Kinetic Monte Carlo and Cellular Particle Dynamics Simulations of Multicellular Systems

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

Analysis of Transient Processes in a Radiophysical Flow System

Transient processes in a third-order radiophysical flow system are studied and a map of the transient process duration versus initial conditions is constructed and analyzed. The results are compared to the arrangement of submanifolds of the stable and unstable cycles in the Poincare section of the system studied.Comment: 3 pages, 2 figure

Statistics of extremal intensities for Gaussian interfaces

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not coincide with the distribution of the integrated power spectrum (i.e. roughness of the surface), nor does it obey any of the known extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit distribution is, however, recovered in three cases: (i) in the non-dispersive (white noise) limit, (ii) for high dimensions, and (iii) when only short-wavelength modes are kept. In the last two cases the limit distribution emerges in novel scenarios.Comment: 15 pages, including 7 ps figure

Symmetries and Fixed Point Stability of Stochastic Differential Equations Modeling Self-Organized Criticality

A stochastic nonlinear partial differential equation is built for two different models exhibiting self-organized criticality, the Bak, Tang, and Wiesenfeld (BTW) sandpile model and the Zhang's model. The dynamic renormalization group (DRG) enables to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.Comment: 19 pages, RevTex, includes 6 PostScript figures, Phys. Rev. E (March 97?

Lovastatin sensitized human glioblastoma cells to TRAIL-induced apoptosis

Synergy study with chemotherapeutic agents is a common in vitro strategy in the search for effective cancer therapy. For non-chemotherapeutic agents, efficacious synergistic effects are uncommon. Here, we have examined two non-chemotherapeutic agents for synergistic effects: lovastatin and Tumor Necrosis Factor (TNF)-related apoptosis-inducing ligand (TRAIL) for synergistic effects; on three human malignant glioblastoma cell lines, M059K, M59J, and A172. Cells treated with lovastatin plus TRAIL for 48 h showed 50% apoptotic cell death, whereas TRAIL alone (1,000 ng/ml) did not, suggesting that lovastatin sensitized the glioblastoma cells to TRAIL attack. Cell cycle analysis indicated that lovastatin increased G0–G1 arrest in these cells. Annexin V study demonstrated that apoptosis was the predominant mode of cell death. We conclude that the combination of lovastatin and TRAIL enhances apoptosis synergistically. Moreover, lovastatin sensitized glioblastoma cells to TRAIL, suggesting a new strategy to treat glioblastoma

Effect of nonstationarities on detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy'', heterogeneous and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts -- a ``cutting'' procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitude, and (iii) generating a signal comprised of segments with different properties -- e.g. different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities.Comment: 17 pages, 10 figures, corrected some typos, added one referenc