Search arXivSearch

arXiv · 1205.1158

The Geometry of Morphogenesis and the Morphogenetic Field Concept

Abstract

The process of morphogenesis, which can be defined as an evolution of the form of an organism, is one of the most intriguing mysteries in the life sciences. It is clear, that gene expression patterns cannot explain the development of the precise geometry of an organism and its parts in space. Here, we suggest a set of postulates and possible approaches for discovering the correspondence between molecular biological information and its realization in a given geometry of an organism in space-time. First, we suggest that the geometry of the organism and its parts is coded by a molecular code located on the cell surfaces in such a way that, with each cell, there can be associated a corresponding matrix, containing this code. As a particular model, we propose coding by several types of oligosaccharide residues of glycoconjugates. Second, we provide a notion of cell event, and suggest a description of development as a tree of cell events, where under cell event we understand the changing of cell state, e.g. the processes of cell division, cell growth/death, shift or differentiation. Next we suggest describing these cell motion laws using the notion of a "morphogenetic field", meaning by the field an object in an "event space" over a "cell space", which govern the transformation of the coded biological information into an instructive signal for a cell event for a given cell, depending on the position of a cell in the developing embryo. The matrix on a cell surface will be changed after each cell event according to the rule(s) dictated by the morphogenetic field of an organism. Finally, we provide some ideas on the connection between morphogenetic code on a cell surface, cell motion law(s) and the geometry of an embryo.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nadya Morozova, Mikhail Shubin. 2013-07-20. The Geometry of Morphogenesis and the Morphogenetic Field Concept. https://arxiv.org/abs/1205.1158

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

2D reaction-diffusion model-based biopsy simulation for dynamic tumor growth parameter estimation

Once diagnosed, cancer requires a fast, reliable and preferably cost-efficient assessment of the current state and potential progression of the disease. A new method for estimating tumor cell diffusivity $D$ and proliferation rate $γ$ in the context of the mechanistic reaction-diffusion equation from single-point-in-time routine biopsies aims to deliver just that, and quantities computed from the parameter estimates have recently been tested as a new biomarkers for risk-stratification in radiotherapy. Here, we extend the findings of this previous work by providing a first theoretical validation. The method is applied to in-silico biopsies which are generated by solving the two-dimensional reaction-diffusion equation for different growth terms (exponential and logistic) with a Dirac-Delta initial condition, and transforming the continuous results into spatial point patterns via a form of reverse coarse-graining. If no information about tumor age is used, in short-term experiments the original dispersion length $\sqrt{D/γ}$ could be retrieved with a relative root mean squared error (RRMSE) of around 8% and an $\text{R}^2$-value of 0.97. In long-term experiments, the RRMSEs ranged from 8 to 14% and the $\text{R}^2$-values from 0.75 to 0.98. The scaled front velocity $\sqrt{D \cdotγ}$, which can only be estimated if information about tumor age is available, was retrieved with an RRMSE of 7% and an $\text{R}^2$ of 0.98 in both, the short-term and the long-term experiments.

q-bio.OT

Flash-Radiomics: A Scalable Hybrid CPU-CUDA Engine for Standardized Scalar Radiomics and Accelerated Spatial Mapping

Background and Objectives: Spatial mapping retains the spatial distribution of radiomic features, but computational cost and fragmented software limit its use. We developed Flash-Radiomics with scalar extraction and spatial mapping, a central processing unit (CPU) backend, a hybrid Compute Unified Device Architecture (CUDA) backend, consistent feature names, and Hierarchical Data Format version 5 (HDF5) storage. Methods: We evaluated Image Biomarker Standardisation Initiative (IBSI) compliance, CPU-CUDA concordance, and end-to-end processing time. Compliance testing included 825 chapter 1 (IBSI-1) tests covering 165 high-consensus features and 323 chapter 2 (IBSI-2) tests with numerical references. Concordance testing included 1,148 scalar pairs and 93 spatial-map pairs. End-to-end processing time was measured five times per input volume of interest (VOI) size. Comparisons included the Medical Image Radiomics Processor (MIRP) and PyRadiomics for 102 shared scalar features and PyRadiomics for 93 shared spatial maps. Results: Both backends passed all 1,148 IBSI tests, and all paired results were concordant. At the largest scalar input, CPU required 76.343 s and hybrid CUDA 81.915 s; CPU was 4.7 times faster than MIRP and 190.7 times faster than PyRadiomics. At the largest spatial input completed by both backends, hybrid CUDA reduced processing time by 68.6% relative to CPU (79.280 versus 252.791 s). At PyRadiomics' largest completed spatial input, hybrid CUDA was 84.9 times faster. Conclusions: Flash-Radiomics unified standardized scalar extraction, spatial mapping, concordant CPU-CUDA results, and HDF5 storage. CPU processing time was similar or shorter for scalar extraction, whereas hybrid CUDA was faster for spatial mapping under the tested conditions.

q-bio.OT

EPI-KAN: A Method For Estimating and Forecasting Time-Dependent COVID-19 Parameters

We introduce EPI-KAN, a novel method for estimating COVID-19 time-varying parameters. EPI-KAN uses historical epidemiological data, Physics-Informed Neural Network (PINN), and the novel Kolmogorov-Arnold Network (KAN). The method harnesses the novel Kolmogorov-Arnold Network (KAN), which is a type of artificial neural network. For the KAN in this paper, we learn activation functions that are represented using Fourier series, hence we abbreviate as KAN-F. In this study, we estimate parameters in the context of an SIRD compartmental differential equations. The time-dependent parameters are the transmission rate $β(t)$, recovery rate $γ(t)$, and mortality rate $μ(t)$. We define three KAN-F functions $\widehatβ$, $\widehatγ$, $\widehatμ$ that model the true parameters $β(t)$, $γ(t)$, $μ(t)$, respectively. We test two model architectures for the KAN-F: the first has 8 input variables consisting of $S$, $I$, $R$, $D$, and their numerical gradients at any time $t$, while the second has 4 input variables excluding the numerical gradients. The objective loss function that has to be minimized is subject to Physics-Informed Neural Network (PINN). Using historical data of COVID-19 from three South-East Asian countries: Indonesia, Singapore, and Malaysia, we are able to estimate $β(t)$, $γ(t)$, and $μ(t)$ on each country with decent accuracy and efficiency. The time period of choice coincides with the period where SARS-CoV-2 Delta variant (B.1.617.2) was dominant. In addition to estimating the rates during the training period, we also predict transmission rates over 30 days during forecast period. We found that the output of KAN-F over the forecast period can give good predictions if we scale the output by a factor of 17\% for Indonesia and 30\% for Singapore and Malaysia.

q-bio.OT