The role of dimerisation and nuclear transport in the Hes1 gene regulatory network

Hes1 is a member of the family of basic helix-loop-helix transcription factors and the Hes1 gene regulatory network (GRN) may be described as the canonical example of transcriptional control in eukaryotic cells, since it involves only the Hes1 protein and its own mRNA. Recently, the Hes1 protein has been established as an excellent target for an anti-cancer drug treatment, with the design of a small molecule Hes1 dimerisation inhibitor representing a promising if challenging approach to therapy. In this paper, we extend a previous spatial stochastic model of the Hes1 GRN to include nuclear transport and dimerisation of Hes1 monomers. Initially, we assume that dimerisation occurs only in the cytoplasm, with only dimers being imported into the nucleus. Stochastic simulations of this novel model using the URDME software show that oscillatory dynamics in agreement with experimental studies are retained. Furthermore, we find that our model is robust to changes in the nuclear transport and dimerisation parameters. However, since the precise dynamics of the nuclear import of Hes1 and the localisation of the dimerisation reaction are not known, we consider a second modelling scenario in which we allow for both Hes1 monomers and dimers to be imported into the nucleus, and we allow dimerisation of Hes1 to occur everywhere in the cell. Once again, computational solutions of this second model produce oscillatory dynamics in agreement with experimental studies. We also explore sensitivity of the numerical solutions to nuclear transport and dimerisation parameters. Finally, we compare and contrast the two different modelling scenarios using numerical experiments that simulate dimer disruption, and suggest a biological experiment that could distinguish which model more faithfully captures the Hes1 GRN.PostprintPeer reviewe

Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions

Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A + B -> C, or A + A -> C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site).Comment: 33 pages, submitted to Physical Biolog

Altered developmental programs and oriented cell divisions lead to bulky bones during salamander limb regeneration

There are major differences in duration and scale at which limb development and regeneration proceed, raising the question to what extent regeneration is a recapitulation of development. We address this by analyzing skeletal elements using a combination of micro-CT imaging, molecular profiling and clonal cell tracing. We find that, in contrast to development, regenerative skeletal growth is accomplished based entirely on cartilage expansion prior to ossification, not limiting the transversal cartilage expansion and resulting in bulkier skeletal parts. The oriented extension of salamander cartilage and bone appear similar to the development of basicranial synchondroses in mammals, as we found no evidence for cartilage stem cell niches or growth plate-like structures during neither development nor regeneration. Both regenerative and developmental ossification in salamanders start from the cortical bone and proceeds inwards, showing the diversity of schemes for the synchrony of cortical and endochondral ossification among vertebrates

Analysis of neural crest-derived clones reveals novel aspects of facial development

Cranial neural crest cells populate the future facial region and produce ectomesenchyme-derived tissues, such as cartilage, bone, dermis, smooth muscle, adipocytes, and many others. However, the contribution of individual neural crest cells to certain facial locations and the general spatial clonal organization of the ectomesenchyme have not been determined. We investigated how neural crest cells give rise to clonally organized ectomesenchyme and how this early ectomesenchyme behaves during the developmental processes that shape the face. Using a combination of mouse and zebrafish models, we analyzed individual migration, cell crowd movement, oriented cell division, clonal spatial overlapping, and multilineage differentiation. The early face appears to be built from multiple spatially defined overlapping ectomesenchymal clones. During early face development, these clones remain oligopotent and generate various tissues in a given location. By combining clonal analysis, computer simulations, mouse mutants, and live imaging, we show that facial shaping results from an array of local cellular activities in the ectomesenchyme. These activities mostly involve oriented divisions and crowd movements of cells during morphogenetic events. Cellular behavior that can be recognized as individual cell migration is very limited and short-ranged and likely results from cellular mixing due to the proliferation activity of the tissue. These cellular mechanisms resemble the strategy behind limb bud morphogenesis, suggesting the possibility of common principles and deep homology between facial and limb outgrowth

Oriented clonal cell dynamics enables accurate growth and shaping of vertebrate cartilage.

Cartilaginous structures are at the core of embryo growth and shaping before the bone forms. Here we report a novel principle of vertebrate cartilage growth that is based on introducing transversally-oriented clones into pre-existing cartilage. This mechanism of growth uncouples the lateral expansion of curved cartilaginous sheets from the control of cartilage thickness, a process which might be the evolutionary mechanism underlying adaptations of facial shape. In rod-shaped cartilage structures (Meckel, ribs and skeletal elements in developing limbs), the transverse integration of clonal columns determines the well-defined diameter and resulting rod-like morphology. We were able to alter cartilage shape by experimentally manipulating clonal geometries. Using in silico modeling, we discovered that anisotropic proliferation might explain cartilage bending and groove formation at the macro-scale

Solving the chemical master equation using sliding windows

<p>Abstract</p> <p>Background</p> <p>The chemical master equation (CME) is a system of ordinary differential equations that describes the evolution of a network of chemical reactions as a stochastic process. Its solution yields the probability density vector of the system at each point in time. Solving the CME numerically is in many cases computationally expensive or even infeasible as the number of reachable states can be very large or infinite. We introduce the sliding window method, which computes an approximate solution of the CME by performing a sequence of local analysis steps. In each step, only a manageable subset of states is considered, representing a "window" into the state space. In subsequent steps, the window follows the direction in which the probability mass moves, until the time period of interest has elapsed. We construct the window based on a deterministic approximation of the future behavior of the system by estimating upper and lower bounds on the populations of the chemical species.</p> <p>Results</p> <p>In order to show the effectiveness of our approach, we apply it to several examples previously described in the literature. The experimental results show that the proposed method speeds up the analysis considerably, compared to a global analysis, while still providing high accuracy.</p> <p>Conclusions</p> <p>The sliding window method is a novel approach to address the performance problems of numerical algorithms for the solution of the chemical master equation. The method efficiently approximates the probability distributions at the time points of interest for a variety of chemically reacting systems, including systems for which no upper bound on the population sizes of the chemical species is known a priori.</p

Oriented clonal cell dynamics enables accurate growth and shaping of vertebrate cartilage

Cartilaginous structures are at the core of embryo growth and shaping before the bone forms. Here we report a novel principle of vertebrate cartilage growth that is based on introducing transversally-oriented clones into pre-existing cartilage. This mechanism of growth uncouples the lateral expansion of curved cartilaginous sheets from the control of cartilage thickness, a process which might be the evolutionary mechanism underlying adaptations of facial shape. In rod-shaped cartilage structures (Meckel, ribs and skeletal elements in developing limbs), the transverse integration of clonal columns determines the well-defined diameter and resulting rod-like morphology. We were able to alter cartilage shape by experimentally manipulating clonal geometries. Using in silico modeling, we discovered that anisotropic proliferation might explain cartilage bending and groove formation at the macro-scale

Robustness analysis of spatiotemporal models in the presence of extrinsic fluctuations

© 2017 Society for Industrial and Applied Mathematics. We analyze the governing partial differential equations of a model of pole-to-pole oscillations of the MinD protein in a bacterial cell. The sensitivity to extrinsic noise in the parameters of the model is explored. Our analysis shows that overall, the oscillations are robust to extrinsic perturbations in the sense that small perturbations in reaction coefficients result in small differences in the frequency and in the amplitude. However, a combination of analysis and simulation also reveals that the oscillations are more sensitive to some extrinsic time scales than to others