Dynamic density functional theory of solid tumor growth: Preliminary models.
Ontology highlight
ABSTRACT:
SUBMITTER: Chauviere A
PROVIDER: S-EPMC3321520 | biostudies-other | 2012 Mar
REPOSITORIES: biostudies-other
Similar Datasets
Project description:Dynamic density functional theory (DDFT) is emerging as a useful theoretical technique for modeling the dynamics of correlated systems. We extend DDFT to quantum systems for application to dense plasmas through a quantum hydrodynamics (QHD) approach. The DDFT-based QHD approach includes correlations in the the equation of state self-consistently, satisfies sum rules and includes irreversibility arising from collisions. While QHD can be used generally to model non-equilibrium, heterogeneous plasmas, we employ the DDFT-QHD framework to generate a model for the electronic dynamic structure factor, which offers an avenue for measuring hydrodynamic properties, such as transport coefficients via x-ray Thomson scattering.
| S-EPMC5681597 | biostudies-literature
Project description:Thiamin diphosphate (ThDP) is a key coenzyme in sugar metabolism. The 4'-aminopyrimidine ring of ThDP cycles through several ionization and tautomeric states during enzyme catalysis, but it is not fully understood which states are adopted during the individual steps of the catalytic cycle. Thiamin has been synthesized with labels selectively inserted into the C2 and C6' positions, as well as into the amino group, creating [C2, C6'-(13)C(2)] thiamin and [N4'-(15)N] thiamin. Magic-angle spinning (MAS) NMR spectroscopy has been employed to record the (13)C and (15)N chemical shift anisotropy (CSA) tensors for C2, C6', and N4' atoms. Our results indicate that the isotropic chemical shifts as well as the principal components of the (13)C and (15)N CSA tensors are very sensitive to the protonation states in these compounds and, therefore, permit differentiating between the two ionization states, 4-aminopyrimidine and 4-aminopyrimidinium. Using density functional theory (DFT), we have calculated the magnetic shielding anisotropy tensors of C2, C6', and N4' and found excellent agreement between the computed and the experimental tensors. Our findings indicate that MAS NMR spectroscopy in conjunction with DFT calculations is a sensitive probe of ionization states in the thiamin cofactor. The results of this study will serve as a guide for characterization of ionization and tautomeric states of thiamin in complexes with thiamin-dependent enzymes.
| S-EPMC3227141 | biostudies-literature
Project description:Enforcing a straight-line condition of the total energy upon removal/addition of fractional electrons on eigen states has been successfully applied to atoms and molecules for calculating ionization potentials and electron affinities, but fails for solids due to the extended nature of the eigen orbitals. Here we have extended the straight-line condition to the removal/addition of fractional electrons on Wannier functions constructed within the occupied/unoccupied subspaces. It removes the self-interaction energies of those Wannier functions, and yields accurate band gaps for solids compared to experiments. It does not have any adjustable parameters and the computational cost is at the DFT level. This method can also work for molecules, providing eigen energies in good agreement with experimental ionization potentials and electron affinities. Our approach can be viewed as an alternative approach of the standard LDA+U procedure.
| S-EPMC4845067 | biostudies-literature
Project description:The relationships between cellular, structural and dynamical properties of tumors have traditionally been studied separately. Here, we construct a quantitative, predictive theory of solid tumor growth, metabolic rate, vascularization and necrosis that integrates the relationships between these properties. To accomplish this, we develop a comprehensive theory that describes the interface and integration of the tumor vascular network and resource supply with the cardiovascular system of the host. Our theory enables a quantitative understanding of how cells, tissues, and vascular networks act together across multiple scales by building on recent theoretical advances in modeling both healthy vasculature and the detailed processes of angiogenesis and tumor growth. The theory explicitly relates tumor vascularization and growth to metabolic rate, and yields extensive predictions for tumor properties, including growth rates, metabolic rates, degree of necrosis, blood flow rates and vessel sizes. Besides these quantitative predictions, we explain how growth rates depend on capillary density and metabolic rate, and why similar tumors grow slower and occur less frequently in larger animals, shedding light on Peto's paradox. Various implications for potential therapeutic strategies and further research are discussed.
| S-EPMC3182997 | biostudies-literature
Project description:Following recent developments in multilevel embedding methods, we introduce a novel density matrix-based multilevel approach within the framework of density functional theory (DFT). In this multilevel DFT, the system is partitioned in an active and an inactive fragment, and all interactions are retained between the two parts. The decomposition of the total system is performed upon the density matrix. The orthogonality between the two parts is maintained by solving the Kohn-Sham equations in the MO basis for the active part only, while keeping the inactive density matrix frozen. This results in the reduction of computational cost. We outline the theory and implementation and discuss the differences and similarities with state-of-the-art DFT embedding methods. We present applications to aqueous solutions of methyloxirane and glycidol.
| S-EPMC7880574 | biostudies-literature
Project description:Chemical reactions constitute the central feature of many liquid, material, and biomolecular processes. Conventional molecular dynamics (MD) is inadequate for simulating chemical reactions given the fixed bonding topology of most force fields, while modeling chemical reactions using ab initio molecular dynamics is limited to shorter time and length scales given its high computational cost. As such, the multiscale reactive molecular dynamics method provides one promising alternative for simulating complex chemical systems at atomistic detail on a reactive potential energy surface. However, the parametrization of such models is a key barrier to their applicability and success. In this work, we present reactive MD models derived from constrained density functional theory that are both accurate and transferable. We illustrate the features of these models for proton dissociation reactions of amino acids in both aqueous and protein environments. Specifically, we present models for ionizable glutamate and lysine that predict accurate absolute pKa values in water as well as their significantly shifted pKa in staphylococcal nuclease (SNase) without any modification of the models. As one outcome of the new methodology, the simulations show that the deprotonation of ionizable residues in SNase can be closely coupled with side chain rotations, which is a concept likely generalizable to many other proteins. Furthermore, the present approach is not limited to only pKa prediction but can enable the fully atomistic simulation of many other reactive systems along with a determination of the key aspects of the reaction mechanisms.
| S-EPMC8480781 | biostudies-literature
Project description:A primary goal of collective population behavior studies is to determine the rules governing crowd distributions in order to predict future behaviors in new environments. Current top-down modeling approaches describe, instead of predict, specific emergent behaviors, whereas bottom-up approaches must postulate, instead of directly determine, rules for individual behaviors. Here, we employ classical density functional theory (DFT) to quantify, directly from observations of local crowd density, the rules that predict mass behaviors under new circumstances. To demonstrate our theory-based, data-driven approach, we use a model crowd consisting of walking fruit flies and extract two functions that separately describe spatial and social preferences. The resulting theory accurately predicts experimental fly distributions in new environments and provides quantification of the crowd "mood". Should this approach generalize beyond milling crowds, it may find powerful applications in fields ranging from spatial ecology and active matter to demography and economics.
| S-EPMC6117271 | biostudies-literature
Project description:BackgroundMathematical models describing growth kinetics are very important for predicting many biological phenomena such as tumor volume, speed of disease progression, and determination of an optimal radiation and/or chemotherapy schedule. Growth models such as logistic, Gompertz, Richards, and Weibull have been extensively studied and applied to a wide range of medical and biological studies. We introduce a class of three and four parameter models called "hyperbolastic models" for accurately predicting and analyzing self-limited growth behavior that occurs e.g. in tumors. To illustrate the application and utility of these models and to gain a more complete understanding of them, we apply them to two sets of data considered in previously published literature.ResultsThe results indicate that volumetric tumor growth follows the principle of hyperbolastic growth model type III, and in both applications at least one of the newly proposed models provides a better fit to the data than the classical models used for comparison.ConclusionWe have developed a new family of growth models that predict the volumetric growth behavior of multicellular tumor spheroids with a high degree of accuracy. We strongly believe that the family of hyperbolastic models can be a valuable predictive tool in many areas of biomedical and epidemiological research such as cancer or stem cell growth and infectious disease outbreaks.
| S-EPMC1084364 | biostudies-literature
Project description:Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer--the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron-nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if δ, Δ < ω(0I), where δ and Δ are the homogeneous linewidth and inhomogeneous breadth of the EPR spectrum, respectively, we verify that the SE occurs when ω(M) = ω(0S) ± ω(0I), where ω(M), ω(0S) and ω(0I) are, respectively, the microwave, and the EPR and NMR frequencies. Alternatively, when Δ > ω(0I) > δ, the CE dominates the polarization transfer. This two-electron process is optimized when ω(0S(1))-ω(0S(2)) = ω(0I) and ω(M)~ω(0S(1)) or ω(0S(2)), where ω(0S(1)) and ω(0S(2)) are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the microwave irradiation field, the external magnetic field, and the electron-electron and electron-nuclear interactions on DNP enhancements.
| S-EPMC3078165 | biostudies-other
Project description:Using (51)V magic angle spinning solid-state NMR spectroscopy and density functional theory calculations we have characterized the chemical shift and quadrupolar coupling parameters for two eight-coordinate vanadium complexes, [PPh(4)][V(v)(HIDPA)(2)] and [PPh(4)][V(v)(HIDA)(2)]; HIDPA = 2,2'-(hydroxyimino)dipropionate and HIDA = 2,2'-(hydroxyimino)diacetate. The coordination geometry under examination is the less common non-oxo eight coordinate distorted dodecahedral geometry that has not been previously investigated by solid-state NMR spectroscopy. Both complexes were isolated by oxidizing their reduced forms: [V(iv)(HIDPA)(2)](2-) and [V(iv)(HIDA)(2)](2-). V(iv)(HIDPA)(2)(2-) is also known as amavadin, a vanadium-containing natural product present in the Amanita muscaria mushroom and is responsible for vanadium accumulation in nature. The quadrupolar coupling constants, C(Q), are found to be moderate, 5.0-6.4 MHz while the chemical shift anisotropies are relatively small for vanadium complexes, -420 and -360 ppm. The isotropic chemical shifts in the solid state are -220 and -228 ppm for the two compounds, and near the chemical shifts observed in solution. Presumably this is a consequence of the combined effects of the increased coordination number and the absence of oxo groups. Density functional theory calculations of the electric field gradient parameters are in good agreement with the NMR results while the chemical shift parameters show some deviation from the experimental values. Future work on this unusual coordination geometry and a combined analysis by solid-state NMR and density functional theory should provide a better understanding of the correlations between experimental NMR parameters and the local structure of the vanadium centers.
| S-EPMC4212903 | biostudies-literature