A model checking approach to the parameter estimation of biochemical pathways

Model checking has historically been an important tool to verify models of a wide variety of systems. Typically a model has to exhibit certain properties to be classed ‘acceptable’. In this work we use model checking in a new setting; parameter estimation. We characterise the desired behaviour of a model in a temporal logic property and alter the model to make it conform to the property (determined through model checking). We have implemented a computational system called MC2(GA) which pairs a model checker with a genetic algorithm. To drive parameter estimation, the fitness of set of parameters in a model is the inverse of the distance between its actual behaviour and the desired behaviour. The model checker used is the simulation-based Monte Carlo Model Checker for Probabilistic Linear-time Temporal Logic with numerical constraints, MC2(PLTLc). Numerical constraints as well as the overall probability of the behaviour expressed in temporal logic are used to minimise the behavioural distance. We define the theory underlying our parameter estimation approach in both the stochastic and continuous worlds. We apply our approach to biochemical systems and present an illustrative example where we estimate the kinetic rate constants in a continuous model of a signalling pathway

Quantitative Analysis of the Effect of Cancer Invasiveness and Collagen Concentration on 3D Matrix Remodeling

Extracellular matrix (ECM) remodeling is a key component of cell migration and tumor metastasis, and has been associated with cancer progression. Despite the importance of matrix remodeling, systematic and quantitative studies on the process have largely been lacking. Furthermore, it remains unclear if the disrupted tensional homeostasis characteristic of malignancy is due to initially altered ECM and tissue properties, or to the alteration of the tissue by tumor cells. To explore these questions, we studied matrix remodeling by two different prostate cancer cell lines in a three-dimensional collagen system. Over one week, we monitored structural changes in gels of varying collagen content using confocal reflection microscopy and quantitative image analysis, tracking metrics of fibril fraction, pore size, and fiber length and diameter. Gels that were seeded with no cells (control), LNCaP cells, and DU-145 cells were quantitatively compared. Gels with higher collagen content initially had smaller pore sizes and higher fibril fractions, as expected. However, over time, LNCaP- and DU-145-populated matrices showed different structural properties compared both to each other and to the control gels, with LNCaP cells appearing to favor microenvironments with lower collagen fiber fractions and larger pores than DU-145 cells. We posit that the DU-145 cells' preference for denser matrices is due to their higher invasiveness and proteolytic capabilities. Inhibition of matrix proteases resulted in reduced fibril fractions for high concentration gels seeded with either cell type, supporting our hypothesis. Our novel quantitative results probe the dynamics of gel remodeling in three dimensions and suggest that prostate cancer cells remodel their ECM in a synergistic manner that is dependent on both initial matrix properties as well as their invasiveness

A Cellular Potts Model simulating cell migration on and in matrix environments

Cell migration on and through extracellular matrix plays a critical role in a wide variety of physiological and pathological phenomena, and in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, gap size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migratory phenotype on both two-dimensional substrates and within three-dimensional environments, in a close comparison with experimental evidence. As distinct features of our approach, the cells are represented by compartmentalized discrete objects, differentiated in the nucleus and in the cytosolic region, while the extracellular matrix is composed of a fibrous mesh and of a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological ECM distribution and, further, a biphasic dependence of migration on the matrix density, and in part adhesion, in both two-dimensional and three-dimensional settings. Moreover, we demonstrate that the directional component of cell movement is strongly correlated with the topological distribution of the ECM fibrous network. In the three-dimensional networks, we also investigate the effects of the matrix mechanical microstructure, observing that, at a given distribution of fibers, cell motility has a subtle bimodal relation with the elasticity of the scaffold. Finally, cell locomotion requires deformation of the cell's nucleus and/or cell-derived proteolysis of steric fibrillar obstacles within rather rigid matrices characterized by small pores, not, however, for sufficiently large pores. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomen in health, disease and tissue engineering applications. The research that led to the present paper was partially supported by a grant of the group GNFM of INdA

Suzaku observation of the LINER NGC 4102

Low ionisation nuclear emission-line region (LINER) nuclei have been claimed to be different than other active galactic nuclei (AGN) due to the presence of complex absorbing structures along the line-of-sight and/or an inefficient mode of accretion onto the supermassive black hole. However, this issue is still open. We have investigated the broad band X-ray spectrum of NGC 4102, one of the most luminous LINERs in the Swift/BAT survey. We studied a 80 ksec Suzaku spectrum of NGC 4102, together with archival Chandra and Swift/BAT observations. We also studied the optical (3.5m/TWIN at Calar Alto observatory) and near-infrared (WHT/LIRIS at Observatorio Roque los Muchachos) spectra that were taken contemporaneous to the Suzaku data. There is strong evidence that NGC 4102 is a Compton-thick AGN, as suggested by the Swift/BAT detected intrinsic continuum and the presence of a strong narrow, neutral FeKa emission line. We have also detected ionised FeXXV emission lines in the Suzaku spectrum of the source. NGC 4102 shows a variable soft excess found at a significantly higher flux state by the time of Suzaku observations when compared to Chandra observations. Finally, a complex structure of absorbers is seen with at least two absorbers apart from the Compton-thick one, derived from the X-ray spectral analysis and the optical extinction.Comment: 11 pages, 6 figures and 3 tables. Accepted for publication in Astronomy & Astrophysic

Systems Biology Modeling Reveals a Possible Mechanism of the Tumor Cell Death upon Oncogene Inactivation in EGFR Addicted Cancers

Despite many evidences supporting the concept of “oncogene addiction” and many hypotheses rationalizing it, there is still a lack of detailed understanding to the precise molecular mechanism underlying oncogene addiction. In this account, we developed a mathematic model of epidermal growth factor receptor (EGFR) associated signaling network, which involves EGFR-driving proliferation/pro-survival signaling pathways Ras/extracellular-signal-regulated kinase (ERK) and phosphoinositol-3 kinase (PI3K)/AKT, and pro-apoptotic signaling pathway apoptosis signal-regulating kinase 1 (ASK1)/p38. In the setting of sustained EGFR activation, the simulation results show a persistent high level of proliferation/pro-survival effectors phospho-ERK and phospho-AKT, and a basal level of pro-apoptotic effector phospho-p38. The potential of p38 activation (apoptotic potential) due to the elevated level of reactive oxygen species (ROS) is largely suppressed by the negative crosstalk between PI3K/AKT and ASK1/p38 pathways. Upon acute EGFR inactivation, the survival signals decay rapidly, followed by a fast increase of the apoptotic signal due to the release of apoptotic potential. Overall, our systems biology modeling together with experimental validations reveals that inhibition of survival signals and concomitant release of apoptotic potential jointly contribute to the tumor cell death following the inhibition of addicted oncogene in EGFR addicted cancers

Recent progress towards development of effective systemic chemotherapy for the treatment of malignant brain tumors

Systemic chemotherapy has been relatively ineffective in the treatment of malignant brain tumors even though systemic chemotherapy drugs are small molecules that can readily extravasate across the porous blood-brain tumor barrier of malignant brain tumor microvasculature. Small molecule systemic chemotherapy drugs maintain peak blood concentrations for only minutes, and therefore, do not accumulate to therapeutic concentrations within individual brain tumor cells. The physiologic upper limit of pore size in the blood-brain tumor barrier of malignant brain tumor microvasculature is approximately 12 nanometers. Spherical nanoparticles ranging between 7 nm and 10 nm in diameter maintain peak blood concentrations for several hours and are sufficiently smaller than the 12 nm physiologic upper limit of pore size in the blood-brain tumor barrier to accumulate to therapeutic concentrations within individual brain tumor cells. Therefore, nanoparticles bearing chemotherapy that are within the 7 to 10 nm size range can be used to deliver therapeutic concentrations of small molecule chemotherapy drugs across the blood-brain tumor barrier into individual brain tumor cells. The initial therapeutic efficacy of the Gd-G5-doxorubicin dendrimer, an imageable nanoparticle bearing chemotherapy within the 7 to 10 nm size range, has been demonstrated in the orthotopic RG-2 rodent malignant glioma model. Herein I discuss this novel strategy to improve the effectiveness of systemic chemotherapy for the treatment of malignant brain tumors and the therapeutic implications thereof

Negative feedback regulation of the ERK1/2 MAPK pathway

The extracellular signal-regulated kinase 1/2 (ERK1/2) mitogen-activated protein kinase (MAPK) signalling pathway regulates many cellular functions, including proliferation, differentiation, and transformation. To reliably convert external stimuli into specific cellular responses and to adapt to environmental circumstances, the pathway must be integrated into the overall signalling activity of the cell. Multiple mechanisms have evolved to perform this role. In this review, we will focus on negative feedback mechanisms and examine how they shape ERK1/2 MAPK signalling. We will first discuss the extensive number of negative feedback loops targeting the different components of the ERK1/2 MAPK cascade, specifically the direct posttranslational modification of pathway components by downstream protein kinases and the induction of de novo gene synthesis of specific pathway inhibitors. We will then evaluate how negative feedback modulates the spatiotemporal signalling dynamics of the ERK1/2 pathway regarding signalling amplitude and duration as well as subcellular localisation. Aberrant ERK1/2 activation results in deregulated proliferation and malignant transformation in model systems and is commonly observed in human tumours. Inhibition of the ERK1/2 pathway thus represents an attractive target for the treatment of malignant tumours with increased ERK1/2 activity. We will, therefore, discuss the effect of ERK1/2 MAPK feedback regulation on cancer treatment and how it contributes to reduced clinical efficacy of therapeutic agents and the development of drug resistance