Unraveling liver complexity from molecular to organ level: challenges and perspectives.

Biological responses are determined by information processing at multiple and highly interconnected scales. Within a tissue the individual cells respond to extracellular stimuli by regulating intracellular signaling pathways that in turn determine cell fate decisions and influence the behavior of neighboring cells. As a consequence the cellular responses critically impact tissue composition and architecture. Understanding the regulation of these mechanisms at different scales is key to unravel the emergent properties of biological systems. In this perspective, a multidisciplinary approach combining experimental data with mathematical modeling is introduced. We report the approach applied within the Virtual Liver Network to analyze processes that regulate liver functions from single cell responses to the organ level using a number of examples. By facilitating interdisciplinary collaborations, the Virtual Liver Network studies liver regeneration and inflammatory processes as well as liver metabolic functions at multiple scales, and thus provides a suitable example to identify challenges and point out potential future application of multi-scale systems biology.

Impact of oxygen environment on mesenchymal stem cell expansion and chondrogenic differentiation.

INTRODUCTION: In vitro expansion and differentiation of mesenchymal stem cells (MSC) rely on specific environmental conditions, and investigations have demonstrated that one crucial factor is oxygen environment. OBJECTIVES: In order to understand the impact of oxygen tension on MSC culture and chondrogenic differentiation in vitro, we developed a mathematical model of these processes and applied it in predicting optimal assays. METHODS AND RESULTS: We compared ovine MSCs under physiologically low and atmospheric oxygen tension. Low oxygen tension improved their in vitro population growth as demonstrated by monoclonal expansion and colony forming assays. Moreover, it accelerated induction of the chondrogenic phenotype in subsequent three-dimensional differentiation cultures. We introduced a hybrid stochastic multiscale model of MSC organization in vitro. The model assumes that cell adaptation to non-physiological high oxygen tension reversibly changes the structure of MSC populations with respect to differentiation. In simulation series, we demonstrated that these changes profoundly affect chondrogenic potential of the populations. Our mathematical model provides a consistent explanation of our experimental findings. CONCLUSIONS: Our approach provides new insights into organization of MSC populations in vitro. The results suggest that MSC differentiation is largely reversible and that lineage plasticity is restricted to stem cells and early progenitors. The model predicts a significant impact of short-term low oxygen treatment on MSC differentiation and optimal chondrogenic differentiation at 10-11% pO(2).

Comparing the growth kinetics of cell populations in two and three dimensions.

We study the kinetics of growing cell populations by means of a kinetic Monte Carlo method. By applying the same growth mechanism to a two-dimensional (2D) and a three-dimensional (3D) model, and making direct comparison with experimental studies, we show that both models exhibit similar behavior. Based on this we propose a method for establishment of a mapping between the 2D and 3D results. Additionally, we present an analytic approach to obtain the time evolution, and show in case of the 3D model how synchronization effects can influence the growth kinetics. Finally, we compare the results of our models to experimental data of the growth kinetics of 2D monolayers and 3D NIH3T3 xenografts in mice.

Classifying the expansion kinetics and critical surface dynamics of growing cell populations.

We systematically study the growth kinetics and the critical surface dynamics of cell monolayers by a class of computationally efficient cellular automaton models avoiding lattice artifacts. Our numerically derived front velocity relationship indicates the limitations of the Fisher-Kolmogorov-Petrovskii-Piskounov equation for tumor growth simulations. The critical surface dynamics corresponds to the Kardar-Parisi-Zhang universality class, which disagrees with the interpretation by Bru et al. of their experimental observations as generic molecular-beam-epitaxy-like growth, questioning their conjecture that a successful therapy should lead away from molecular beam epitaxy.

Individual cell-based models of the spatial-temporal organization of multicellular systems--achievements and limitations.

Computational approaches of multicellular assemblies have reached a stage where they may contribute to unveil the processes that underlie the organization of tissues and multicellular aggregates. In this article, we briefly review and present some new results on a number of 3D lattice free individual cell-based mathematical models of epithelial cell populations. The models we consider here are parameterized by bio-physical and cell-biological quantities on the level of an individual cell. Eventually, they aim at predicting the dynamics of the biological processes on the tissue level. We focus on a number of systems, the growth of cell populations in vitro, and the spatial-temporal organization of regenerative tissues. For selected examples we compare different model approaches and show that the qualitative results are robust with respect to many model details. Hence, for the qualitative features and largely for the quantitative features many model details do not matter as long as characteristic biological features and mechanisms are correctly represented. For a quantitative prediction, the control of the bio-physical and cell-biological parameters on the molecular scale has to be known. At this point, slide-based cytometry may contribute. It permits to track the fate of cells and other tissue subunits in time and validated the organization processes predicted by the mathematical models.

Buckling instabilities of one-layered growing tissues.

Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and in a coarse grained analytical approach. The polarity of the one-layered tissue is considered by a bending term. Cell division gives rise to a locally increasing metric. An exponential and a power-law growth regime are identified. In both regimes, folding occurs as soon as the bending contribution becomes too small to compensate the destabilizing effect of the cell proliferation. The potential biological relevance is discussed.

Modeling the interplay of generic and genetic mechanisms in cleavage, blastulation, and gastrulation.

Early development of multicellular organisms is marked by a rapid initial increase in their cell numbers, accompanied by spectacular morphogenetic processes leading to the gradual formation of organs of characteristic shapes. During morphogenesis, through differentiation under strict genetic control, cells become more and more specialized. Morphogenesis also requires coordinated cell movement and elaborate interactions between cells, governed by fundamental physical or generic principles. As a consequence, early development must rely on an intricate interplay of generic and genetic mechanisms. We present the results of computer simulations of the first nontrivial morphogenetic transformations in the life of multicellular organisms: initial cleavages, blastula formation, and gastrulation. The same model, which is based on the physical properties of individual cells and their interactions, describes all these processes. The genetic code determines the values of the model parameters. The model accurately reproduces the major steps of early development. It predicts that physical constraints strongly influence the timing of gastrulation. Gastrulation must occur prior to the appearance of dynamical instability, which would destabilize and eventually derail normal development. Within our model, to avoid the instability, we suddenly change the values of some of the model parameters. We interpret this change as a consequence of specific gene activity. After changing the physical characteristics of some cells, normal development resumes, and gastrulation proceeds.

Scaling laws and similarity detection in sequence alignment with gaps.

We study the problem of similarity detection by sequence alignment with gaps, using a recently established theoretical framework based on the morphology of alignment paths. Alignments of sequences without mutual correlations are found to have scale-invariant statistics. This is the basis for a scaling theory of alignments of correlated sequences. Using a simple Markov model of evolution, we generate sequences with well-defined mutual correlations and quantify the fidelity of an alignment in an unambiguous way. The scaling theory predicts the dependence of the fidelity on the alignment parameters and on the statistical evolution parameters characterizing the sequence correlations. Specific criteria for the optimal choice of alignment parameters emerge from this theory. The results are verified by extensive numerical simulations.

A statistical theory of sequence alignment with gaps.

A statistical theory of local alignment algorithms with gaps is presented. Both the linear and logarithmic phases, as well as the phase transition separating the two phases, are described in a quantitative way. Markov sequences without mutual correlations are shown to have scale-invariant alignment statistics. Deviations from scale invariance indicate the presence of mutual correlations detectable by alignment algorithms. Conditions are obtained for the optimal detection of a class of mutual sequence correlations.

Solvation of platinum anti-cancer drugs in methanol-water mixtures.

Solubilities and transfer chemical potentials of carboplatin, cisplatin, iproplatin, and several related platinum complexes have been determined in methanol-water mixtures. The range of solvation behaviour is discussed in relation to possible oral administration of complexes of this type.

Solubilities and solvation of aluminum(III), iron(III), and indium(III) 8-hydroxyquinolinates in methanol/water mixtures.

Solubilities are reported for aluminum, indium, and iron(III) complexes of 8-hydroxyquinoline and its 5-nitro, 5-sulfonato, and 7-iodo-5-sulfonato derivatives in water, methanol, and water/methanol mixtures, at 298.2 K. Transfer chemical potentials for the respective complexes have been derived from these data, and their trends are discussed in terms of solvation of the complexes by water and methanol.