Growing tissues: A simulation study

Tissues represent an interesting type of matter: active matter. The basic elements of tissues, the cells, divide or die, consume energy on the scale of their constituents, exert forces onto their surrounding and dissipate energy, which results in non-equilibrium systems. Tissue growth is involved in many biological processes and understanding its generic phenomena is, thus, not only important from a physical point of view. In this thesis, we are interested in the mechanics of issue growth in the context of the homeostatic pressure theory. The homeostatic pressure is defined as the pressure that has to be exerted onto a tissue, growing in a biochemically constant environment, in order to balance cell division and cell death. However, experimental observations show that tissue growth is dominated by surface effects in the sense that high division rates at the surface can compensate for an on average dying core. Thus, the homeostatic pressure is better defined as a bulk property. We study the growth with a negative homeostatic pressure, which means that without the surface growth effect such a tissue has to be kept under tension to ensure a stable steady state. A mesoscale simulation technique is used, where individual cells are represented by two point particles, interacting like soft sticky spheres. Growth is modeled by a force that repels the particles of one cell until new particles are introduced, when the cell reaches a certain size. Additionally, DPD like interactions and a constant rate of cell death concludes the active part. This approach is used to explore the dependence of the homeostatic pressure on different model parameters. Additionally, we measure the bulk growth rates of tissue spheroids under different mechanical stresses and compare our results to the data of in vitro experiments of tissue spheroids under pressure. We fit the simulations to this experimental data and extract a homeostatic pressure of the order of -1 to -2kPa. Furthermore, we find a new tissue state: a tensile membrane. In this state, the tissue forms a relatively thin sheet, where a characteristic tension develops for tissues with a negative homeostatic pressure. It is sustained by growth at the surface and death in the bulk. In addition, we study the interface dynamics of two competing tissues with a homeostatic pressure difference. In the theory of homeostatic pressure, this difference leads to a take-over of the tissue with the higher homeostatic pressure. Starting from a theoretical point of view, we solve the dynamics for the one dimensional problem without diffusion and find the interface to propagate at a constant velocity. We use the same simulation technique as above to study the interface dynamics in two dimensions and compare our results to the analytical solution. The dependence of the interface velocity on the homeostatic pressure difference between the tissues as well as the predicted stress profiles match well with the simulations. Furthermore, we analyze the scaling behavior of the interface width w, which develops initially as a power law w~t^beta and saturates depending on the system size L for later times w_sat~L^alpha. We find a growth exponent beta=0.4 and a roughness exponent alpha=0.25. While the growth exponent roughly fits into the KPZ universality class, the measured roughness exponent is substantially smaller. At last, we study divisional alignment in expanding monolayered cell sheets. We extend the simulations with a previously established motility mechanism and compare the results to the experimental data of MDCK cell sheets that invade narrow microchannels. In the experiments, we find a strong correlation between the division orientation and the emergent flow. However, cell division correlates best with the main axis of the strain rate tensor, which is related to the main axis of the stress tensor. This supports the notion that divisions are aligned by the local stress as opposed to the local velocity. Apart from boundary phenomena and a surprising flow of cells perpendicular to the main migration direction, the simulations are able to reproduce the experimentally observed quantities very well

Quantum information analysis of electronic states at different molecular structures

We have studied transition metal clusters from a quantum information theory perspective using the density-matrix renormalization group (DMRG) method. We demonstrate the competition between entanglement and interaction localization. We also discuss the application of the configuration interaction based dynamically extended active space procedure which significantly reduces the effective system size and accelerates the speed of convergence for complicated molecular electronic structures to a great extent. Our results indicate the importance of taking entanglement among molecular orbitals into account in order to devise an optimal orbital ordering and carry out efficient calculations on transition metal clusters. We propose a recipe to perform DMRG calculations in a black-box fashion and we point out the connections of our work to other tensor network state approaches

Replacement of the Cobalt Center of Vitamin B 12 by Nickel: Nibalamin and Nibyric Acid Prepared from Metal‐Free B 12 Ligands Hydrogenobalamin and Hydrogenobyric Acid

The (formal) replacement of Co in cobalamin (Cbl) by NiII generates nibalamin (Nibl), a new transition‐metal analogue of vitamin B12. Described here is Nibl, synthesized by incorporation of a NiII ion into the metal‐free B12 ligand hydrogenobalamin (Hbl), itself prepared from hydrogenobyric acid (Hby). The related NiII corrin nibyric acid (Niby) was similarly synthesized from Hby, the metal‐free cobyric acid ligand. The solution structures of Hbl, and Niby and Nibl, were characterized by spectroscopic studies. Hbl features two inner protons bound at N2 and N4 of the corrin ligand, as discovered in Hby. X‐ray analysis of Niby shows the structural adaptation of the corrin ligand to NiII ions and the coordination behavior of NiII. The diamagnetic Niby and Nibl, and corresponding isoelectronic CoI corrins, were deduced to be isostructural. Nibl is a structural mimic of four‐coordinate base‐off Cbls, as verified by its ability to act as a strong inhibitor of bacterial adenosyltransferase

Spin in Density-Functional Theory

The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. While density-functional theory (DFT) is widely applied in this area, the sometimes severe limitations of its currently available approximate realizations often preclude its application as a predictive theory. Here, we review the foundations of DFT applied to open-shell systems, both within the nonrelativistic and the relativistic framework. In particular, we provide an in-depth discussion of the exact theory, with a focus on the role of the spin density and possibilities for targeting specific spin states. It turns out that different options exist for setting up Kohn-Sham DFT schemes for open-shell systems, which imply different definitions of the exchange-correlation energy functional and lead to different exact conditions on this functional. Finally, we suggest some possible directions for future developments

Accurate ab initio spin densities

We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys. 2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insights into chemically interesting features of the molecule under study such as the distribution of $\alpha$- and $\beta$-electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput. 2011, 7, 2740].Comment: 37 pages, 13 figure

Solution, Crystal and in Silico Structures of the Organometallic Vitamin B 12 ‐Derivative Acetylcobalamin and of its Novel Rhodium‐Analogue Acetylrhodibalamin

The natural vitamin B12‐derivatives are intriguing complexes of cobalt that entrap the metal within the strikingly skewed and ring‐contracted corrin ligand. Here, we describe the synthesis of the Rh(III)‐corrin acetylrhodibalamin (AcRhbl) from biotechnologically produced metal‐free hydrogenobyric acid and analyze the effect of the replacement of the cobalt‐center of the organometallic vitamin B12‐derivative acetylcobalamin (AcCbl) with its group‐IX homologue rhodium, to give AcRhbl. The structures of AcCbl and AcRhbl were thoroughly analyzed in aqueous solution, in crystals and by in silico methods, in order to gain detailed insights into the structural adaptations to the two homologous metals. Indeed, the common, nucleotide‐appended corrin‐ligand in these two metal corrins features extensive structural similarity. Thus, the rhodium‐corrin AcRhbl joins the small group of B12‐mimics classified as ‘antivitamins B12’, isostructural metal analogues of the natural cobalt‐corrins that hold significant potential in biological and biomedical applications as selective inhibitors of key cellular processes

Zinc Substitution of Cobalt in Vitamin B12: Zincobyric acid and Zincobalamin as Luminescent Structural B12-Mimics

Replacing the central cobalt ion of vitamin B12 by other metals has been a long‐held aspiration within the B12‐field. Herein, we describe the synthesis from hydrogenobyric acid of zincobyric acid (Znby) and zincobalamin (Znbl), the Zn‐analogues of the natural cobalt‐corrins cobyric acid and vitamin B12, respectively. The solution structures of Znby and Znbl were studied by NMR‐spectroscopy. Single crystals of Znby were produced, providing the first X‐ray crystallographic structure of a zinc corrin. The structures of Znby and of computationally generated Znbl were found to resemble the corresponding CoII‐corrins, making such Zn‐corrins potentially useful for investigations of B12‐dependent processes. The singlet excited state of Znby had a short life‐time, limited by rapid intersystem crossing to the triplet state. Znby allowed the unprecedented observation of a corrin triplet (ET=190 kJ mol−1) and was found to be an excellent photo‐sensitizer for 1O2 (ΦΔ=0.70)

The Hydrogenobyric Acid Structure Reveals the Corrin Ligand as an Entatic State Module Empowering B12‐Cofactors for Catalysis

The B12 cofactors instill a natural curiosity regarding the primordial selection and evolution of their corrin ligand. Surprisingly, this important natural macrocycle has evaded molecular scrutiny, and its specific role in predisposing the incarcerated cobalt-ion for organometallic catalysis has remained obscure. Herein, we report the biosynthesis of the cobalt-free B12 corrin moiety, hydrogenobyric acid (Hby), a compound crafted through pathway redesign. Detailed insights from single crystal X-ray and solution structures of Hby have revealed a distorted helical cavity, redefining the pattern for binding cobalt-ions. Consequently, the corrin ligand coordinates cobalt-ions in de-symmetrized ‘entatic’ states, thereby promoting the activation of B12-cofactors for their challenging chemical transitions. The availability of Hby also provides a route to the synthesis of transition metal analogs of B12