Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

A biophysical model of synaptic plasticity and metaplasticity can account for the dynamics of the backward shift of hippocampal place fields.

Hippocampal place cells in the rat undergo experience-dependent changes when the rat runs stereotyped routes. One such change, the backward shift of the place field center of mass, has been linked by previous modeling efforts to spike-timing-dependent plasticity (STDP). However, these models did not account for the termination of the place field shift and they were based on an abstract implementation of STDP that ignores many of the features found in cortical plasticity. Here, instead of the abstract STDP model, we use a calcium-dependent plasticity (CaDP) learning rule that can account for many of the observed properties of cortical plasticity. We use the CaDP learning rule in combination with a model of metaplasticity to simulate place field dynamics. Without any major changes to the parameters of the original model, the present simulations account both for the initial rapid place field shift and for the subsequent slowing down of this shift. These results suggest that the CaDP model captures the essence of a general cortical mechanism of synaptic plasticity, which may underlie numerous forms of synaptic plasticity observed both in vivo and in vitro.

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.

High-resolution dynamic computer simulation analysis of the behavior of sample components with pI values outside the pH gradient established by carrier ampholyte CIEF

The behavior of sample components whose pI values are outside the pH gradient established by 101 hypothetical biprotic carrier ampholytes covering a pH 6-8 range was investigated by computer simulation under constant current conditions with concomitant constant electroosmosis toward the cathode. Data obtained with the sample being applied between zones of carrier ampholytes and on the anodic side of the carrier ampholytes were studied and found to evolve into zone structures comprising three regions between anolyte and catholyte. The focusing region with the pH gradient is bracketed by two isotachopheretic zone structures comprising selected sample and carrier components as isotachophoretic zones. The isotachophoretic structures electrophoretically migrate in opposite direction and their lengths increase with time due to the gradual isotachophoretic decay at the pH gradient edges. Due to electroosmosis, however, the overall pattern is being transported toward the cathode. Sample components whose pI values are outside the established pH gradient are demonstrated to form isotachophoretic zones behind the leading cation of the catholyte (components with pI values larger than 8) and the leading anion of the anolyte (components with pI values smaller than 6). Amphoteric compounds with appropriate pI values or nonamphoteric components can act as isotachophoretic spacer compounds between sample compounds or between the leader and the sample with the highest mobility. The simulation data obtained provide for the first time insight into the dynamics of amphoteric sample components that do not focus within the established pH gradient.

Dynamic high-resolution computer simulation of isotachophoretic enantiomer separation and zone stability

The development of electrophoretic computer models and their use for simulation of electrophoretic processes has increased significantly during the last few years. Recently, GENTRANS and SIMUL5 were extended with algorithms that describe chemical equilibria between solutes and a buffer additive in a fast 1:1 interaction process, an approach that enables simulation of the electrophoretic separation of enantiomers. For acidic cationic systems with sodium and H3 0(+) as leading and terminating components, respectively, acetic acid as counter component, charged weak bases as samples, and a neutral CD as chiral selector, the new codes were used to investigate the dynamics of isotachophoretic adjustment of enantiomers, enantiomer separation, boundaries between enantiomers and between an enantiomer and a buffer constituent of like charge, and zone stability. The impact of leader pH, selector concentration, free mobility of the weak base, mobilities of the formed complexes and complexation constants could thereby be elucidated. For selected examples with methadone enantiomers as analytes and (2-hydroxypropyl)-β-CD as selector, simulated zone patterns were found to compare well with those monitored experimentally in capillary setups with two conductivity detectors or an absorbance and a conductivity detector. Simulation represents an elegant way to provide insight into the formation of isotachophoretic boundaries and zone stability in presence of complexation equilibria in a hitherto inaccessible way.

Dynamic high-resolution computer simulation of electrophoretic enantiomer separations with neutral cyclodextrins as chiral selectors.

GENTRANS, a comprehensive one-dimensional dynamic simulator for electrophoretic separations and transport, was extended for handling electrokinetic chiral separations with a neutral ligand. The code can be employed to study the 1:1 interaction of monovalent weak and strong acids and bases with a single monovalent weak or strong acid or base additive, including a neutral cyclodextrin, under real experimental conditions. It is a tool to investigate the dynamics of chiral separations and to provide insight into the buffer systems used in chiral capillary zone electrophoresis (CZE) and chiral isotachophoresis. Analyte stacking across conductivity and buffer additive gradients, changes of additive concentration, buffer component concentration, pH, and conductivity across migrating sample zones and peaks, and the formation and migration of system peaks can thereby be investigated in a hitherto inaccessible way. For model systems with charged weak bases and neutral modified β-cyclodextrins at acidic pH, for which complexation constants, ionic mobilities, and mobilities of selector-analyte complexes have been determined by CZE, simulated and experimentally determined electropherograms and isotachopherograms are shown to be in good agreement. Simulation data reveal that CZE separations of cationic enantiomers performed in phosphate buffers at low pH occur behind a fast cationic migrating system peak that has a small impact on the buffer composition under which enantiomeric separation takes place.

Atmospheric Dynamics of Hot Exoplanets

The characterization of exoplanetary atmospheres has come of age in the last decade, as astronomical techniques now allow for albedos, chemical abundances, temperature profiles and maps, rotation periods and even wind speeds to be measured. Atmospheric dynamics sets the background state of density, temperature and velocity that determines or influences the spectral and temporal appearance of an exoplanetary atmosphere. Hot exoplanets are most amenable to these characterization techniques; in the present review, we focus on highly-irradiated, large exoplanets (the "hot Jupiters"), as astronomical data begin to confront theoretical questions. We summarize the basic atmospheric quantities inferred from the astronomical observations. We review the state of the art by addressing a series of current questions and look towards the future by considering a separate set of exploratory questions. Attaining the next level of understanding will require a concerted effort of constructing multi-faceted, multi-wavelength datasets for benchmark objects. Understanding clouds presents a formidable obstacle, as they introduce degeneracies into the interpretation of spectra, yet their properties and existence are directly influenced by atmospheric dynamics. Confronting general circulation models with these multi-faceted, multi-wavelength datasets will help us understand these and other degeneracies. The coming decade will witness a decisive confrontation of theory and simulation by the next generation of astronomical data.

Quantum Simulation of Non-Abelian Lattice Gauge Theories

We use quantum link models to construct a quantum simulator for U(N) and SU(N) lattice gauge theories. These models replace Wilson’s classical link variables by quantum link operators, reducing the link Hilbert space to a finite number of dimensions. We show how to embody these quantum link models with fermionic matter with ultracold alkaline-earth atoms using optical lattices. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can thus address the corresponding dynamics in real time. Using exact diagonalization results we show that these systems share qualitative features with QCD, including chiral symmetry breaking and we study the expansion of a chirally restored region in space in real time.

Real-time simulation of large open quantum spin systems driven by dissipation

We consider a large quantum system with spins 12 whose dynamics is driven entirely by measurements of the total spin of spin pairs. This gives rise to a dissipative coupling to the environment. When one averages over the measurement results, the corresponding real-time path integral does not suffer from a sign problem. Using an efficient cluster algorithm, we study the real-time evolution from an initial antiferromagnetic state of the two-dimensional Heisenberg model, which is driven to a disordered phase, not by a Hamiltonian, but by sporadic measurements or by continuous Lindblad evolution.

Real-time simulation of nonequilibrium transport of magnetization in large open quantum spin systems driven by dissipation

Using quantum Monte Carlo, we study the nonequilibrium transport of magnetization in large open strongly correlated quantum spin-12 systems driven by purely dissipative processes that conserve the uniform or staggered magnetization, disregarding unitary Hamiltonian dynamics. We prepare both a low-temperature Heisenberg ferromagnet and an antiferromagnet in two parts of the system that are initially isolated from each other. We then bring the two subsystems in contact and study their real-time dissipative dynamics for different geometries. The flow of the uniform or staggered magnetization from one part of the system to the other is described by a diffusion equation that can be derived analytically.

Effects of climate, fire, and humans on forest dynamics: forest simulations compared to the palaeological record

In order to find out which factors influenced the forest dynamics in northern Italy during the Holocene, a palaeoecological approach involving pollen analysis was combined with ecosystem modelling. The dynamic and distribution based forest model DisCForm was run with different input scenarios for climate, species immigration, fire, and human impact and the similarity of the simulations with the original pollen record was assessed. From the comparisons of the model output and the pollen core, it appears that immigration was most important in the first part of the Holocene, and that fire and human activity had a major influence in the second half. Species not well represented in the simulation outputs are species with a higher abundance in the past than today (Corylus), with their habitat in riparian forests (Alnus) or with a strong response to human impact (Castanea).

Computational fluid dynamics modelling in cardiovascular medicine.

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards 'digital patient' or 'virtual physiological human' representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Computer simulation of electrophoretic aspects of enantiomer migration and separation in capillary electrochromatography with a neutral selector.

A computer simulation study describing the electrophoretic separation and migration of methadone enantiomers in presence of free and immobilized (2-hydroxypropyl)-β-CD is presented. The 1:1 interaction of methadone with the neutral CD was simulated by using experimentally determined mobilities and complexation constants for the complexes in a low-pH BGE comprising phosphoric acid and KOH. The use of complex mobilities represents free solution conditions with the chiral selector being a buffer additive, whereas complex mobilities set to zero provide data that mimic migration and separation with the chiral selector being immobilized, that is CEC conditions in absence of unspecific interaction between analytes and the chiral stationary phase. Simulation data reveal that separations are quicker, electrophoretic displacement rates are reduced, and sensitivity is enhanced in CEC with on-column detection in comparison to free solution conditions. Simulation is used to study electrophoretic analyte behavior at the interface between sample and the CEC column with the chiral selector (analyte stacking) and at the rear end when analytes leave the environment with complexation (analyte destacking). The latter aspect is relevant for off-column analyte detection in CEC and is described here for the first time via the dynamics of migrating analyte zones. Simulation provides insight into means to counteract analyte dilution at the column end via use of a BGE with higher conductivity. Furthermore, the impact of EOF on analyte migration, separation, and detection for configurations with the selector zone being displaced or remaining immobilized under buffer flow is simulated. In all cases, the data reveal that detection should occur within or immediately after the selector zone.

Modeling postglacial vegetation dynamics of temperate forests on the Olympic Peninsula (WA, USA) with special regard to snowpack

Past and future forest composition and distribution in temperate mountain ranges is strongly influenced by temperature and snowpack. We used LANDCLIM, a spatially explicit, dynamic vegetation model, to simulate forest dynamics for the last 16,000 years and compared the simulation results to pollen and macrofossil records at five sites on the Olympic Peninsula (Washington, USA). To address the hydrological effects of climate-driven variations in snowpack on simulated forest dynamics, we added a simple snow accumulation-and-melt module to the vegetation model and compared simulations with and without the module. LANDCLIM produced realistic present-day species composition with respect to elevation and precipitation gradients. Over the last 16,000 years, simulations driven by transient climate data from an atmosphere-ocean general circulation model (AOGCM) and by a chironomid-based temperature reconstruction captured Late-glacial to Late Holocene transitions in forest communities. Overall, the reconstruction-driven vegetation simulations matched observed vegetation changes better than the AOGCM-driven simulations. This study also indicates that forest composition is very sensitive to snowpack-mediated changes in soil moisture. Simulations without the snow module showed a strong effect of snowpack on key bioclimatic variables and species composition at higher elevations. A projected upward shift of the snow line and a decrease in snowpack might lead to drastic changes in mountain forests composition and even a shift to dry meadows due to insufficient moisture availability in shallow alpine soils.

The IDE geographical simulation model : predicting long-term effects of infrastructure development projects

It is important to be able to predict changes in the location of populations and industries in regions that are in the process of economic integration. The IDE Geographical Simulation Model (IDE-GSM) has been developed with two major objectives: (1) to determine the dynamics of locations of populations and industries in East Asia in the long-term, and (2) to analyze the impact of specific infrastructure projects on the regional economy at sub-national levels. The basic structure of the IDE-GSM is introduced in this article and accompanied with results of test analyses on the effects of the East West Economic Corridor on regions in Continental South East Asia. Results indicate that border costs appear to play a big role in the location choice of populations and industries, often a more important role than physical infrastructures themselves.