The structure of the asteroid 4 Vesta as revealed by models of planet-scale collisions

Asteroid 4Vesta seems to be a major intact protoplanet, with a surface composition similar to that of the HED (howardite-eucrite-diogenite) meteorites. The southern hemisphere is dominated by a giant impact scar, but previous impact models have failed to reproduce the observed topography. The recent discovery that Vesta's southern hemisphere is dominated by two overlapping basins provides an opportunity to model Vesta's topography more accurately. Here we report three-dimensional simulations of Vesta's global evolution under two overlapping planet-scale collisions. We closely reproduce its observed shape, and provide maps of impact excavation and ejecta deposition. Spiral patterns observed in the younger basin Rheasilvia, about one billion years old, are attributed to Coriolis forces during crater collapse. Surface materials exposed in the north come from a depth of about 20kilometres, according to our models, whereas materials exposed inside the southern double-excavation come from depths of about 60-100kilometres. If Vesta began as a layered, completely differentiated protoplanet, then our model predicts large areas of pure diogenites and olivine-rich rocks. These are not seen, possibly implying that the outer 100kilometres or so of Vesta is composed mainly of a basaltic crust (eucrites) with ultramafic intrusions (diogenites).

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator.

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Genetic and hormonal factors modulate spreading depression and transient hemiparesis in mouse models of familial hemiplegic migraine type 1.

Familial hemiplegic migraine type 1 (FHM1) is an autosomal dominant subtype of migraine with aura that is associated with hemiparesis. As with other types of migraine, it affects women more frequently than men. FHM1 is caused by mutations in the CACNA1A gene, which encodes the alpha1A subunit of Cav2.1 channels; the R192Q mutation in CACNA1A causes a mild form of FHM1, whereas the S218L mutation causes a severe, often lethal phenotype. Spreading depression (SD), a slowly propagating neuronal and glial cell depolarization that leads to depression of neuronal activity, is the most likely cause of migraine aura. Here, we have shown that transgenic mice expressing R192Q or S218L FHM1 mutations have increased SD frequency and propagation speed; enhanced corticostriatal propagation; and, similar to the human FHM1 phenotype, more severe and prolonged post-SD neurological deficits. The susceptibility to SD and neurological deficits is affected by allele dosage and is higher in S218L than R192Q mutants. Further, female S218L and R192Q mutant mice were more susceptible to SD and neurological deficits than males. This sex difference was abrogated by ovariectomy and senescence and was partially restored by estrogen replacement, implicating ovarian hormones in the observed sex differences in humans with FHM1. These findings demonstrate that genetic and hormonal factors modulate susceptibility to SD and neurological deficits in FHM1 mutant mice, providing a potential mechanism for the phenotypic diversity of human migraine and aura.

Family models of independence/interdependence and their intergenerational similarity in Germany, Turkey, and India

Family change theory suggests three ideal-typical family models characterized by different combinations of emotional and material interdependencies in the family. Its major proposition is that in economically developing countries with a collectivistic background a family model of emotional interdependence emerges from a family model of complete interdependence. The current study aims to identify and compare patterns of family-related value orientations related to family change theory across three cultures and two generations. Overall, N = 919 dyads of mothers and their adolescent children from Germany, Turkey, and India participated in the study. Three clusters were identified representing the family models of independence, interdependence, and emotional interdependence, respectively. Especially the identification of an emotionally interdependent value pattern using a person-oriented approach is an important step in the empirical validation of family change theory. The preference for the three family models differed across as well as within cultures and generations according to theoretical predictions. Dyadic analyses pointed to substantial intergenerational similarities and also to differences in family models, reflecting both cultural continuity as well as change in family-related value orientations.

Values of children and family models of adolescents: An eleven-culture study

Starting from Kagitcibasi's (2007) conceptualization of family models, this study compared N = 2961 adolescents' values across eleven cultures and explored whether patterns of values were related to the three proposed family models through cluster analyses. Three clusters with value profiles corresponding to the family models of interdependence, emotional interdependence, and independence were identified on the cultural as well as on the individual level. Furthermore, individual-level clusters corresponded to culture-level clusters in terms of individual cluster membership. The results largely support Kagitcibasi's proposition of changing family models and demonstrate their representation as individual-level value profiles across cultures.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

THE MECHANISM OF TUMORIGENESIS IN THE IMMORTALIZED HUMAN PANCREATIC CELL LINES: CELL CULTURE MODELS OF HUMAN PANCREATIC CANCER

The mechanism of tumorigenesis in the immortalized human pancreatic cell lines: cell culture models of human pancreatic cancer Pancreatic ductal adenocarcinoma (PDAC) is the most lethal cancer in the world. The most common genetic lesions identified in PDAC include activation of K-ras (90%) and Her2 (70%), loss of p16 (95%) and p14 (40%), inactivation p53 (50-75%) and Smad4 (55%). However, the role of these signature gene alterations in PDAC is still not well understood, especially, how these genetic lesions individually or in combination contribute mechanistically to human pancreatic oncogenesis is still elusive. Moreover, a cell culture transformation model with sequential accumulation of signature genetic alterations in human pancreatic ductal cells that resembles the multiple-step human pancreatic carcinogenesis is still not established. In the present study, through the stepwise introduction of the signature genetic alterations in PDAC into the HPV16-E6E7 immortalized human pancreatic duct epithelial (HPDE) cell line and the hTERT immortalized human pancreatic ductal HPNE cell line, we developed the novel experimental cell culture transformation models with the most frequent gene alterations in PDAC and further dissected the molecular mechanism of transformation. We demonstrated that the combination of activation of K-ras and Her2, inactivation of p16/p14 and Smad4, or K-ras mutation plus p16 inactivation, was sufficient for the tumorigenic transformation of HPDE or HPNE cells respectively. We found that these transformed cells exhibited enhanced cell proliferation, anchorage-independent growth in soft agar, and grew tumors with PDAC histopathological features in orthotopic mouse model. Molecular analysis showed that the activation of K-ras and Her2 downstream effector pathways –MAPK, RalA, FAK, together with upregulation of cyclins and c-myc were involved in the malignant transformation. We discovered that MDM2, BMP7 and Bmi-1 were overexpressed in the tumorigenic HPDE cells, and that Smad4 played important roles in regulation of BMP7 and Bmi-1 gene expression and the tumorigenic transformation of HPDE cells. IPA signaling pathway analysis of microarray data revealed that abnormal signaling pathways are involved in transformation. This study is the first complete transformation model of human pancreatic ductal cells with the most common gene alterations in PDAC. Altogether, these novel transformation models more closely recapitulate the human pancreatic carcinogenesis from the cell origin, gene lesion, and activation of specific signaling pathway and histopathological features.

Representation via Probabilities: Models of Probabilistic Modeling

How do probabilistic models represent their targets and how do they allow us to learn about them? The answer to this question depends on a number of details, in particular on the meaning of the probabilities involved. To classify the options, a minimalist conception of representation (Su\'arez 2004) is adopted: Modelers devise substitutes (``sources'') of their targets and investigate them to infer something about the target. Probabilistic models allow us to infer probabilities about the target from probabilities about the source. This leads to a framework in which we can systematically distinguish between different models of probabilistic modeling. I develop a fully Bayesian view of probabilistic modeling, but I argue that, as an alternative, Bayesian degrees of belief about the target may be derived from ontic probabilities about the source. Remarkably, some accounts of ontic probabilities can avoid problems if they are supposed to apply to sources only.

Models of DNA sequence evolution

Models of DNA sequence evolution and methods for estimating evolutionary distances are needed for studying the rate and pattern of molecular evolution and for inferring the evolutionary relationships of organisms or genes. In this dissertation, several new models and methods are developed.^ The rate variation among nucleotide sites: To obtain unbiased estimates of evolutionary distances, the rate heterogeneity among nucleotide sites of a gene should be considered. Commonly, it is assumed that the substitution rate varies among sites according to a gamma distribution (gamma model) or, more generally, an invariant+gamma model which includes some invariable sites. A maximum likelihood (ML) approach was developed for estimating the shape parameter of the gamma distribution $(\alpha)$ and/or the proportion of invariable sites $(\theta).$ Computer simulation showed that (1) under the gamma model, $\alpha$ can be well estimated from 3 or 4 sequences if the sequence length is long; and (2) the distance estimate is unbiased and robust against violations of the assumptions of the invariant+gamma model.^ However, this ML method requires a huge amount of computational time and is useful only for less than 6 sequences. Therefore, I developed a fast method for estimating $\alpha,$ which is easy to implement and requires no knowledge of tree. A computer program was developed for estimating $\alpha$ and evolutionary distances, which can handle the number of sequences as large as 30.^ Evolutionary distances under the stationary, time-reversible (SR) model: The SR model is a general model of nucleotide substitution, which assumes (i) stationary nucleotide frequencies and (ii) time-reversibility. It can be extended to SRV model which allows rate variation among sites. I developed a method for estimating the distance under the SR or SRV model, as well as the variance-covariance matrix of distances. Computer simulation showed that the SR method is better than a simpler method when the sequence length $L>1,000$ bp and is robust against deviations from time-reversibility. As expected, when the rate varies among sites, the SRV method is much better than the SR method.^ The evolutionary distances under nonstationary nucleotide frequencies: The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, I developed formulas for correcting the estimation biases of the paralinear and LogDet distances. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, I developed a method for estimating the variance-covariance matrix of the paralinear distance, so that statistical tests of phylogenies can be conducted when the nucleotide frequencies are nonstationary. Third, a new method for testing the molecular clock hypothesis was developed in the nonstationary case. ^

A comparison of Markov and generalized linear models of hospital mortality

This paper reports a comparison of three modeling strategies for the analysis of hospital mortality in a sample of general medicine inpatients in a Department of Veterans Affairs medical center. Logistic regression, a Markov chain model, and longitudinal logistic regression were evaluated on predictive performance as measured by the c-index and on accuracy of expected numbers of deaths compared to observed. The logistic regression used patient information collected at admission; the Markov model was comprised of two absorbing states for discharge and death and three transient states reflecting increasing severity of illness as measured by laboratory data collected during the hospital stay; longitudinal regression employed Generalized Estimating Equations (GEE) to model covariance structure for the repeated binary outcome. Results showed that the logistic regression predicted hospital mortality as well as the alternative methods but was limited in scope of application. The Markov chain provides insights into how day to day changes of illness severity lead to discharge or death. The longitudinal logistic regression showed that increasing illness trajectory is associated with hospital mortality. The conclusion is reached that for standard applications in modeling hospital mortality, logistic regression is adequate, but for new challenges facing health services research today, alternative methods are equally predictive, practical, and can provide new insights. ^