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Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles. Computer simulations based on Metropolis Monte Carlo (MMC) algorithms were successful in explaining and predicting the resulting stationary structures (corresponding to the lowest adhesion energy state). Here we present two alternatives to the MMC approach for modeling cellular motion and self-assembly: (1) a kinetic Monte Carlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC, both KMC and CPD methods are capable of simulating the dynamics of the cellular system in real time. In the KMC approach a transition rate is associated with possible rearrangements of the cellular system, and the corresponding time evolution is expressed in terms of these rates. In the CPD approach cells are modeled as interacting cellular particles (CPs) and the time evolution of the multicellular system is determined by integrating the equations of motion of all CPs. The KMC and CPD methods are tested and compared by simulating two experimentally well known phenomena: (1) cell-sorting within an aggregate formed by two types of cells with different adhesivities, and (2) fusion of two spherical aggregates of living cells., Comment: 11 pages, 7 figures; submitted to Phys Rev E

We report a high energy-resolution neutron backscattering study, combined with in-situ diffraction, to investigate slow molecular motions on nanosecond time scales in the fluid phase of phospholipid bilayers of 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine (DMPC) and DMPC/40% cholesterol (wt/wt). A cooperative structural relaxation process was observed. From the in-plane scattering vector dependence of the relaxation rates in hydrogenated and deuterated samples, combined with results from a 0.1 microsecond long all atom molecular dynamics simulation, it is concluded that correlated dynamics in lipid membranes occurs over several lipid distances, spanning a time interval from pico- to nanoseconds.

We use a long, all-atom molecular dynamics (MD) simulation combined with theoretical modeling to investigate the dynamics of selected lipid atoms and lipid molecules in a hydrated diyristoyl-phosphatidylcholine (DMPC) lipid bilayer. From the analysis of a 0.1 $\mu$s MD trajectory we find that the time evolution of the mean square displacement, [\delta{r}(t)]^2, of lipid atoms and molecules exhibits three well separated dynamical regions: (i) ballistic, with [\delta{r}(t)]^2 ~ t^2 for t < 10 fs; (ii) subdiffusive, with [\delta{r}(t)]^2 ~ t^{\beta} with \beta<1, for 10 ps < t < 10 ns; and (iii) Fickian diffusion, with [\delta{r}(t)]^2 ~ t for t > 30 ns. We propose a memory function approach for calculating [\delta{r}(t)]^2 over the entire time range extending from the ballistic to the Fickian diffusion regimes. The results are in very good agreement with the ones from the MD simulations. We also examine the implications of the presence of the subdiffusive dynamics of lipids on the self-intermediate scattering function and the incoherent dynamics structure factor measured in neutron scattering experiments., Comment: Submitted to Phys. Rev. E

Often gaining insight into the functioning of biomolecular systems requires to follow their dynamics along a microscopic reaction coordinate (RC) on a macroscopic time scale, which is beyond the reach of current all atom molecular dynamics (MD) simulations. A practical approach to this inherently multiscale problem is to model the system as a fictitious overdamped Brownian particle that diffuses along the RC in the presence of an effective potential of mean force (PMF) due to the rest of the system. By employing the recently proposed FR method [I. Kosztin et al., J. of Chem. Phys. 124, 064106 (2006)], which requires only a small number of fast nonequilibrium MD simulations of the system in both forward and time reversed directions along the RC, we reconstruct the PMF: (1) of deca-alanine as a function of its end-to-end distance, and (2) that guides the motion of potassium ions through the gramicidin A channel. In both cases the computed PMFs are found to be in good agreement with previous results obtained by different methods. Our approach appears to be about one order of magnitude faster than the other PMF calculation methods and, in addition, it also provides the position dependent diffusion coefficient along the RC. Thus, the obtained PMF and diffusion coefficient can be used in a suitable stochastic model to estimate important characteristics of the studied systems, e.g., the mean folding time of the stretched deca-alanine and the mean diffusion time of the potassium ion through gramicidin A., Comment: 10 pages, 10 figures, submitted to PRE

A distinguishing feature of a multicellular living system is that it operates at various scales, from the intracellular to organismal. Very little is known at present on how tissue level properties are related to cell and subcellular properties. Modern measurement techniques provide quantitative results at both the intracellular and tissue level, but not on the connection between these. In the present work we outline a framework to address this connection. We specifically concentrate on the morphogenetic process of tissue fusion, by following the coalescence of two contiguous multicellular aggregates. The time evolution of this process can accurately be described by the theory of viscous liquids. We also study fusion by Monte Carlo simulations and a novel Cellular Particle Dynamics (CPD) model, which is similar to the earlier introduced Subcellular Element Model (Newman, 2005). Using the combination of experiments, theory and modeling we are able to relate the measured tissue level biophysical quantities to subcellular parameters. Our approach has validity beyond the particular morphogenetic process considered here and provides a general way to relate biophysical properties across scales., Comment: 24 pages, 10 figures, To appear in Current Topics in Developmental Biology

The notion of tissue surface tension has provided a physical understanding of morphogenetic phenomena such as tissue spreading or cell sorting. The measurement of tissue surface tension so far relied on strong approximations on the geometric profile of a spherical droplet compressed between parallel plates. We solved the Laplace equation for this geometry and tested its solution on true liquids and embryonic tissue fragments as well as multicellular aggregates. The analytic solution provides the surface tension in terms of easily and accurately measurable geometric parameters. Experimental results show that the various tissues and multicellular aggregates studied here are incompressible and, similarly to true liquids, possess effective surface tensions that are independent of the magnitude of the compressive force and the volume of the droplet., Comment: 4 pages, 3 figures, submitted to Phys. Rev. Lett

A general approach for calculating spectral and optical properties of pigment-protein complexes of known atomic structure is presented. The method, that combines molecular dynamics simulations, quantum chemistry calculations and statistical mechanical modeling, is demonstrated by calculating the absorption and circular dichroism spectra of the B800-B850 BChls of the LH2 antenna complex from Rs. molischianum at room temperature. The calculated spectra are found to be in good agreement with the available experimental results. The calculations reveal that the broadening of the B800 band is mainly caused by the interactions with the polar protein environment, while the broadening of the B850 band is due to the excitonic interactions. Since it contains no fitting parameters, in principle, the proposed method can be used to predict optical spectra of arbitrary pigment-protein complexes of known structure., Comment: ReVTeX4, 11 pages, 9 figures, submitted to J. Chem. Phys

In general, the direct application of the Jarzynski equality (JE) to reconstruct potentials of mean force (PMFs) from a small number of nonequilibrium unidirectional steered molecular dynamics (SMD) paths is hindered by the lack of sampling of extremely rare paths with negative dissipative work. Such trajectories, that transiently violate the second law, are crucial for the validity of JE. As a solution to this daunting problem, we propose a simple and efficient method, referred to as the FR method, for calculating simultaneously both the PMF U(z) and the corresponding diffusion coefficient D(z) along a reaction coordinate z for a classical many particle system by employing a small number of fast SMD pullings in both forward (F) and time reverse (R) directions, without invoking JE. By employing Crook's transient fluctuation theorem (that is more general than JE) and the stiff spring approximation, we show that: (i) the mean dissipative work W_d in the F and R pullings are equal, (ii) both U(z) and W_d can be expressed in terms of the easily calculable mean work of the F and R processes, and (iii) D(z) can be expressed in terms of the slope of W_d. To test its viability, the FR method is applied to determine U(z) and D(z) of single-file water molecules in single-walled carbon nanotubes (SWNTs). The obtained U(z) is found to be in very good agreement with the results from other PMF calculation methods, e.g., umbrella sampling. Finally, U(z) and D(z) are used as input in a stochastic model, based on the Fokker-Planck equation, for describing water transport through SWNTs on a mesoscopic time scale that in general is inaccessible to MD simulations., Comment: ReVTeX4, 13 pages, 6 EPS figures, Submitted to Journal of Chemical Physics

Light harvesting complexes 2 (LH2) from Rhodospirillum (Rs.) molischianum and Rhodopseudomonas (Rps.) acidophila form ring complexes out of eight or nine identical subunits, respectively. Here, we investigate computationally what factors govern the different ring sizes. Starting from the crystal structure geometries, we embed two subunits of each species into their native lipid-bilayer/water environment. Using molecular dynamics simulations with umbrella sampling and steered molecular dynamics, we probe the free energy profiles along two reaction coordinates, the angle and the distance between two subunits. We find that two subunits prefer to arrange at distinctly different angles, depending on the species, at about 42.5 deg for Rs. molischianum and at about 38.5 deg for Rps. acidophila, which is likely to be an important factor contributing to the assembly into different ring sizes. Our calculations suggest a key role of surface contacts within the transmembrane domain in constraining these angles, whereas the strongest interactions stabilizing the subunit dimers are found in the C-, and to a lesser extent, N-terminal domains. The presented computational approach provides a promising starting point to investigate the factors contributing to the assembly of protein complexes, in particular if combined with modeling of genetic variants., Comment: 28 pages, 7 figures, LaTeX2e - requires elsart.cls (included), submitted to Chemical Physics

Channel proteins, that selectively conduct molecules across cell membranes, often exhibit an asymmetric structure. By means of a stochastic model, we argue that channel asymmetry in the presence of non-equilibrium fluctuations, fueled by the cell's metabolism as observed recently, can dramatically influence the transport through such channels by a ratchet-like mechanism. For an aquaglyceroporin that conducts water and glycerol we show that a previously determined asymmetric glycerol potential leads to enhanced inward transport of glycerol, but for unfavorably high glycerol concentrations also to enhanced outward transport that protects a cell against poisoning., Comment: REVTeX4, 4 pages, 3 figures; Accepted for publication in Phys. Rev. Lett

The dynamics of pigment-pigment and pigment-protein interactions in light-harvesting complexes is studied with a novel approach which combines molecular dynamics (MD) simulations with quantum chemistry (QC) calculations. The MD simulations of an LH-II complex, solvated and embedded in a lipid bilayer at physiological conditions (with total system size of 87,055 atoms) revealed a pathway of a water molecule into the B800 binding site, as well as increased dimerization within the B850 BChl ring, as compared to the dimerization found for the crystal structure. The fluctuations of pigment (B850 BChl) excitation energies, as a function of time, were determined via ab initio QC calculations based on the geometries that emerged from the MD simulations. From the results of these calculations we constructed a time-dependent Hamiltonian of the B850 exciton system from which we determined the linear absorption spectrum. Finally, a polaron model is introduced to describe quantum mechanically both the excitonic and vibrational (phonon) degrees of freedom. The exciton-phonon coupling that enters into the polaron model, and the corresponding phonon spectral function are derived from the MD/QC simulations. It is demonstrated that, in the framework of the polaron model, the absorption spectrum of the B850 excitons can be calculated from the autocorrelation function of the excitation energies of individual BChls, which is readily available from the combined MD/QC simulations. The obtained result is in good agreement with the experimentally measured absorption spectrum., Comment: REVTeX3.1, 23 pages, 13 (EPS) figures included. A high quality PDF file of the paper is available at http://www.ks.uiuc.edu/Publications/Papers/PDF/DAMJ2001/DAMJ2001.pdf

In the last few years evidence has been accumulating that there are a multiplicity of energy scales which characterize superconductivity in the underdoped cuprates. In contrast to the situation in BCS superconductors, the phase coherence temperature Tc is different from the energy gap onset temperature T*. In addition, thermodynamic and tunneling spectroscopies have led to the inference that the order parameter $\Delta_{sc}$ is to be distinguished from the excitation gap $\Delta$; in this way, pseudogap effects persist below Tc. It has been argued by many in the community that the presence of these distinct energy scales demonstrates that the pseudogap is unrelated to superconductivity. In this paper we show that this inference is incorrect. We demonstrate that the difference between the order parameter and excitation gap and the contrasting dependences of T* and Tc on hole concentration $x$ and magnetic field $H$ follow from a natural generalization of BCS theory. This simple generalized form is based on a BCS-like ground state, but with self consistently determined chemical potential in the presence of arbitrary attractive coupling $g$. We have applied this mean field theory with some success to tunneling, transport, thermodynamics and magnetic field effects. We contrast the present approach with the phase fluctuation scenario and discuss key features which might distinguish our precursor superconductivity picture from that involving a competing order parameter., Comment: 4 pages, 2 EPS figures, use LaTeX package espcrc2.sty from Elsevier, submitted to SNS'01 conference proceedings

In this paper we demonstrate how, using a natural generalization of BCS theory, superconducting phase coherence manifests itself in phase insensitive measurements, when there is a smooth evolution of the excitation gap \Delta from above to below Tc. In this context, we address the underdoped cuprates. Our premise is that just as Fermi liquid theory is failing above Tc, BCS theory is failing below. The order parameter \Delta_{sc} is different from the excitation gap \Delta. Equivalently there is a (pseudo)gap in the excitation spectrum above Tc which is also present in the underlying normal state of the superconducting phase, and can be directly inferred from specific heat and vortex core experiments. At the same time many features of BCS theory, e.g., fermionic quasiparticles below Tc, are clearly present. These observations can be reconciled by a natural extension of BCS theory, which includes finite center-of-mass momentum pair excitations, in addition to the usual fermionic quasiparticles. Applying this theory we find that the Bose condensation of Cooper pairs, which is reflected in \Delta_{sc}, leads to sharp peaks in the spectral function once $T \le T_c$. These are manifested in ARPES spectra as well as in specific heat jumps, which become more like the behavior in a \lambda transition as the pseudogap develops. We end with a discussion of tunneling experiments and condensation energy issues. Comparison between theoretical and experimental plots of C_v, and of tunneling and vortex core spectroscopy measurements is good., Comment: 12 pages, 8 figures, ReVTeX 3.1

On the basis of the observed short coherence lengths in the cuprates we argue that a BCS-Bose-Einstein condensation (BEC) crossover approach is an appropriate starting point for correcting the mean field approach of BCS and, thereby, for addressing pseudogap phenomena in these materials. Our version of the BCS-BEC approach is based on a particular Greens' function decoupling scheme which should be differentiated from others in the literature, and which yields (i) the Leggett crossover ground state (for all coupling constants g, at T=0) and (ii) BCS theory (for all $ T \leq T_c$ over a range of small g). In this paper we provide a simple physical picture of the pseudogap phase above and below $T_c$, and review the quantitative and qualitative implications of this theory, which, for the most part have been published in a series of recent papers., Comment: M2S-HTSC-VI conference paper, (4 pages, 1 figure), using Elsevier style espcrc2.sty

We explore a BCS Bose Einstein crossover scenario for $0 \leq T \leq T_c$ and its implications for the superfluid density and specific heat. The low lying excitations consist of nodal (fermionic) quasi-particles as well as excited (bosonic) pair states. Semi-quantitative comparison with cuprate data is reasonable, with no compelling indications for Landau parameter effects., Comment: M2S-HTSC-VI conference paper (2 pages, 1 figures), using Elsevier style espcrc2.sty

In this paper we present predictions for thermodynamic and transport properties of a BCS Bose-Einstein crossover theory, below Tc, which theory satisfies the reasonable constraints that it yield (i) the Leggett ground state and (ii) BCS theory at weak coupling and all temperatures. The nature of the strong coupling limit is inferred, along with the behavior of the Knight shift, superfluid density, and specific heat. Comparisons with existing data on short coherence length superconductors, such as organic and high Tc systems, are presented, which provide some support for the present picture., Comment: REVTeX 3.1, 4 pages, 3 EPS figures, significant revisions, to appear in PRL

In this paper we study the BCS Bose Einstein condensation (BEC) crossover scenario within the superconducting state, using a T-matrix approach which yields the ground state proposed by Leggett. Here we extend this ground state analysis to finite temperatures T and interpret the resulting physics. We find two types of bosonic-like excitations of the system: long lived, incoherent pair excitations and collective modes of the superconducting order parameter, which have different dynamics. Using a gauge invariant formalism, this paper addresses their contrasting behavior as a function of T and superconducting coupling constant g. At a more physical level, our paper emphasizes how, at finite T, BCS-BEC approaches introduce an important parameter \Delta^2_{pg} = \Delta^2 - \Delta_{sc}^2 into the description of superconductivity. This parameter is governed by the pair excitations and is associated with particle-hole asymmetry effects which are important for sufficiently large g. In the fermionic regime, \Delta_{pg}^2 represents the difference between the square of the excitation gap \Delta^2 and that of the superconducting order parameter \Delta_{sc}^2. The parameter \Delta_{pg}^2, which is necessarily zero in the BCS (mean field) limit increases monotonically with the strength of the attractive interaction g. It follows that there is a significant physical distinction between this BCS-BEC crossover approach (in which g is the essential variable which determines \Delta_{pg}) and the widely discussed (Coulomb-modulated) phase fluctuation scenario in which the plasma frequency is the tuning parameter., Comment: RevTeX3.x, 22 pages, 6 EPS figures (included)

We argue that incoherent pair tunneling in a cuprate superconductor junction with an optimally doped superconducting and an underdoped normal lead can be used to detect the presence of pairing correlations in the pseudogap phase of the underdoped lead. We estimate that the junction characteristics most suitable for studying the pair tunneling current are close to recently manufactured cuprate tunneling devices., Comment: ReVTeX 3.1; 4 pages, 2 EPS figures (included)

We propose a theoretical description of the superconducting state of under- to overdoped cuprates, based on the short coherence length of these materials and the associated strong pairing fluctuations. The calculated $T_c$ and the zero temperature excitation gap $\Delta(0)$, as a function of hole concentration $x$, are in semi-quantitative agreement with experiment. Although the ratio $T_c/\Delta(0)$ has a strong $x$ dependence, different from the universal BCS value, and $\Delta(T)$ deviates significantly from the BCS prediction, we obtain, quite remarkably, quasi-universal behavior, for the normalized superfluid density $\rho_s(T)/\rho_s(0)$ and the Josephson critical current $I_c(T)/I_c(0)$, as a function of $T/T_c$. While experiments on $\rho_s(T)$ are consistent with these results, future measurements on $I_c(T)$ are needed to test this prediction., Comment: 4 pages, 3 figures, REVTeX, submitted to Phys. Rev. Lett

The existence of a normal state spectral gap in underdoped cuprates raises important questions about the associated superconducting phase. For example, how does this pseudogap evolve into its below Tc counterpart? In this paper we characterize this unusual superconductor by investigating the nature of the ``residual'' pseudogap below Tc and, find that it leads to an important distinction between the superconducting excitation gap and order parameter. Our approach is based on a conserving diagrammatic BCS Bose-Einstein crossover theory which yields the precise BCS result in weak coupling at any T

We investigate the behavior of the superconducting transition temperature within a previously developed BCS-Bose Einstein crossover picture. This picture, based on a decoupling scheme of Kadanoff and Martin, further extended by Patton, can be used to derive a simple form for the superconducting transition temperature in the presence of a pseudogap. We extend previous work which addressed the case of s-wave pairing in jellium, to explore the solutions for T_c as a function of variable coupling in more physically relevant situations. We thereby ascertain the effects of reduced dimensionality, periodic lattices and a d-wave pairing interaction. Implications for the cuprate superconductors are discussed., Comment: REVTeX, 11 pages, 6 EPS figures included, Replace with published version

A new method for calculating the free energy of an inhomogeneous superconductor is presented. This method is based on the quasiclassical limit (or Andreev approximation) of the Bogoliubov-de Gennes (or wave function) formulation of the theory of weakly coupled superconductors. The method is applicable to any pure bulk superconductor described by a pair potential with arbitrary spatial dependence, in the presence of supercurrents and external magnetic field. We find that both the local density of states and the free energy density of an inhomogeneous superconductor can be expressed in terms of the diagonal resolvent of the corresponding Andreev Hamiltonian, resolvent which obeys the so-called Gelfand-Dikii equation. Also, the connection between the well known Eilenberger equation for the quasiclassical Green's function and the less known Gelfand-Dikii equation for the diagonal resolvent of the Andreev Hamiltonian is established. These results are used to construct a general algorithm for calculating the (gauge invariant) gradient expansion of the free energy density of an inhomogeneous superconductor at arbitrary temperatures., Comment: REVTeX, 28 pages

We show that, under certain conditions, the low temperature behavior of the magnetic penetration depth $\lambda(T)$ of a pure d-wave superconductor is determined by nonlocal electrodynamics and, contrary to the general belief, the deviation $\Delta\lambda(T) = \lambda(T)-\lambda(0)$ is proportional to T^2 and not T. We predict that the $\Delta\lambda(T)\propto T^2$ dependence, due to nonlocality, should be observable experimentally in nominally clean high-T_c superconductors below a crossover temperature $T^* = (\xi_o/\lambda_o)\Delta_o \sim 1 K$. Possible complications due to impurities, surface quality and crystal axes orientation are discussed., Comment: REVTeX3.0; 4 pages, 1 EPS figure (included); Submitted to Phys. Rev. Lett

A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H2+ ion and of the H2 molecule. A computer program on which the sample calculations are based is available upon request., Comment: RevTeX 3.0, 14 pages, 8 EPS figures (included)

The boundary integral method for calculating the stationary states of a quantum particle in nano-devices and quantum billiards is presented in detail at an elementary level. According to the method, wave functions inside the domain of the device or billiard are expressed in terms of line integrals of the wave function and its normal derivative along the domain's boundary; the respective energy eigenvalues are obtained as the roots of Fredholm determinants. Numerical implementations of the method are described and applied to determine the energy level statistics of billiards with circular and stadium shapes and demonstrate the quantum mechanical characteristics of chaotic motion. The treatment of other examples as well as the advantages and limitations of the boundary integral method are discussed., Comment: RevTeX3.0, 24 pages, 9 EPS figures (included); To be published in Int. J. of Mod. Phys. C

A new type of classical billiard - the Andreev billiard - is investigated using the tangent map technique. Andreev billiards consist of a normal region surrounded by a superconducting region. In contrast with previously studied billiards, Andreev billiards are integrable in zero magnetic field, {\it regardless of their shape}. A magnetic field renders chaotic motion in a generically shaped billiard, which is demonstrated for the Bunimovich stadium by examination of both Poincar\'e sections and Lyapunov exponents. The issue of the feasibility of certain experimental realizations is addressed., Comment: ReVTeX3.0, 4 pages, 3 figures appended as postscript file (uuencoded with uufiles)