodon of P site tRNA [14] and 17 A from the 5' end of the anticodon of A site tRNA [15]. It is also shown that a considerable but reasonable modification in the conformation of the anticodon loops could lead to accommodation of three deacylated tRNA(Phe) molecules at a time on 70S ribosome in the presence of poly(U) as observed experimentally [6]. A sterochemical explanation for the negatively-linked allosteric interactions between the A and E sites is also shown in the present model.     

Profilin-actin complexes directly elongate actin filaments at the barbed end.

We demonstrate that the profilin-G-actin complex can elongate actin filaments directly at the barbed end but cannot bind to the pointed end. During elongation, the profilin-actin complex binds to the barbed filament end, whereupon profilin is released, leaving the actin molecule behind. This was first proposed by Tilney [Tilney, L. G., et al. (1983) J. Cell Biol. 97, 112-124] and demonstrated by Pollard and Cooper [(1984) Biochemistry 23, 6631-6641] by electron microscopy. We show that a model without any outside energy supply, in contrast to the mechanism proposed by Pollard and Cooper, can be fitted to our and their [Kaiser et al. (1986) J. Cell Biol. 102, 221-226] findings. Input of outside energy is necessary only if profilin-mediated elongation continues after free G-actin has been lowered to or below the critical concentration observed at the barbed end in the absence of profilin.     

Predicting genotoxicity of aromatic and heteroaromatic amines using electrotopological state indices

A quantitative structure-activity relationship (QSAR) model relating electrotopological state (E-state) indices and mutagenic potency was previously described by Cash [Mutat. Res. 491 (2001) 31-37] using a data set of 95 aromatic amines published by Debnath et al. [Environ. Mol. Mutagen. 19 (1992) 37-52]. Mutagenic potency was expressed as the number of Salmonella typhimurium TA98 revertants per nmol (LogR). Earlier work on the development of QSARs for the prediction of genotoxicity indicated that numerous methods could be effectively employed to model the same aromatic amines data set, namely, Debnath et al.; Maran et al. [Quant. Struct.-Act. Relat. 18 (1999) 3-10]; Basak et al. [J. Chem. Inf. Comput. Sci. 41 (2001) 671-678]; Gramatica et al. [SAR QSAR Environ. Res. 14 (2003) 237-250]. However, results obtained from external validations of those models revealed that the effective predictivity of the QSARs was well below the potential indicated by internal validation statistics (Debnath et al., Gramatica et al.). The purpose of the current research is to externally validate the model published by Cash using a data set of 29 aromatic amines reported by Glende et al. [Mutat. Res. 498 (2001) 19-37; Mutat. Res. 515 (2002) 15-38] and to further explore the potential utility of using E-state sums for the prediction of mutagenic potency of aromatic amines.     

Blood lactate concentration increases as a continuous function in progressive exercise

The relationship between arterialized blood lactate concentration [( La-]) and O2 uptake (VO2) was examined during a total of 23 tests by eight subjects. Exercise was on a cycle ergometer with work rate incremented from loadless pedaling to exhaustion as a 50-W/min ramp function. Two different mathematical models were studied. One model employed a log-log transformation of [La-] and VO2 to yield [La-] threshold as proposed by Beaver et al. (J. Appl. Physiol. 59: 1936-1940, 1985). The other model was a continuous exponential plus constant of the form La- = a + b[exp(cVO2)]. In 21 of 23 data sets, the mean square error (MSE) of the continuous model was less than that of the log-log model (P less than 0.001). The MSE was on average 3.5 times greater in the log-log model than in the continuous model. The residuals were randomly distributed about the line of best fit for the continuous model. In contrast, the log-log model showed a nonrandom pattern indicating an inappropriate model. As an index of the position of the [La-]-VO2 continuous model, the VO2 at which the rate of increase of [La-] equaled the rate of increase of VO2 (d[La-]/dVO2 = 1) was determined. This VO2 was 2.241 +/- 0.081 l/min, which averaged 64.6% of maximal VO2. It is proposed that this lactate slope index could be used as a relative indicator of fitness instead of the previously applied threshold concept. The change in [La-] could be better described mathematically by a continuous model rather than the threshold model of Beaver et al.     

Relations Between Bacterial Biomass and Carbon Cycle in Marine Sediments: An Early Diagenetic Model

A new model for early diagenetic processes has been developed through a new formula explicitly accounting for microbial population dynamics. Following a mechanistic approach based on enzymatic reactions, a new model has been proposed for oxic mineralisation and denitrification. It incorporates the dynamics of bacterial metabolism. We find a general formula for inhibition processes of which some other mathematical expressions are particular cases. Moreover a fast numerical algorithm has been developed. It allows us to perform simulations of different diagenetic models in non-steady states. We use this algorithm to compare our model to a classical one (Soetaert et al., 1996). Dynamical evolutions of a perturbation of particulate organic carbon (POC) input are studied for both models. The results are very similar for stationary cases. But with variable inputs, the bacterial biomass dynamics brings about noticeable differences, and these are discussed.     

An NMR study of the helix V-loop E region of the 5S RNA from Escherichia coli

Experiments are described that complete the assignment of the imino proton NMR spectrum of the fragment 1 domain from the 5S RNA of Escherichia coli. Most of the new assignments fall in the helix V-loop E portion of the molecule (bases 70-78 and 98-106), the region most sensitive to the binding of ribosomal protein L25. The spectroscopic data are incompatible with the standard, phylogenetically derived model for 5S RNA, which makes all the base pairs possible in loop E with the sequences aligned in parallel (C70-G106, C71-G105, etc.) [see Delihas et al. (1984) Prog. Nucleic Acid Res. Mol. Biol. 31, 161-190]. Furthermore, the alternative loop E model proposed for spinach chloroplast 5S RNA by Romby et al. [(1988) Biochemistry 27, 4721-4730] does not apply to the closely homologous 5S RNA from E. coli. The 5S RNAs from E. coli and spinach chloroplasts do not have the same secondary structures in solution despite their strong sequence homologies, and neither appears to conform to the standard model for 5S RNA in the loop E region.     

Neuroinfections in developed versus developing countries

In recent supplement of neuroendocrinology letters, first time the authors from West and East, North and South of EU and the "Third World" present data on neuroinfections in high technology society - on nosocomial meningitis and vice versa in low technology and income countries of sub-Saharan Africa. 14 years survey of 171 cases of nosocomial paediatric meningitis is presented by Rudinsky et al. [1] and subpopulations of Acinetobacter baumannii and Pseudomonas aeruginosa [1,2] within last 20 years are briefly analyzed by Huttova et al. [2] and Ondrusova et al. [3]. All cases were complicating high technology procedures, such as neurosurgery, very low birth weight neonates after shunt implants etc. Current problems of management of nosocomial meningitis are reviewed by Bauer et al. [4] and consequence of inappropriate therapy by Huttova et al. [5]. Another high technology associated infection is septic embolisation followed by brain abscess and meningitis in patients with endocarditis after cardiac surgery (Kovac et al.) [6]. Experience from more than 600 cases is discussed in the article by Karvaj et al. [7] who outlines extremely high mortality in patients with endocarditis embolizing to central nervous system - up to 60%. The rest of papers are in contrary to problems of neuroinfections in EU and US focused on meningitis and cerebral malaria as commonest neuroinfections in the third world: 261 cases of cerebral malaria are discussed in a brief research note by Sudanese team of tropical programme in area of famine and civil war in southern Sudan (Bartkovjak and Ianetti et al.) [8]. Fungal neuroinfections complicating AIDS are of decreasing trend as reported by Njambi et al. from Kenya [9] and data from 497 cases from Uganda, Ethiopia and Burundi are presented by Benca et al. [10]. Finally an outbreak of meningococcal meningitis is reported by Benca et al. [11] from meningitis belt in Darfur and southern Sudan. We hope that the supplement may show difference in etiology, risk factors, therapy and outcome of neuroinfections (which is a burning public health and social problem in tropics) in other third world countries versus developed high-tech medical settings of US, EU and other high income countries, as presented by Benca et al. [12].     

Robust multipoint simultaneous identical-by-descent mapping for two linked loci

A challenging issue in genetic mapping of complex human diseases is localizing disease susceptibility genes when the genetic effects are small to moderate. There are greater complexities when multiple loci are linked to a chromosomal region. Liang et al. [Hum Hered 2001;51:64-78] proposed a robust multipoint method that can simultaneously estimate both the position of a trait locus and its effect on disease status by using affected sib pairs (ASPs). Based on the framework of generalized estimating equations (GEEs), the estimate and standard error of the position of a trait locus are robust to different genetic models. To utilize other relative pairs collected in pedigree data, Schaid et al. [Am J Hum Genet 2005;76:128-138] extended Liang's method to various types of affected relative pairs (ARPs) by two approaches: unconstrained and constrained methods. However, the above methods are limited to situations in which only one trait locus exists on the chromosome of interest. The mean functions are no longer correctly specified when there are multiple causative loci linked to a chromosomal region. To overcome this, Biernacka et al. [Genet Epidemiol 2005;28:33-47] considered the multipoint methods for ASPs to allow for two linked disease genes. We further generalize the approach to cover other types of ARPs. To reflect realistic situations for complex human diseases, we set modest sizes of genetic effects in our simulation. Our results suggest that several hundred independent pedigrees are needed, and markers with high information, to provide reliable estimates of trait locus positions and their confidence intervals. Bootstrap resampling can correct the downward bias of the robust variance for location estimates. These methods are applied to a prostate cancer linkage study on chromosome 20 and compared with the results for the one-locus model [Am J Hum Genet 2005;76:128-138]. We have implemented the multipoint IBD mapping for one and two linked loci in our software GEEARP, which allows analyses for five general types of ARPs.     

Spreading speeds as slowest wave speeds for cooperative systems

It is well known that in many scalar models for the spread of a fitter phenotype or species into the territory of a less fit one, the asymptotic spreading speed can be characterized as the lowest speed of a suitable family of traveling waves of the model. Despite a general belief that multi-species (vector) models have the same property, we are unaware of any proof to support this belief. The present work establishes this result for a class of multi-species model of a kind studied by Lui [Biological growth and spread modeled by systems of recursions. I: Mathematical theory, Math. Biosci. 93 (1989) 269] and generalized by the authors [Weinberger et al., Analysis of the linear conjecture for spread in cooperative models, J. Math. Biol. 45 (2002) 183; Lewis et al., Spreading speeds and the linear conjecture for two-species competition models, J. Math. Biol. 45 (2002) 219]. Lui showed the existence of a single spreading speed c(*) for all species. For the systems in the two aforementioned studies by the authors, which include related continuous-time models such as reaction-diffusion systems, as well as some standard competition models, it sometimes happens that different species spread at different rates, so that there are a slowest speed c(*) and a fastest speed c(f)(*). It is shown here that, for a large class of such multi-species systems, the slowest spreading speed c(*) is always characterized as the slowest speed of a class of traveling wave solutions.     

Novel biochemical pathways of endoglin in vascular cell physiology

The broad role of the transforming growth factor beta (TGFbeta) signaling pathway in vascular development, homeostasis, and repair is well appreciated. Endoglin is emerging as a novel, complex, and poorly understood regulatory component of the TGFbeta receptor complex, whose importance is underscored by its recognition as the site of mutations causing hereditary hemorrhagic telangiectasia (HHT) [McAllister et al., 1994]. Extensive analyses of endoglin function in normal developmental mouse models [Bourdeau et al., 1999; Li et al., 1999; Arthur et al., 2000] and in HHT animal models [Bourdeau et al., 2000; Torsney et al., 2003] exemplify the importance of understanding endoglin's biochemical functions. However, novel mechanisms underlying the regulation of these pathways continue to emerge. These mechanisms include modification of TGFbeta receptor signaling at the ligand and receptor activation level, direct effects of endoglin on cell adhesion and migration, and emerging roles for endoglin in the determination of stem cell fate and tissue patterning. The purpose of this review is to highlight the cellular and molecular studies that underscore the central role of endoglin in vascular development and disease.     

Experimental verification of the roles of intrinsic matrix viscoelasticity and tension-compression nonlinearity in the biphasic response of cartilage

A biphasic-CLE-QLV model proposed in our recent study [2001, J. Biomech. Eng., 123, pp. 410-417] extended the biphasic theory of Mow et al. [1980, J. Biomech. Eng., 102, pp. 73-84] to include both tension-compression nonlinearity and intrinsic viscoelasticity of the cartilage solid matrix by incorporating it with the conewise linear elasticity (CLE) model [1995, J. Elasticity, 37, pp. 1-38] and the quasi-linear viscoelasticity (QLV) model [Biomechanics: Its foundations and objectives, Prentice Hall, Englewood Cliffs, 1972]. This model demonstrates that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelastic effects, as well as tension-compression nonlinearity. The objective of this study is to directly test this biphasic-CLE-QLV model against experimental data from unconfined compression stress-relaxation tests at slow and fast strain rates as well as dynamic loading. Twelve full-thickness cartilage cylindrical plugs were harvested from six bovine glenohumeral joints and multiple confined and unconfined compression stress-relaxation tests were performed on each specimen. The material properties of specimens were determined by curve-fitting the experimental results from the confined and unconfined compression stress relaxation tests. The findings of this study demonstrate that the biphasic-CLE-QLV model is able to describe the strain-rate-dependent mechanical behaviors of articular cartilage in unconfined compression as attested by good agreements between experimental and theoretical curvefits (r2 = 0.966 +/- 0.032 for testing at slow strain rate; r2 = 0.998 +/- 0.002 for testing at fast strain rate) and predictions of the dynamic response (r2 = 0.91 +/- 0.06). This experimental study also provides supporting evidence for the hypothesis that both tension-compression nonlinearity and intrinsic viscoelasticity of the solid matrix of cartilage are necessary for modeling the transient and equilibrium responses of this tissue in tension and compression. Furthermore, the biphasic-CLE-QLV model can produce better predictions of the dynamic modulus of cartilage in unconfined dynamic compression than the biphasic-CLE and biphasic poroviscoelastic models, indicating that intrinsic viscoelasticity and tension-compression nonlinearity of articular cartilage may play important roles in the load-support mechanism of cartilage under physiologic loading.     

Temporal dynamics of bacterial aging and rejuvenation

Single-celled organisms dividing by binary fission were thought not to age [1-4]. A 2005 study by Stewart et al. [5] reversed the dogma by demonstrating that Escherichia coli were susceptible to aging. A follow-up study by Wang et al. [6] countered those results by demonstrating that E. coli cells trapped in microfluidic devices are able to sustain robust growth without aging. The present study reanalyzed these conflicting data by applying a population genetic model for aging in bacteria [7]. Our reanalysis showed that in E. coli, as predicted by the model, (1) aging and rejuvenation occurred simultaneously in a population; (2) lineages receiving sequentially the maternal old pole converged to a stable attractor state; (3) lineages receiving sequentially the maternal new pole converged to an equivalent but separate attractor state; (4) cells at the old pole attractor had a longer doubling time than ones at the new pole attractor; and (5) the robust growth state identified by Wang et al. corresponds to our predicted attractor for lineages harboring the maternal old pole. Thus, the previous data, rather than opposing each other, together provide strong evidence for bacterial aging.     

Comparative models for human apolipoprotein A-I bound to lipid in discoidal high-density lipoprotein particles

We have constructed a series of models for apolipoprotein A-I (apo A-I) bound to discoidal high-density lipoprotein (HDL) particles, based upon the molecular belt model [Segrest, J. P., et al. (1999) J. Biol. Chem. 274, 31755-31758] and helical hairpin models [Rogers, D. P., et al. (1998) Biochemistry 37, 11714-11725], and compared these with picket fence models [Phillips, J. C., et al. (1997) Biophys. J. 73, 2337-2346]. Molecular belt models for discoidal HDL particles with differing diameters are presented, illustrating that the belt model can explain the discrete changes in HDL particle size observed experimentally. Hairpin models are discussed for the binding of apo A-I to discoidal HDL particles with diameters identical to those for the molecular belt model. Two models are presented for the binding of three monomers of apo A-I to a 150 A diameter discoidal HDL particle. In one model, two monomers of apo A-I bind to the exterior of the HDL particle in an antiparallel belt, with a third monomer of apo A-I bound to the disk in a hairpin conformation. In the second model, all three monomers of apo A-I are bound to the discoidal HDL particle in a hairpin conformation. Previously published experimental data for each model are reviewed, with FRET favoring either the belt or hairpin models over the picket fence models for HDL particles with diameters of 105 A. Naturally occurring mutations appear to favor the belt model for the 105 A particles, while the 150 A HDL particles favor the presence of at least one hairpin.     

A Comparison of Continuous and Discrete-time West Nile Virus Models

The first recorded North American epidemic of West Nile virus was detected in New York state in 1999, and since then the virus has spread and become established in much of North America. Mathematical models for this vector-transmitted disease with cross-infection between mosquitoes and birds have recently been formulated with the aim of predicting disease dynamics and evaluating possible control methods. We consider discrete and continuous time versions of the West Nile virus models proposed by Wonham et al. [Proc. R. Soc. Lond. B 271:501–507, 2004] and by Thomas and Urena [Math. Comput. Modell. 34:771–781, 2001], and evaluate the basic reproduction number as the spectral radius of the next-generation matrix in each case. The assumptions on mosquito-feeding efficiency are crucial for the basic reproduction number calculation. Differing assumptions lead to the conclusion from one model [Wonham, M.J. et al., [Proc. R. Soc. Lond. B] 271:501–507, 2004] that a reduction in bird density would exacerbate the epidemic, while the other model [Thomas, D.M., Urena, B., Math. Comput. Modell. 34:771–781, 2001] predicts the opposite: a reduction in bird density would help control the epidemic.     

Reconstructing visual experiences from brain activity evoked by natural movies

Quantitative modeling of human brain activity can provide crucial insights about cortical representations [1, 2] and can form the basis for brain decoding devices [3-5]. Recent functional magnetic resonance imaging (fMRI) studies have modeled brain activity elicited by static visual patterns and have reconstructed these patterns from brain activity [6-8]. However, blood oxygen level-dependent (BOLD) signals measured via fMRI are very slow [9], so it has been difficult to model brain activity elicited by dynamic stimuli such as natural movies. Here we present a new motion-energy [10, 11] encoding model that largely overcomes this limitation. The model describes fast visual information and slow hemodynamics by separate components. We recorded BOLD signals in occipitotemporal visual cortex of human subjects who watched natural movies and fit the model separately to individual voxels. Visualization of the fit models reveals how early visual areas represent the information in movies. To demonstrate the power of our approach, we also constructed a Bayesian decoder [8] by combining estimated encoding models with a sampled natural movie prior. The decoder provides remarkable reconstructions of the viewed movies. These results demonstrate that dynamic brain activity measured under naturalistic conditions can be decoded using current fMRI technology.