Bifurcation in Markov Chains with Ecological Examples.

The adjacency matrix of a weighted directed graph contains information on both connectivity and the strength of that connection. When the special case of Markov chains are considered, the additional constraints permit the characterization of the eigenvalues of its transition matrix, and the change of the nature of those eigenvalues as the probabilities (weights) change. A change in the nature of the eigenvalues, bifurcations, signals a change in the dynamic approach to a limiting probability of a chain as well as other aspects that can be of interest in applications. In this paper, we first characterize eigenvalues of any weighted directed cycles and any 3-state Markov chain. Then we define and characterize a special case, zero trace chains, which is useful in an ecology application discussed.

The actin cytoskeletal network plays a role in yeast prion transmission and contributes to prion stability.

Chaperone networks are required for the shearing and generation of transmissible propagons from pre-existing prion aggregates. However, other cellular networks needed for maintaining yeast prions are largely uncharacterized. Here, we establish a novel role for actin networks in prion maintenance. The [PIN+ ] prion, also known as [RNQ+ ], exists as stable variants dependent upon the chaperone machinery for the transmission of propagons to daughter cells during cell division and cytoplasmic transfer. Loss of the Hsp104 molecular chaperone leads to the growth of prion particles until they are too large to be transmitted. Here, we isolated a unique [PIN+ ] variant, which is unstable in actin mutants. This prion loss is observed over many generations, and coincides with the detection of both high molecular weight species of Rnq1 and large visible aggregates that are asymmetrically retained during cell division. Our data suggest that the irregular actin networks found in these mutants may influence propagon number by slowly permitting aggregate growth over time, resulting in the generation of nontransmissible large aggregates. Thus, we show the potential contribution of cytoskeletal networks in the transmission of prion propagons, which parallels models that have been proposed for cell-to-cell transmission of small amyloids in neurodegenerative protein aggregation diseases.

A model of the cost of delaying treatment of Hashimotos thyroiditis: thyroid cancer initiation and growth.

Hashimoto's thyroiditis (HT) is an autoimmune disorder that drives the function of thyroid gland to the sequential clinical states:euthyroidism (normal condition), subclinical hypothyroidism (asymptomatic period) and overt hypothyroidism (symptomatic period). In this disease, serum thyroidstimulating hormone (TSH) levels increase monotonically, stimulating the thyroid follicular cells chronically and initiating benign (non-cancerous) thyroid nodules at various sites of the thyroid gland. This process can also encourage growth of papillary thyroid microcarcinoma. Due to prolonged TSH stimulation, thyroid nodules may grow and become clinically relevant without the administration of treatment by thyroid hormone replacement. Papillary thyroid cancer (80% of thyroid cancer) whose incidence is increasing worldwide, is associated with Hashimoto's thyroiditis. A stochastic model is developed here to produce the statistical distribution of thyroid nodule sizes and growth by taking serum TSH value as the continuous input to the model using TSH values from the output of the patientspecific deterministic model developed for the clinical progression of Hashimoto's thyroiditis.

Untangling thyroid autoimmunity through modeling and simulation.

Thyroid autoimmunity is characterized by a large number of identified factors, and determining the relative importance of genetics and environment, for instance, can be difficult. In addition, the definition and progression of the individual diseases can also be challenging, and questions such as "when to begin treatment" or even "should treatment be begun" can be problematic. One approach to handling situations in which there are many factors is utilizing mathematical modeling. In a model, quantities that are clinically measurable are related through equations, based on known and inferred relationships between the systems involved. In situations where these relationships are complicated, the resulting simulations can provide information not previous recognized as logically resulting from those relationships. One advantage of this approach is that patient-specific parameter estimates can be used to personalize disease monitoring and treatment. In this paper, models involving Hashimoto's (autoimmune) thyroiditis, Graves' disease, and the roles of leptin, vitamin D3, and adipose tissue are described. In the case of Hashimoto's, a model consisting of a system of differential equations is presented which allows a patient specific description of the progression of the disease. The conditions leading to Hashitoxicosis are also described through that model. The patient specific model of the treatment of Graves' disease is also described. Finally, the roles of the inflammatory adipokines, especially leptin, and vitamin D3 is explored as it relates to the initiation of thyroid autoimmunity. The result of this approach is an enhanced view of the initiation and progression of autoimmunity in the thyroid.

Thyroid Autoimmunity: An Interplay of Factors.

The literature on thyroid autoimmunity has identified many potential factors at play for the initiation and progression of autoimmune thyroid diseases. These factors include genetic susceptibility, environmental factors, some drugs, iodine and selenium, infection, molecular mimics, and immune system defects. The sheer number of feasible factors makes sorting out the necessary agents from the fellow travelers difficult. In addition, many of these factors have the capability to interact-further confusing the picture. Another difficulty in interpreting these data is that most proposed mechanisms are not able to accomplish the triggering event in which the tolerance to self-antigens is actually overcome. In addition, some findings may be describing the conditions present after a disease is diagnosed and may be consequences of the disease rather than a cause. Recent description of the role of adipokines, which include leptin, tumor necrosis factor-alpha, and interleukin-6, in contributing to the inflammatory environment of the thyroid, along with the presence of thyroid Toll-like receptors for pathogen-associated patterns have the potential to deliver that necessary adjuvant signal to break tolerance, seen as necessary in animal autoimmune models. An additional factor, vitamin D3, due to its interaction both with white adipose tissue (WAT) and the immune system, has a complicated and somewhat controversial story with respect to thyroid autoimmunity. Conflicting results can result when not all factors are considered together. AIMS: To describe the many factors at play in thyroid autoimmunity and how they interact. CONCLUSION: Thyroid autoimmunity is the result of an interplay of factors, with adipokines produced by WAT and vitamin D providing immune modulating signals external to the thyroid, while thyrocyte innate responses to environmental conditions provide the necessary adjuvant signal. Shaping the response to be reactive to particular self-antigens and likelihood of a response are due to genetics and molecular mimics.

A patient-specific treatment model for Graves' hyperthyroidism.

BACKGROUND: Graves' is disease an autoimmune disorder of the thyroid gland caused by circulating anti-thyroid receptor antibodies (TRAb) in the serum. TRAb mimics the action of thyroid stimulating hormone (TSH) and stimulates the thyroid hormone receptor (TSHR), which results in hyperthyroidism (overactive thyroid gland) and goiter. Methimazole (MMI) is used for hyperthyroidism treatment for patients with Graves' disease. METHODS: We have developed a model using a system of ordinary differential equations for hyperthyroidism treatment with MMI. The model has four state variables, namely concentration of MMI (in mg/L), concentration of free thyroxine - FT4 (in pg/mL), and concentration of TRAb (in U/mL) and the functional size of the thyroid gland (in mL) with thirteen parameters. With a treatment parameter, we simulate the time-course of patients' progression from hyperthyroidism to euthyroidism (normal condition). We validated the model predictions with data from four patients. RESULTS: When there is no MMI treatment, there is a unique asymptotically stable hyperthyroid state. After the initiation of MMI treatment, the hyperthyroid state moves towards subclinical hyperthyroidism and then euthyroidism. CONCLUSION: We can use the model to describe or test and predict patient treatment schedules. More specifically, we can fit the model to individual patients' data including loading and maintenance doses and describe the mechanism, hyperthyroidism→euthyroidism. The model can be used to predict when to discontinue the treatment based on FT4 levels within the physiological range, which in turn help maintain the remittance of euthyroidism and avoid relapses of hyperthyroidism. Basically, the model can guide with decision-making on oral intake of MMI based on FT4 levels.

Toxicity and infectivity: insights from de novo prion formation.

Prions are infectious misfolded proteins that assemble into oligomers and large aggregates, and are associated with neurodegeneration. It is believed that the oligomers contribute to cytotoxicity, although genetic and environmental factors have also been shown to have additional roles. The study of the yeast prion [PSI +] has provided valuable insights into how prions form and why they are toxic. Our recent work suggests that SDS-resistant oligomers arise and remodel early during the prion formation process, and lysates containing these newly formed oligomers are infectious. Previous work shows that toxicity is associated with prion formation and this toxicity is exacerbated by deletion of the VPS5 gene. Here, we show that newly made oligomer formation and infectivity of vps5∆ lysates are similar to wild-type strains. However using green fluorescent protein fusions, we observe that the assembly of fluorescent cytoplasmic aggregates during prion formation is different in vps5∆ strains. Instead of large immobile aggregates, vps5∆ strains have an additional population of small mobile foci. We speculate that changes in the cellular milieu in vps5∆ strains may reduce the cell's ability to efficiently recruit and sequester newly formed prion particles into central deposition sites, resulting in toxicity.

Cutaneous malignant melanoma incidences analyzed worldwide by sex, age, and skin type over personal Ultraviolet-B dose shows no role for sunburn but implies one for Vitamin D3.

Because the incidence of cutaneous malignant melanoma (CMM) was reported to increase with increasing terrestrial UVR (290-400 nm) doses in the US back in 1975 and a recent publication showed no association exists with UVR exposure at all, we set out to fully elucidate the role of UVR in CMM. To achieve this goal, we analyzed the CMM incidences over latitude and estimated the average personal UVR dose in the US and numerous countries (> 50) on 5 continents around the world. Using data from the International Agency for Research on Cancer in 2005, we performed worldwide analysis of CMM over UVR dose by sex, age group (0-14, 15-29, 30-49, 50-69, 70-85+) and Fitzpatrick skin types I-VI. Surprisingly, increasing UVR doses, which represent erythemally-weighted doses comprised primarily of UVB (290-315 nm) radiation, did not significantly correlate with increasing CMM incidence for people with any skin type anywhere in the world. Paradoxically, we found significant correlations between increasing CMM and decreasing UVB dose in Europeans with skin types I-IV. Both Europeans and Americans in some age groups have significant increasing CMM incidences with decreasing UVB dose, which shows UVB is not the main driver in CMM and suggests a possible role for lower cutaneous vitamin D3 levels and UVA (315-400 nm) radiation. CMM may be initiated or promoted by UVA radiation because people are exposed to it indoors through windows and outdoors through some sunscreen formulations. Thus, our findings may explain why some broad-spectrum sunscreen formulations do not protect against getting CMM.

De novo [PSI +] prion formation involves multiple pathways to form infectious oligomers.

Prion and other neurodegenerative diseases are associated with misfolded protein assemblies called amyloid. Research has begun to uncover common mechanisms underlying transmission of amyloids, yet how amyloids form in vivo is still unclear. Here, we take advantage of the yeast prion, [PSI +], to uncover the early steps of amyloid formation in vivo. [PSI +] is the prion form of the Sup35 protein. While [PSI +] formation is quite rare, the prion can be greatly induced by overexpression of the prion domain of the Sup35 protein. This de novo induction of [PSI +] shows the appearance of fluorescent cytoplasmic rings when the prion domain is fused with GFP. Our current work shows that de novo induction is more complex than previously thought. Using 4D live cell imaging, we observed that fluorescent structures are formed by four different pathways to yield [PSI +] cells. Biochemical analysis of de novo induced cultures indicates that newly formed SDS resistant oligomers change in size over time and lysates made from de novo induced cultures are able to convert [psi -] cells to [PSI +] cells. Taken together, our findings suggest that newly formed prion oligomers are infectious.

Deriving a provisional tolerable intake for intravenous exposure to silver nanoparticles released from medical devices.

Silver nanoparticles (AgNP) are incorporated into medical devices for their anti-microbial characteristics. The potential exposure and toxicity of AgNPs is unknown due to varying physicochemical particle properties and lack of toxicological data. The aim of this safety assessment is to derive a provisional tolerable intake (pTI) value for AgNPs released from blood-contacting medical devices. A literature review of in vivo studies investigating critical health effects induced from intravenous (i. v.) exposure to AgNPs was evaluated by the Annapolis Accords principles and Toxicological Data Reliability Assessment Tool (ToxRTool). The point of departure (POD) was based on an i. v. 28-day repeated AgNP (20 nm) dose toxicity study reporting an increase in relative spleen weight in rats with a 5% lower confidence bound of the benchmark dose (BMDL05) of 0.14 mg/kg bw/day. The POD was extrapolated to humans by a modifying factor of 1,000 to account for intraspecies variability, interspecies differences and lack of long-term toxicity data. The pTI for long-term i. v. exposure to 20 nm AgNPs released from blood-contacting medical devices was 0.14 µg/kg bw/day. This pTI may not be appropriate for nanoparticles of other physicochemical properties or routes of administration. The methodology is appropriate for deriving pTIs for nanoparticles in general.

Untangling the most probable role for vitamin D3 in autism.

Recent studies indicate an important role for vitamin D3 in autism spectrum disorder (ASD), although its mechanism is not completely understood. The most puzzling aspect of ASD is that identical twins, who share identical DNA, do not have 100% concordance rates (∼88% for identical and ∼31% for fraternal twins). These findings provide major clues into the etiology: ASD must involve an environmental factor present in the prenatal milieu that both identical twins are not always exposed to because they do not always share it (i.e., placentas). Combined with the exponential increasing rates of ASD around the world, these observations suggest a contagious disease is probably transferred to the fetus via the placenta becoming infected by a cervical virus. Vitamin D3 boosts immune responses clearing viral infections and increases serotonin and estrogen brain levels. Here we review the different roles and untangle the most probable one vitamin D3 plays in ASD.

Worldwide cutaneous malignant melanoma incidences analyzed by sex, age, and skin type over time (1955-2007): Is HPV infection of androgenic hair follicular melanocytes a risk factor for developing melanoma exclusively in people of European-ancestry?

The cutaneous malignant melanoma (CMM) incidence has been increasing in an exponential manner in certain populations around the world for over 7 decades. To help illuminate the etiology, we performed worldwide temporal (1955-2007) CMM incidence analysis by sex, age (0-14, 15-29, 30-49, 50-69, 70-85+), and skin type on 6 continents using data from the International Agency for Research on Cancer. We observe an exponential increase in the CMM incidence over time and an increase of about 2 orders of magnitude between age groups 0-14 and 15-29 exclusively in European-ancestry populations around the world independent of skin type (I-III or III-IV). Other populations like the Chinese (III-IV) had much lower CMM incidences that either remained stable or temporally decreased but did not display a dramatic increase between the youngest age groups. The dramatic increase in the incidence between the youngest age groups found only in European-ancestry populations suggests one of the most important risk factors for CMM may be developing androgenic hair, the occurrence of which appears to correlate with the distribution of CMM over male and female body sites. Besides that potential new risk factor, the increasing CMM incidence with increasing age, known not to be from cumulative UV doses, may be associated with age-related changes to skin, i.e., thinning epidermis causing lower vitamin D3 levels, and hair, i.e., whitening from higher reactive oxygen species. The temporal exponential increasing CMM incidence in European-ancestry populations may be due to Human Papilloma Virus infection of follicular hair melanocytes, found in CMM biopsies.

An ensemble model of QSAR tools for regulatory risk assessment.

Quantitative structure activity relationships (QSARs) are theoretical models that relate a quantitative measure of chemical structure to a physical property or a biological effect. QSAR predictions can be used for chemical risk assessment for protection of human and environmental health, which makes them interesting to regulators, especially in the absence of experimental data. For compatibility with regulatory use, QSAR models should be transparent, reproducible and optimized to minimize the number of false negatives. In silico QSAR tools are gaining wide acceptance as a faster alternative to otherwise time-consuming clinical and animal testing methods. However, different QSAR tools often make conflicting predictions for a given chemical and may also vary in their predictive performance across different chemical datasets. In a regulatory context, conflicting predictions raise interpretation, validation and adequacy concerns. To address these concerns, ensemble learning techniques in the machine learning paradigm can be used to integrate predictions from multiple tools. By leveraging various underlying QSAR algorithms and training datasets, the resulting consensus prediction should yield better overall predictive ability. We present a novel ensemble QSAR model using Bayesian classification. The model allows for varying a cut-off parameter that allows for a selection in the desirable trade-off between model sensitivity and specificity. The predictive performance of the ensemble model is compared with four in silico tools (Toxtree, Lazar, OECD Toolbox, and Danish QSAR) to predict carcinogenicity for a dataset of air toxins (332 chemicals) and a subset of the gold carcinogenic potency database (480 chemicals). Leave-one-out cross validation results show that the ensemble model achieves the best trade-off between sensitivity and specificity (accuracy: 83.8 % and 80.4 %, and balanced accuracy: 80.6 % and 80.8 %) and highest inter-rater agreement [kappa (κ): 0.63 and 0.62] for both the datasets. The ROC curves demonstrate the utility of the cut-off feature in the predictive ability of the ensemble model. This feature provides an additional control to the regulators in grading a chemical based on the severity of the toxic endpoint under study.

A Novel Scoring Based Distributed Protein Docking Application to Improve Enrichment.

Molecular docking is a computational technique which predicts the binding energy and the preferred binding mode of a ligand to a protein target. Virtual screening is a tool which uses docking to investigate large chemical libraries to identify ligands that bind favorably to a protein target. We have developed a novel scoring based distributed protein docking application to improve enrichment in virtual screening. The application addresses the issue of time and cost of screening in contrast to conventional systematic parallel virtual screening methods in two ways. Firstly, it automates the process of creating and launching multiple independent dockings on a high performance computing cluster. Secondly, it uses a Nȧi̇ve Bayes scoring function to calculate binding energy of un-docked ligands to identify and preferentially dock (Autodock predicted) better binders. The application was tested on four proteins using a library of 10,573 ligands. In all the experiments, (i). 200 of the 1,000 best binders are identified after docking only ~14 percent of the chemical library, (ii). 9 or 10 best-binders are identified after docking only ~19 percent of the chemical library, and (iii). no significant enrichment is observed after docking ~70 percent of the chemical library. The results show significant increase in enrichment of potential drug leads in early rounds of virtual screening.

Exponentially increasing incidences of cutaneous malignant melanoma in Europe correlate with low personal annual UV doses and suggests 2 major risk factors.

For several decades the incidence of cutaneous malignant melanoma (CMM) steadily increased in fair-skinned, indoor-working people around the world. Scientists think poor tanning ability resulting in sunburns initiate CMM, but they do not understand why the incidence continues to increase despite the increased use of sunscreens and formulations offering more protection. This paradox, along with lower incidences of CMM in outdoor workers, although they have significantly higher annual UV doses than indoor workers have, perplexes scientists. We found a temporal exponential increase in the CMM incidence indicating second-order reaction kinetics revealing the existence of 2 major risk factors. From epidemiology studies, we know one major risk factor for getting CMM is poor tanning ability and we now propose the other major risk factor may be the Human Papilloma Virus (HPV) because clinicians find ß HPVs in over half the biopsies. Moreover, we uncovered yet another paradox; the increasing CMM incidences significantly correlate with decreasing personal annual UV dose, a proxy for low vitamin D3 levels. We also discovered the incidence of CMM significantly increased with decreasing personal annual UV dose from 1960, when it was almost insignificant, to 2000. UV and other DNA-damaging agents can activate viruses, and UV-induced cytokines can hide HPV from immune surveillance, which may explain why CMM also occurs in anatomical locations where the sun does not shine. Thus, we propose the 2 major risk factors for getting CMM are intermittent UV exposures that result in low cutaneous levels of vitamin D3 and possibly viral infection.

Thyroid autoimmunity as a window to autoimmunity: An explanation for sex differences in the prevalence of thyroid autoimmunity.

Autoimmune thyroid diseases (AITDs), predominately Graves׳ disease and Hashimoto׳s thyroiditis, comprise the most common autoimmune diseases in humans. Both have the production of anti-thyroid antibody as an important aspect and both are much more prevalent in females, being at least 10 times more common than in males. Using these two clues, a hypothesis for the initiation of thyroid autoimmunity is proposed that helps to make the case that the thyroid is one of the most sensitive sites for autoimmunity and helps account for the prevalence and the observed sex differences in AITDs and associated diseases, such as type 1 diabetes and Latent Autoimmune Diabetes in Adults (LADA). The primary mechanisms proposed involve the underlying state of inflammation as a result of the adipokines, especially leptin, TNF-α, and IL-6, and the receptors able to recognize pathogen-associated molecular patterns (PAMP׳s) and damage-associated molecular patterns (DAMP׳s) through Toll-like receptors (TLR) and others receptors present on thyrocytes. The adipokines are produced by adipose tissue, but have hormone-like and immune modulating properties. As the levels of leptin are significantly higher in females, an explanation for the sex difference in thyroid autoimmunity emerges. The ability of the thyrocytes to participate in innate immunity through the TLR provides an adjuvant-like signal and allows for the action of other agents, such as environmental factors, viruses, bacteria, and even stress to provide the initiation step to break tolerance to thyroid self-antigens. Seeing the thyroid as one of the most sensitive sites for autoimmunity, means that for many autoimmune disorders, if autoimmunity is present, it is likely to also be present in the thyroid - and that that condition in the thyroid was probably earlier. The evidence is seen in multiple autoimmune syndrome.

Novel Uses of In Vitro Data to Develop Quantitative Biological Activity Relationship Models for in Vivo Carcinogenicity Prediction.

The availability of large in vitro datasets enables better insight into the mode of action of chemicals and better identification of potential mechanism(s) of toxicity. Several studies have shown that not all in vitro assays can contribute as equal predictors of in vivo carcinogenicity for development of hybrid Quantitative Structure Activity Relationship (QSAR) models. We propose two novel approaches for the use of mechanistically relevant in vitro assay data in the identification of relevant biological descriptors and development of Quantitative Biological Activity Relationship (QBAR) models for carcinogenicity prediction. We demonstrate that in vitro assay data can be used to develop QBAR models for in vivo carcinogenicity prediction via two case studies corroborated with firm scientific rationale. The case studies demonstrate the similarities between QBAR and QSAR modeling in: (i) the selection of relevant descriptors to be used in the machine learning algorithm, and (ii) the development of a computational model that maps chemical or biological descriptors to a toxic endpoint. The results of both the case studies show: (i) improved accuracy and sensitivity which is especially desirable under regulatory requirements, and (ii) overall adherence with the OECD/REACH guidelines. Such mechanism based models can be used along with QSAR models for prediction of mechanistically complex toxic endpoints.

Pharyngeal and cervical cancer incidences significantly correlate with personal UV doses among whites in the United States.

Because we found UV-exposed oral tissue cells have reduced DNA repair and apoptotic cell death compared with skin tissue cells, we asked if a correlation existed between personal UV dose and the incidences of oral and pharyngeal cancer in the United States. We analyzed the International Agency for Research on Cancer's incidence data for oral and pharyngeal cancers by race (white and black) and sex using each state's average annual personal UV dose. We refer to our data as 'white' rather than 'Caucasian,' which is a specific subgroup of whites, and 'black' rather than African-American because blacks from other countries around the world reside in the U.S. Most oropharyngeal carcinomas harboured human papilloma virus (HPV), so we included cervical cancer as a control for direct UV activation. We found significant correlations between increasing UV dose and pharyngeal cancer in white males (p=0.000808) and females (p=0.0031) but not in blacks. Shockingly, we also found cervical cancer in whites to significantly correlate with increasing UV dose (p=0.0154). Thus, because pharyngeal and cervical cancer correlate significantly with increasing personal UV dose in only the white population, both direct (DNA damage) and indirect (soluble factors) effects may increase the risk of HPV-associated cancer.

A patient-specific model of the negative-feedback control of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis.

The purpose of modelling the negative-feedback control mechanism of the hypothalamus-pituitary-thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis is to describe the clinical course of euthyroidism, subclinical hypothyroidism and overt hypothyroidism for patients. Thyroid hormone thyroxine (T4) and triiodothyronine (T3) levels are controlled by negative-feedback control through thyroid-stimulating hormone (TSH). T4, like other hormones, can be bound or unbound; the unbound T4 (FT4) is used as a marker for hypothyroidism. Autoimmune thyroiditis is a disease in which the thyroid-infiltrating lymphocytes attack autoantigens in follicle cells, destroying them over a long time. To describe the operation of the feedback control, we developed a mathematical model involving four clinical variables: TSH, FT4, anti-thyroid peroxidase antibodies and the thyroid gland's functional size. The first three variables are regularly measured while the last variable is determined through relationships between the other three variables. The problem of two different time scales for circulating hormones and thyroid damage is addressed using singular perturbation theory. Analysis of the mathematical model establishes stability and conditions under which the diseased state can maintain the slow movement toward diseased state equilibrium. Although we have used four variables in modelling the feedback control through the HPT axis, the predicted clinical course given any set of parameters is shown to depend on the steady-state levels of TSH and FT4. This observation makes possible the development of the clinical charts based only on the levels of TSH, time and potential steady-state values. To validate the model predictions, a dataset obtained from a Sicilian adult population has been employed.