Magnetic-Resonance-Based Electrical Property Mapping Using Global Maxwell Tomography With an 8-Channel Head Coil at 7 Tesla: A Simulation Study.

OBJECTIVE: Global Maxwell Tomography (GMT) is a recently introduced volumetric technique for noninvasive estimation of electrical properties (EP) from magnetic resonance measurements. Previous work evaluated GMT using ideal radiofrequency (RF) excitations. The aim of this simulation study was to assess GMT performance with a realistic RF coil. METHODS: We designed a transmit-receive RF coil with 8 decoupled channels for 7T head imaging. We calculated the RF transmit field ( B1+) inside heterogeneous head models for different RF shimming approaches, and used them as input for GMT to reconstruct EP for all voxels. RESULTS: Coil tuning/decoupling remained relatively stable when the coil was loaded with different head models. Mean error in EP estimation changed from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] for relative permittivity and conductivity, respectively, when changing head model without re-tuning the coil. Results slightly improved when an SVD-based RF shimming algorithm was applied, in place of excitation with one coil at a time. Despite errors in EP, RF transmit field ( B1+) and absorbed power could be predicted with less than [Formula: see text] error over the entire head. GMT could accurately detect a numerically inserted tumor. CONCLUSION: This work demonstrates that GMT can reliably reconstruct EP in realistic simulated scenarios using a tailored 8-channel RF coil design at 7T. Future work will focus on construction of the coil and optimization of GMT's robustness to noise, to enable in-vivo GMT experiments. SIGNIFICANCE: GMT could provide accurate estimations of tissue EP, which could be used as biomarkers and could enable patient-specific estimation of RF power deposition, which is an unsolved problem for ultra-high-field magnetic resonance imaging.

Computation of ultimate SAR amplification factors for radiofrequency hyperthermia in non-uniform body models: impact of frequency and tumour location.

PURPOSE: We introduce a method for calculation of the ultimate specific absorption rate (SAR) amplification factors (uSAF) in non-uniform body models. The uSAF is the greatest possible SAF achievable by any hyperthermia (HT) phased array for a given frequency, body model and target heating volume. METHODS: First, we generate a basis-set of solutions to Maxwell's equations inside the body model. We place a large number of electric and magnetic dipoles around the body model and excite them with random amplitudes and phases. We then compute the electric fields created in the body model by these excitations using an ultra-fast volume integral solver called MARIE. We express the field pattern that maximises the SAF in the target tumour as a linear combination of these basis fields and optimise the combination weights so as to maximise SAF (concave problem). We compute the uSAFs in the Duke body models at 10 frequencies in the 20-900 MHz range and for twelve 3 cm-diameter tumours located at various depths in the head and neck. RESULTS: For both shallow and deep tumours, the frequency yielding the greatest uSAF was ∼900 MHz. Since this is the greatest frequency that we simulated, we hypothesise that the globally optimal frequency is actually greater. CONCLUSIONS: The uSAFs computed in this work are very large (40-100 for shallow tumours and 4-17 for deep tumours), indicating that there is a large room for improvement of the current state-of-the-art head and neck HT devices.

Non-canonical Activation of Akt in Serum-Stimulated Fibroblasts, Revealed by Comparative Modeling of Pathway Dynamics.

The dynamic behaviors of signaling pathways can provide clues to pathway mechanisms. In cancer cells, excessive phosphorylation and activation of the Akt pathway is responsible for cell survival advantages. In normal cells, serum stimulation causes brief peaks of extremely high Akt phosphorylation before reaching a moderate steady-state. Previous modeling assumed this peak and decline behavior (i.e., "overshoot") was due to receptor internalization. In this work, we modeled the dynamics of the overshoot as a tool for gaining insight into Akt pathway function. We built an ordinary differential equation (ODE) model describing pathway activation immediately upstream of Akt phosphorylation at Thr308 (Aktp308). The model was fit to experimental measurements of Aktp308, total Akt, and phosphatidylinositol (3,4,5)-trisphosphate (PIP3), from mouse embryonic fibroblasts with serum stimulation. The canonical Akt activation model (the null hypothesis) was unable to recapitulate the observed delay between the peak of PIP3 (at 2 minutes), and the peak of Aktp308 (at 30-60 minutes). From this we conclude that the peak and decline behavior of Aktp308 is not caused by PIP3 dynamics. Models for alternative hypotheses were constructed by allowing an arbitrary dynamic curve to perturb each of 5 steps of the pathway. All 5 of the alternative models could reproduce the observed delay. To distinguish among the alternatives, simulations suggested which species and timepoints would show strong differences. Time-series experiments with membrane fractionation and PI3K inhibition were performed, and incompatible hypotheses were excluded. We conclude that the peak and decline behavior of Aktp308 is caused by a non-canonical effect that retains Akt at the membrane, and not by receptor internalization. Furthermore, we provide a novel spline-based method for simulating the network implications of an unknown effect, and we demonstrate a process of hypothesis management for guiding efficient experiments.

The self-limiting dynamics of TGF-ß signaling in silico and in vitro, with negative feedback through PPM1A upregulation.

The TGF-ß/Smad signaling system decreases its activity through strong negative regulation. Several molecular mechanisms of negative regulation have been published, but the relative impact of each mechanism on the overall system is unknown. In this work, we used computational and experimental methods to assess multiple negative regulatory effects on Smad signaling in HaCaT cells. Previously reported negative regulatory effects were classified by time-scale: degradation of phosphorylated R-Smad and I-Smad-induced receptor degradation were slow-mode effects, and dephosphorylation of R-Smad was a fast-mode effect. We modeled combinations of these effects, but found no combination capable of explaining the observed dynamics of TGF-ß/Smad signaling. We then proposed a negative feedback loop with upregulation of the phosphatase PPM1A. The resulting model was able to explain the dynamics of Smad signaling, under both short and long exposures to TGF-ß. Consistent with this model, immuno-blots showed PPM1A levels to be significantly increased within 30 min after TGF-ß stimulation. Lastly, our model was able to resolve an apparent contradiction in the published literature, concerning the dynamics of phosphorylated R-Smad degradation. We conclude that the dynamics of Smad negative regulation cannot be explained by the negative regulatory effects that had previously been modeled, and we provide evidence for a new negative feedback loop through PPM1A upregulation. This work shows that tight coupling of computational and experiments approaches can yield improved understanding of complex pathways.

Systematic parameter estimation in data-rich environments for cell signalling dynamics.

MOTIVATION: Computational models of biological signalling networks, based on ordinary differential equations (ODEs), have generated many insights into cellular dynamics, but the model-building process typically requires estimating rate parameters based on experimentally observed concentrations. New proteomic methods can measure concentrations for all molecular species in a pathway; this creates a new opportunity to decompose the optimization of rate parameters. RESULTS: In contrast with conventional parameter estimation methods that minimize the disagreement between simulated and observed concentrations, the SPEDRE method fits spline curves through observed concentration points, estimates derivatives and then matches the derivatives to the production and consumption of each species. This reformulation of the problem permits an extreme decomposition of the high-dimensional optimization into a product of low-dimensional factors, each factor enforcing the equality of one ODE at one time slice. Coarsely discretized solutions to the factors can be computed systematically. Then the discrete solutions are combined using loopy belief propagation, and refined using local optimization. SPEDRE has unique asymptotic behaviour with runtime polynomial in the number of molecules and timepoints, but exponential in the degree of the biochemical network. SPEDRE performance is comparatively evaluated on a novel model of Akt activation dynamics including redox-mediated inactivation of PTEN (phosphatase and tensin homologue). AVAILABILITY AND IMPLEMENTATION: Web service, software and supplementary information are available at www.LtkLab.org/SPEDRE SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Plasmin triggers a switch-like decrease in thrombospondin-dependent activation of TGF-ß1.

Transforming growth factor-ß1 (TGF-ß1) is a potent regulator of extracellular matrix production, wound healing, differentiation, and immune response, and is implicated in the progression of fibrotic diseases and cancer. Extracellular activation of TGF-ß1 from its latent form provides spatiotemporal control over TGF-ß1 signaling, but the current understanding of TGF-ß1 activation does not emphasize cross talk between activators. Plasmin (PLS) and thrombospondin-1 (TSP1) have been studied individually as activators of TGF-ß1, and in this work we used a systems-level approach with mathematical modeling and in vitro experiments to study the interplay between PLS and TSP1 in TGF-ß1 activation. Simulations and steady-state analysis predicted a switch-like bistable transition between two levels of active TGF-ß1, with an inverse correlation between PLS and TSP1. In particular, the model predicted that increasing PLS breaks a TSP1-TGF-ß1 positive feedback loop and causes an unexpected net decrease in TGF-ß1 activation. To test these predictions in vitro, we treated rat hepatocytes and hepatic stellate cells with PLS, which caused proteolytic cleavage of TSP1 and decreased activation of TGF-ß1. The TGF-ß1 activation levels showed a cooperative dose response, and a test of hysteresis in the cocultured cells validated that TGF-ß1 activation is bistable. We conclude that switch-like behavior arises from natural competition between two distinct modes of TGF-ß1 activation: a TSP1-mediated mode of high activation and a PLS-mediated mode of low activation. This switch suggests an explanation for the unexpected effects of the plasminogen activation system on TGF-ß1 in fibrotic diseases in vivo, as well as novel prognostic and therapeutic approaches for diseases with TGF-ß dysregulation.

Reactive oxygen species (ROS) and sensitization to TRAIL-induced apoptosis, in Bayesian network modelling of HeLa cell response to LY303511.

BACKGROUND: The compound LY303511 (LY30) has been proven to induce production of ROS and to sensitize cancer cells to TRAIL-induced apoptosis, but the mechanisms and mediators of LY30-induced effects are potentially complex. Bayesian networks are a modelling technique for making probabilistic inferences about complex networks of uncertain causality. METHODS: Fluorescent indicators for ROS, reactive nitrogen species (RNS), and free calcium were measured in time-series after LY30 treatment. This "correlative" dataset was used as input for Bayesian modelling to predict the causal dependencies among the measured species. Predictions were compared against a separate "causal" dataset, in which cells had been treated with FeTPPS to scavenge peroxynitrite, EGTA-am to chelate calcium, and Tiron to scavenge O(2)(-). Finally, cell viability measurements were integrated into an extended model of LY30 effects. RESULTS: LY30 treatment caused a rapid increase of ROS (measured by DCFDA) as well as a significant increase in RNS and calcium. Bayesian modelling predicted that Ca(2+)was a partial cause of the ROS induced by short incubations with LY30, and that RNS was strongly responsible for the ROS induced by long incubations with LY30. Validation experiments confirmed the predicted roles of RNS and calcium, and also demonstrated a causal role for O(2)(-). In cell viability experiments, the additive effects of calcium and peroxynitrite were responsible for 90% of LY30-mediated sensitization to TRAIL-induced apoptosis. CONCLUSIONS: We conclude that LY30 induces interdependent pathways of reactive species and stress signalling, with peroxynitrite and calcium contributing most significantly to apoptosis sensitization.

Steady states and dynamics of urokinase-mediated plasmin activation in silico and in vitro.

Plasmin (PLS) and urokinase-type plasminogen activator (UPA) are ubiquitous proteases that regulate the extracellular environment. Although they are secreted in inactive forms, they can activate each other through proteolytic cleavage. This mutual interplay creates the potential for complex dynamics, which we investigated using mathematical modeling and in vitro experiments. We constructed ordinary differential equations to model the conversion of precursor plasminogen into active PLS, and precursor urokinase (scUPA) into active urokinase (tcUPA). Although neither PLS nor UPA exhibits allosteric cooperativity, modeling showed that cooperativity occurred at the system level because of substrate competition. Computational simulations and bifurcation analysis predicted that the system would be bistable over a range of parameters for cooperativity and positive feedback. Cell-free experiments with recombinant proteins tested key predictions of the model. PLS activation in response to scUPA stimulus was found to be cooperative in vitro. Finally, bistability was demonstrated in vitro by the presence of two significantly different steady-state levels of PLS activation for the same levels of stimulus. We conclude that ultrasensitive, bistable activation of UPA-PLS is possible in the presence of substrate competition. An ultrasensitive threshold for activation of PLS and UPA would have ramifications for normal and disease processes, including angiogenesis, metastasis, wound healing, and fibrosis.

Cell-delivery therapeutics for liver regeneration.

For acute, chronic, or hereditary diseases of the liver, cell transplantation therapies can stimulate liver regeneration or serve as a bridge until liver transplantation can be performed. Recently, fetal hepatocytes, stem cells, liver progenitor cells, or other primitive and proliferative cell types have been employed for cell transplantation therapies, in an effort to improve the survival, proliferation, and engraftment of the transplanted cells. Reviewing earlier studies, which achieved success by transplanting mature hepatocytes, we propose that there is a switch-like regulation of liver regeneration that changes state according to a stimulus threshold of extracellular influences such as cytokines, matrices and neighboring cells. Important determinants of a successful clinical outcome include sufficient quantities and functional levels of the transplanted cells (even for short periods to alter the environment), rather than just engraftment levels or survival durations of the exogenously transplanted cells. The relative importance of these determining factors will impact future choices of cell sources, delivery vehicles, and sites of cell transplantation to stimulate liver regeneration for patients with severe liver diseases.

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.