Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix.

The mechanical interaction between cells and the extracellular matrix (ECM) is fundamental to coordinate collective cell behavior in tissues. Relating individual cell-level mechanics to tissue-scale collective behavior is a challenge that cell-based models such as the cellular Potts model (CPM) are well-positioned to address. These models generally represent the ECM with mean-field approaches, which assume substrate homogeneity. This assumption breaks down with fibrous ECM, which has nontrivial structure and mechanics. Here, we extend the CPM with a bead-spring model of ECM fiber networks modeled using molecular dynamics. We model a contractile cell pulling with discrete focal adhesion-like sites on the fiber network and demonstrate agreement with experimental spatiotemporal fiber densification and displacement. We show that at high network cross-linking, contractile cell forces propagate over at least eight cell diameters, decaying with distance with power law exponent n= 0.35 - 0.65 typical of viscoelastic ECMs. Further, we use in silico atomic force microscopy to measure local cell-induced network stiffening consistent with experiments. Our model lays the foundation for investigating how local and long-ranged cell-ECM mechanobiology contributes to multicellular morphogenesis.

Scaling relations for auxin waves.

We analyze an 'up-the-gradient' model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show that this model admits a family of travelling wave solutions that is parameterized by the height of the auxin-pulse. We uncover scaling relations for the speed and width of these waves and verify these rigorous results with numerical computations. In addition, we provide explicit expressions for the leading-order wave profiles, which allows the influence of the biological parameters in the problem to be readily identified. Our proofs are based on a generalization of the scaling principle developed by Friesecke and Pego to construct pulse solutions to the classic Fermi-Pasta-Ulam-Tsingou model, which describes a one-dimensional chain of coupled nonlinear springs.

A caged lanthanide complex as a paramagnetic shift agent for protein NMR.

A lanthanide complex, named CLaNP (caged lanthanide NMR probe) has been developed for the characterisation of proteins by paramagnetic NMR spectroscopy. The probe consists of a lanthanide chelated by a derivative of DTPA (diethylenetriaminepentaacetic acid) with two thiol reactive functional groups. The CLaNP molecule is attached to a protein by two engineered, surface-exposed, Cys residues in a bidentate manner. This drastically limits the dynamics of the metal relative to the protein and enables measurements of pseudocontact shifts. NMR spectroscopy experiments on a diamagnetic control and the crystal structure of the probe-protein complex demonstrate that the protein structure is not affected by probe attachment. The probe is able to induce pseudocontact shifts to at least 40 A from the metal and causes residual dipolar couplings due to alignment at a high magnetic field. The molecule exists in several isomeric forms with different paramagnetic tensors; this provides a fast way to obtain long-range distance restraints.