Heiko Rieger

Random Walks on Complex Networks

We investigate random walks on complex networks and derive an exact expression for the mean first-passage time (MFPT) between two nodes. We introduce for each node the random walk centrality C, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ensemble of random walkers moving on paradigmatic network models confirm this analytical prediction.

Calcium microdomains at the immunological synapse: how ORAI channels, mitochondria and calcium pumps generate local calcium signals for efficient T-cell activation

Cell polarization enables restriction of signalling into microdomains. Polarization of lymphocytes following formation of a mature immunological synapse (IS) is essential for calcium‐dependent T‐cell activation. Here, we analyse calcium microdomains at the IS with total internal reflection fluorescence microscopy. We find that the subplasmalemmal calcium signal following IS formation is sufficiently low to prevent calcium‐dependent inactivation of ORAI channels. This is achieved by localizing mitochondria close to ORAI channels. Furthermore, we find that plasma membrane calcium ATPases (PMCAs) are re‐distributed into areas beneath mitochondria, which prevented PMCA up‐modulation and decreased calcium export locally. This nano‐scale distribution—only induced following IS formation—maximizes the efficiency of calcium influx through ORAI channels while it decreases calcium clearance by PMCA, resulting in a more sustained NFAT activity and subsequent activation of T cells.

Vascular network remodeling via vessel cooption, regression and growth in tumors

The transformation of the regular vasculature in normal tissue into a highly inhomogeneous tumor specific capillary network is described by a theoretical model incorporating tumor growth, vessel cooption, neo-vascularization, vessel collapse and cell death. Compartmentalization of the tumor into several regions differing in vessel density, diameter and in necrosis is observed for a wide range of parameters in agreement with the vessel morphology found in human melanoma. In accord with data for human melanoma the model predicts that microvascular density (MVD), regarded as an important diagnostic tool in cancer treatment, does not necessarily determine the tempo of tumor progression. Instead it is suggested that the MVD of the original tissue as well as the metabolic demand of the individual tumor cell plays the major role in the initial stages of tumor growth.

Flow correlated percolation during vascular remodeling in growing tumors.

A theoretical model based on the molecular interactions between a growing tumor and a dynamically evolving blood vessel network describes the transformation of the regular vasculature in normal tissues into a highly inhomogeneous tumor specific capillary network. The emerging morphology, characterized by the compartmentalization of the tumor into several regions differing in vessel density, diameter, and necrosis, is in accordance with experimental data for human melanoma. Vessel collapse due to a combination of severely reduced blood flow and solid stress exerted by the tumor leads to a correlated percolation process that is driven towards criticality by the mechanism of hydrodynamic vessel stabilization.

Interstitial Fluid Flow and Drug Delivery in Vascularized Tumors: A Computational Model

Interstitial fluid is a solution that bathes and surrounds the human cells and provides them with nutrients and a way of waste removal. It is generally believed that elevated tumor interstitial fluid pressure (IFP) is partly responsible for the poor penetration and distribution of therapeutic agents in solid tumors, but the complex interplay of extravasation, permeabilities, vascular heterogeneities and diffusive and convective drug transport remains poorly understood. Here we consider–with the help of a theoretical model–the tumor IFP, interstitial fluid flow (IFF) and its impact upon drug delivery within tumor depending on biophysical determinants such as vessel network morphology, permeabilities and diffusive vs. convective transport. We developed a vascular tumor growth model, including vessel co-option, regression, and angiogenesis, that we extend here by the interstitium (represented by a porous medium obeying Darcys law) and sources (vessels) and sinks (lymphatics) for IFF. With it we compute the spatial variation of the IFP and IFF and determine its correlation with the vascular network morphology and physiological parameters like vessel wall permeability, tissue conductivity, distribution of lymphatics etc. We find that an increased vascular wall conductivity together with a reduction of lymph function leads to increased tumor IFP, but also that the latter does not necessarily imply a decreased extravasation rate: Generally the IF flow rate is positively correlated with the various conductivities in the system. The IFF field is then used to determine the drug distribution after an injection via a convection diffusion reaction equation for intra- and extracellular concentrations with parameters guided by experimental data for the drug Doxorubicin. We observe that the interplay of convective and diffusive drug transport can lead to quite unexpected effects in the presence of a heterogeneous, compartmentalized vasculature. Finally we discuss various strategies to increase drug exposure time of tumor cells.

Physical determinants of vascular network remodeling during tumor growth

Abstract.The process in which a growing tumor transforms a hierarchically organized arterio-venous blood vessel network into a tumor specific vasculature is analyzed with a theoretical model. The physical determinants of this remodeling involve the morphological and hydrodynamic properties of the initial network, generation of new vessels (sprouting angiogenesis), vessel dilation (circumferential growth), vessel regression, tumor cell proliferation and death, and the interdependence of these processes via spatio-temporal changes of blood flow parameters, oxygen/nutrient supply and growth factor concentration fields. The emerging tumor vasculature is non-hierarchical, compartmentalized into well-characterized zones, displays a complex geometry with necrotic zones and “hot spots” of increased vascular density and blood flow of varying size, and transports drug injections efficiently. Implications for current theoretical views on tumor-induced angiogenesis are discussed.

Two distinct secretory vesicle-priming steps in adrenal chromaffin cells

The calcium-dependent activator proteins for secretion, CAPS1 and CAPS2, facilitate syntaxin opening during synaptic vesicle priming.

NUMERICAL STUDY OF THE RANDOM TRANSVERSE-FIELD ISING SPIN CHAIN

We study numerically the critical region and the disordered phase of the random transverse-field Ising chain. By using a mapping of Lieb, Schultz, and Mattis to noninteracting fermions, we can obtain a numerically exact solution for rather large system sizes, L\ensuremath{\le}128. Our results confirm the striking predictions of earlier analytical work and, in addition, give results for some probability distributions and scaling functions. \textcopyright{} 1996 The American Physical Society.

Off-equilibrium dynamics in finite-dimensional spin-glass models.

The low-temperature dynamics of the two- and three-dimensional Ising spin-glass model with Gaussian couplings is investigated via extensive Monte Carlo simulations. We find an algebraic decay of the remanent magnetization. For the autocorrelation function C(t,

CRITICAL BEHAVIOR OF THE THREE-DIMENSIONAL RANDOM-FIELD ISING MODEL : TWO-EXPONENT SCALING AND DISCONTINUOUS TRANSITION

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