113 research outputs found
Are the energy and virial routes to thermodynamics equivalent for hard spheres?
The internal energy of hard spheres (HS) is the same as that of an ideal gas,
so that the energy route to thermodynamics becomes useless. This problem can be
avoided by taking an interaction potential that reduces to the HS one in
certain limits. In this paper the square-shoulder (SS) potential characterized
by a hard-core diameter , a soft-core diameter and a
shoulder height is considered. The SS potential becomes the HS one
if (i) , or (ii) , or (iii)
or (iv) and . The
energy-route equation of state for the HS fluid is obtained in terms of the
radial distribution function for the SS fluid by taking the limits (i) and
(ii). This equation of state is shown to exhibit, in general, an artificial
dependence on the diameter ratio . If furthermore the limit
is taken, the resulting equation of state for HS
coincides with that obtained through the virial route. The necessary and
sufficient condition to get thermodynamic consistency between both routes for
arbitrary is derived.Comment: 10 pages, 4 figures; v2: minor changes; to be published in the
special issue of Molecular Physics dedicated to the Seventh Liblice
Conference on the Statistical Mechanics of Liquids (Lednice, Czech Republic,
June 11-16, 2006
Phase coexistence of cluster crystals: beyond the Gibbs phase rule
We report a study of the phase behavior of multiple-occupancy crystals
through simulation. We argue that in order to reproduce the equilibrium
behavior of such crystals it is essential to treat the number of lattice sites
as a constraining thermodynamic variable. The resulting free-energy
calculations thus differ considerably from schemes used for single-occupancy
lattices. Using our approach, we obtain the phase diagram and the bulk modulus
for a generalized exponential model that forms cluster crystals at high
densities. We compare the simulation results with existing theoretical
predictions. We also identify two types of density fluctuations that can lead
to two sound modes and evaluate the corresponding elastic constants.Comment: 4 pages, 3 figure
Procedure to construct a multi-scale coarse-grained model of DNA-coated colloids from experimental data
We present a quantitative, multi-scale coarse-grained model of DNA coated
colloids. The parameters of this model are transferable and are solely based on
experimental data. As a test case, we focus on nano-sized colloids carrying
single-stranded DNA strands of length comparable to the colloids' size. We show
that in this regime, the common theoretical approach of assuming pairwise
additivity of the colloidal pair interactions leads to quantitatively and
sometimes even qualitatively wrong predictions of the phase behaviour of
DNA-grafted colloids. Comparing to experimental data, we find that our
coarse-grained model correctly predicts the equilibrium structure and melting
temperature of the formed solids. Due to limited experimental information on
the persistence length of single-stranded DNA, some quantitative discrepancies
are found in the prediction of spatial quantities. With the availability of
better experimental data, the present approach provides a path for the rational
design of DNA-functionalised building blocks that can self-assemble in complex,
three-dimensional structures.Comment: 17 pages, 10 figures; to be published in Soft Matte
Thermodynamically self-consistent liquid state theories for systems with bounded potentials
The mean spherical approximation (MSA) can be solved semi-analytically for
the Gaussian core model (GCM) and yields - rather surprisingly - exactly the
same expressions for the energy and the virial equations. Taking advantage of
this semi-analytical framework, we apply the concept of the self-consistent
Ornstein-Zernike approximation (SCOZA) to the GCM: a state-dependent function K
is introduced in the MSA closure relation which is determined to enforce
thermodynamic consistency between the compressibility route and either the
virial or energy route. Utilizing standard thermodynamic relations this leads
to two different differential equations for the function K that have to be
solved numerically. Generalizing our concept we propose an
integro-differential-equation based formulation of the SCOZA which, although
requiring a fully numerical solution, has the advantage that it is no longer
restricted to the availability of an analytic solution for a particular system.
Rather it can be used for an arbitrary potential and even in combination with
other closure relations, such as a modification of the hypernetted chain
approximation.Comment: 11 pages, 11 figures, submitted to J. Chem. Phy
Lane-formation vs. cluster-formation in two dimensional square-shoulder systems: A genetic algorithm approach
Introducing genetic algorithms as a reliable and efficient tool to find
ordered equilibrium structures, we predict minimum energy configurations of the
square shoulder system for different values of corona width . Varying
systematically the pressure for different values of we obtain
complete sequences of minimum energy configurations which provide a deeper
understanding of the system's strategies to arrange particles in an
energetically optimized fashion, leading to the competing self-assembly
scenarios of cluster-formation vs. lane-formation.Comment: 5 pages, 6 figure
Quantitative prediction of the phase diagram of DNA-functionalized nano-colloids
We present a coarse-grained model of DNA-functionalized colloids that is
computationally tractable. Importantly, the model parameters are solely based
on experimental data. Using this highly simplified model, we can predict the
phase behavior of DNA-functionalized nano-colloids without assuming pairwise
additivity of the inter-colloidal interactions. Our simulations show that for
nano-colloids, the assumption of pairwise additivity leads to substantial
errors in the estimate of the free energy of the crystal phase. We compare our
results with available experimental data and find that the simulations predict
the correct structure of the solid phase and yield a very good estimate of the
melting temperature. Current experimental estimates for the contour length and
persistence length of single-stranded DNA sequences are subject to relatively
large uncertainties. Using the best available estimates, we obtain predictions
for the crystal lattice constants that are off by a few percent: this indicates
that more accurate experimental data on ssDNA are needed to exploit the full
power of our coarse-grained approach.Comment: 4 pages, 2 figures; accepted for publication in Phys. Rev. Let
Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory
We demonstrate the accuracy of the hypernetted chain closure and of the
mean-field approximation for the calculation of the fluid-state properties of
systems interacting by means of bounded and positive-definite pair potentials
with oscillating Fourier transforms. Subsequently, we prove the validity of a
bilinear, random-phase density functional for arbitrary inhomogeneous phases of
the same systems. On the basis of this functional, we calculate analytically
the freezing parameters of the latter. We demonstrate explicitly that the
stable crystals feature a lattice constant that is independent of density and
whose value is dictated by the position of the negative minimum of the Fourier
transform of the pair potential. This property is equivalent with the existence
of clusters, whose population scales proportionally to the density. We
establish that regardless of the form of the interaction potential and of the
location on the freezing line, all cluster crystals have a universal Lindemann
ratio L = 0.189 at freezing. We further make an explicit link between the
aforementioned density functional and the harmonic theory of crystals. This
allows us to establish an equivalence between the emergence of clusters and the
existence of negative Fourier components of the interaction potential. Finally,
we make a connection between the class of models at hand and the system of
infinite-dimensional hard spheres, when the limits of interaction steepness and
space dimension are both taken to infinity in a particularly described fashion.Comment: 19 pages, 5 figures, submitted to J. Chem. Phys; new version: minor
changes in structure of pape
Generation of defects and disorder from deeply quenching a liquid to form a solid
We show how deeply quenching a liquid to temperatures where it is linearly
unstable and the crystal is the equilibrium phase often produces crystalline
structures with defects and disorder. As the solid phase advances into the
liquid phase, the modulations in the density distribution created behind the
advancing solidification front do not necessarily have a wavelength that is the
same as the equilibrium crystal lattice spacing. This is because in a deep
enough quench the front propagation is governed by linear processes, but the
crystal lattice spacing is determined by nonlinear terms. The wavelength
mismatch can result in significant disorder behind the front that may or may
not persist in the latter stage dynamics. We support these observations by
presenting results from dynamical density functional theory calculations for
simple one- and two-component two-dimensional systems of soft core particles.Comment: 25 pages, 11 figure
Synthesis and Quantitative Structure–Activity Relationship of Imidazotetrazine Prodrugs with Activity Independent of O6-Methylguanine-DNA-methyltransferase, DNA Mismatch Repair and p53.
The antitumor prodrug Temozolomide is compromised by its dependence for activity on DNA mismatch repair (MMR) and the repair of the chemosensitive DNA lesion, O6-methylguanine (O6-MeG), by O6-methylguanine-DNA-methyltransferase (EC 2.1.1.63, MGMT). Tumor response is also dependent on wild-type p53. Novel 3-(2-anilinoethyl)-substituted imidazotetrazines are reported that have activity independent of MGMT, MMR and p53. This is achieved through a switch of mechanism so that bioactivity derives from imidazotetrazine-generated arylaziridinium ions that principally modify guanine-N7 sites on DNA. Mono- and bi-functional analogs are reported and a quantitative structure-activity relationship (QSAR) study identified the p-tolyl-substituted bi-functional congener as optimized for potency, MGMT-independence and MMR-independence. NCI60 data show the tumor cell response is distinct from other imidazotetrazines and DNA-guanine-N7 active agents such as nitrogen mustards and cisplatin. The new imidazotetrazine compounds are promising agents for further development and their improved in vitro activity validates the principles on which they were designed
Integrated mapping of pharmacokinetics and pharmacodynamics in a patient-derived xenograft model of glioblastoma
Therapeutic options for the treatment of glioblastoma remain inadequate despite concerted research efforts in drug development. Therapeutic failure can result from poor permeability of the blood-brain barrier, heterogeneous drug distribution, and development of resistance. Elucidation of relationships among such parameters could enable the development of predictive models of drug response in patients and inform drug development. Complementary analyses were applied to a glioblastoma patient-derived xenograft model in order to quantitatively map distribution and resulting cellular response to the EGFR inhibitor erlotinib. Mass spectrometry images of erlotinib were registered to histology and magnetic resonance images in order to correlate drug distribution with tumor characteristics. Phosphoproteomics and immunohistochemistry were used to assess protein signaling in response to drug, and integrated with transcriptional response using mRNA sequencing. This comprehensive dataset provides simultaneous insight into pharmacokinetics and pharmacodynamics and indicates that erlotinib delivery to intracranial tumors is insufficient to inhibit EGFR tyrosine kinase signaling.National Institutes of Health (U.S.) (U54 CA210180)MIT/Mayo Physical Sciences Center for Drug Distribution and Drug Efficacy in Brain TumorsDana-Farber Cancer Institute (PLGA Fund)Lundbeck FoundationNovo Nordisk Foundatio
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