A Characterization of Scale Invariant Responses in Enzymatic Networks

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately) the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO), whose validity we show is both necessary and sufficient for scale invariance of enzymatic networks. Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions

Anterior-Posterior Neural Axis Plasticity in the developing central nervous system of Xenopus laevis

Plasticity, the ability to redifferentiate and change cellular identity, is an integral part of development as cells must develop and specify while being able to respond to any changes in the environment. Many instances of cell identity changes have been identified during development, but the mechanisms that allow certain cells to do this while others remain in a fixed fate are unclear. The patterning of the neural axis in the central nervous system involves the specification and determination of neural cell identity along the anterior-posterior axis. While the mechanisms that determine the anterior-posterior neural axis early in development are well characterized, the plasticity that underlies this process remains poorly understood. While expression of genes such as Suv4-20h, Prc2, and ezH2 are known to bring about loss of potency-related factors, neither the temporal or spatial parameters of this developmental neural plasticity nor the molecular mechanisms governing the process are understood. This investigation was designed to examine the spatial-temporal limits of plasticity in the development of the vertebrate central nervous system. A rotation transplant system with a labeled donor embryo and unlabeled host embryo was used to transplant neural ectoderm covering the median half of the dorsal ectoderm from the donor embryo and rotate the anterior-posterior axis 180º onto the host embryo. This allowed for the testing of physically perturbing the axis and assaying its ability to re-differentiate. Results suggest that there is a period between mid gastrula (11.5) and late gastrula (12.5) during which the axis has been determined based on expression of regional marker genes along the axis (XCG-1, Otx2, En2, and Krox20) but remains competent to re-differentiation. In addition, the results indicate that the tissue itself loses competency as late gastrula embryos are still able to re-differentiate mid gastrula neural tissue to the correct pattern, but neural transplants from late gastrula embryos are unable to re-differentiate even in the presence of the mid gastrula inducing environment. Hence, the neural tissue remains plastic for a limited time period after acquisition of an anterior-posterior fate during development

Oscillations and temporal signalling in cells

The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration, using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show "ultradian" oscillations, with time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NFkB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour

The Role of Spontaneous Intracellular Calcium Transients in Neurotransmitter Phenotype Specification in Xenopus laevis

Spontaneous intracellular calcium activity has been implicated in a host of processes related to nervous system development, including neural induction, neural tube closure, and synaptogenesis. One of these calcium-influenced processes, neurotransmitter phenotype specification, involves the acquisition of the correct balance and patterning of excitatory and inhibitory neurons, and its regulation is vital to proper nervous system functionality. While a high frequency of intracellular calcium transients in presumptive neurons during development has been correlated with an inhibitory fate, the persistence of this phenomenon in in vitro models has not been conclusively demonstrated. Additionally, we believe that current methods of calcium activity analysis, which are limited to counting fluorescent indicator spikes above a particular threshold, is limiting. To this end, we employed Xenopus laevis presumptive neural tissue as an in vitro model system, imaging calcium activity in developing neural cells. This data was analyzed via a novel pipeline that uses fluorescence trace entropy as a comparative metric rather than relying on predetermined parameters to define particular features (i.e., spikes or waves). Use of this analysis method revealed differences in calcium activity across development, with cells dissected from younger embryos displaying more entropic calcium activity that gradually decreased across development. Relatively small differences were found between cells positive for the expression of particular neural marker genes and cells that did not express these genes, and these differences varied across developmental time points. Most notably, cells positive for different specific neural marker genes displayed significantly different levels of calcium activity entropy from one another. As a whole, these results provide support for the hypothesis that particular patterns of calcium dynamics are associated with the expression of particular genes involved in the neuronal differentiation process

CHEMOTHERAPEUTIC POTENTIAL OF NOVEL XANTHONE SOURCED FROM SWERTIA CHIRATA AGAINST SKIN CARCINOGENESIS

Objective: Swertia chirata forms a rich source of bio-active compounds, among which xanthones form an important part. Among the xanthones present in it, 1,5,8 Tri-hydroxy-3-methoxy xanthone (TMX) was found to be the most active. The present study aims to evaluate the chemotherapeutic potential of it against metastatic skin cancer cell lines. Methods: In this study, the antitumor activity of TMX (the active component of chirata plant) was evaluated in A431, SKMEL-5, and A375 cell line by using in-vitro assays such as cell viability assay, cell cycle analysis, caspase 3 activity assay, intracellular reactive oxygen species (ROS) level determination by dichlorofluorescein diacetate, and quantitative real-time polymerase chain reaction (qRT-PCR). Results: In vitro studies showed that TMX from S. chirata exhibited significant antitumor activity by inducing apoptosis and restricting proliferation in both melanoma and non-melanoma skin cancer cell lines, but no such activity was seen in normal skin cancer cell line WS1. The qRT-PCR analysis revealed that in both the melanoma ad non-melanoma cell lines, TMX could exert its antitumor activity by downregulating c-Myc, cyclin-D1, and β-catenin and up-regulating Wnt antagonist gsk-3β, thereby suppressing wnt self-renewal pathway, but such regulation was absent in normal cell line. Conclusions: TMX from chirata could effectively inhibit the proliferation of metastatic skin cancer (both melanoma and non-melanoma) cell lines while being non-toxic to normal cell lines. The chemotherapeutic potential of TMX against metastatic skin cancer cell lines was achieved by downregulating several key regulatory genes enabling the suppression of the self-renewal pathway, the chief reason behind the invasiveness of cancer cells

Mathematical modeling of SGK1 dynamics in medulloblastoma tumor cells

This work is devoted to mathematical modeling of deregulation of the Wnt/β-catenin signaling pathway in medulloblastoma resulting in abnormal dynamics of target genes. Medulloblastoma is a brain tumor, mostly diagnosed in children. It is associated with several molecular genetic alterations. Specific aberrations of chromosome 6q, leading either to the chromosome copy-number loss (monosomy 6) or gain (trisomy 6), occur in two different subtypes of the tumor. The model is a nine-dimensional system of ordinary differential equations and describes nonlinear dynamics of the key ingredients of the signaling process. The model is based on the law of mass action and accounts for a two-compartment architecture of a cell consisting of the nucleus and cytoplasm. The model helps to understand molecular differences between the two medulloblastoma mutation subtypes that are associated with different patient prognosis. Our studies are based on a collaboration with the group of Prof. Dr. med. Stefan Pfister at the Division of Pediatric Neuro-oncology Research Group of the German Cancer Research Center (DKFZ). The model is used to evaluate data from the gene expression microarray data from the clinics in Heidelberg, Boston and Amsterdam. Numerical simulations lead to new biological hypotheses related to a significant role of the regulatory loop SGK1-GSK3β-MYC, a part of the Wnt/β-catenin signaling pathway. Simulations indicate the advantage of using the pharmacological inhibitor of SGK1 in patients with copy-number gain of chromosome 6q. Finally, the simulation results suggest a beneficial use of an adjuvant therapy in a trisomy 6 treatment. Mathematical analysis of the ordinary differential equations system confirms the wellposedness of the model and provides basic properties of the solutions. Supported by numerical analysis, we conclude about global stability of a unique positive equilibrium corresponding to the homeostasis of the system. We also tackle the parameter estimation problem using statistical assessment of the results and Gauss-Newton method. Sensitivity analysis provides insight into the role of model parameters. In particular, it confirms the sensitivity of the system to the parameter of SGK1 degradation. The model provides a powerful tool to study mechanistically the underlying process and to support the experiments