Using mathematical models to help understand biological pattern formation

One of the characteristics of biological systems is their ability to produce and sustain spatial and spatio-temporal pattern. Elucidating the underlying mechanisms responsible for this phenomenon has been the goal of much experimental and theoretical research. This paper illustrates this area of research by presenting some of the mathematical models that have been proposed to account for pattern formation in biology and considering their implications.To cite this article: P.K. Maini, C. R. Biologies 327 (2004)

Multiscale modeling of oscillations and spiral waves in Dictyostelium populations

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various pre-processing modules. We use this family of models to study spatially unstructured populations by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then extend our models to include spatial structure and show how they naturally give rise to spiral waves. Our models exhibit a wide range of novel phenomena including a density dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations

Network Dynamics, Synchronization, and Self-Propelled Particles in Chemical Systems

Neural networks are a class of biological networks of great importance. They are a key component of the central nervous system that coordinates body functions. The exploration of the detailed mechanism of biological neural networks remains extremely active. Inspired by the structure of biological neural networks, artificial neural networks have been designed to solve a variety of problems in pattern recognition, prediction, optimization and control. However, few studies have been reported that explore the dynamics of biological neural networks using chemical systems. As part of this thesis, an experimentally trainable network based on the photosensitive Belousov-Zhabotinsky reaction is developed, where the individual node is a catalyst loaded micro-particle. The interactions between nodes in the network are created by arranging links with different weights, similar to the excitable and inhibitory synapses in biological neural networks. The distribution of the weights of the excitable links has been studied. The results indicate that a stable distribution of the weights is exhibited.;Synchronization in coupled nonlinear oscillators is a remarkable and ubiquitous phenomenon in nature. Application of periodic global feedback to oscillators allows the creation of new kinds of wave patterns with the coexistence of stable phase states. In experiments with the photosensitive BZ reaction, periodic global feedback is implemented by varying the illumination intensity. In a 1:1 frequency-locked entrainment, 2pi phase fronts called phase kinks have been observed in the photosensitive BZ reaction. Generally, a phase kink represents the existence of stable phase differences, propagating as an analog of traveling waves in 2D excitable media. By modifying the conditions of local forcing, the experiments show that a phase kink can be trapped to form a closed pattern.;Self-propulsion is an essential feature of many living systems. There are numerous realizations of self-propelled particles in biological systems, such as the bacteria Listeria monocytogenes in cells. Such biological phenomena inspire the creation of artificial self-propelled particles. Recently, nonbiological micro- to nanoscale particles, that convert chemical energy into translational motion, have been investigated. Studies show that Pt-coated polystyrene particles, coated on one hemisphere with Pt, exhibit self-propulsion in dilute H2O2 solutions. Here, we experimentally study the dynamical behavior of silica particles that are asymmetrically coated with Pt in H2O2 solutions, similar to Pt-coated polystyrene particles. The focus of our study is on the particle orientation with respect to the direction of motion. This is investigated using velocity autocorrelation and propulsion direction analyses

Iron-Catalyzed Belousov-Zhabotinsky Hydrogels and Liquid Crystals

Reducing stress is an important goal in poultry production. The Saccharomyces cerevisiae-derived yeast fermentation product Original XPC (XPC, Diamond V Mills, Cedar Rapids, IA, United States) has been shown to reduce the severity of enteric infection and reduce measures of stress in poultry exposed to acute or chronic stress. However, the effect of dietary supplementation of yeast fermentate on other physiological parameters and its mode of action in reducing stress remains unclear. This work aimed to investigate the effects of supplementing XPC or its liquid equivalent, AviCare (Diamond V Mills), on measures of stress susceptibility, health and well-being in poultry exposed to acute and chronic stressors. Three consecutive experiments were conducted to evaluate the effects of yeast fermentate supplementation on measures of stress, growth and feed efficiency in Cobb 500 male broilers exposed to acute and rearing stressors. Both XPC and AviCare consistently and equally reduced measures of short- and long-term stress across all 3 experiments, although trends in body weight gain and feed efficiency were inconsistent. A fourth experiment investigated the effects of XPC and AviCare on measures of stress, plasma biochemistry, cecal microbiome and expression of stress- and immune-related genes in Cobb 500 male broilers. Both XPC and AviCare reduced stress by reducing expression of the ACTH receptor, and modulated immune activity by reducing IL10 and CYP1A2 gene expression as well as plasma IL- The Belousov-Zhabotinsky (BZ) reaction is one of the most studied nonlinear dynamic chemical systems due to its autonomous periodic oscillations. It represents a suitable model for various oscillatory phenomena in Nature such as neuron synapsis, cardiac muscle beating and/or tachycardia, cellular formation cycle in molds, and other types of live-organism morphogenesis. The complexity of the BZ reaction chemical mechanism led to the creation of the Fields-Koros-Noyes model (FKN) that allows for studies via theoretical and mathematical models. Thus, experimental studies of this reaction are necessary to create 3D and life-like models. To bring these models into a more naturalistic setting, we researched the BZ reaction through hydrogels containing iron because of its natural occurrence and relevance. Chemically, the BZ reaction requires a catalyst based on iron (Fe), ruthenium (Ru) or cerium (Ce), and most of the current reports employ Ru. Alternatively, we employed Fe complexes as the catalyst due to their lower toxicity compared to Ru. The Fe-based catalyst was incorporated into polymer matrices (PNIPAM-co-PAAm, gelatin + kappa-carrageenan, and gelatin) to obtain hydrogels that exhibited pattern-rich, self-oscillatory response. Hence, the hydrogels served as models to investigate the effect of liquid crystalline structures on oscillations, the effect of geometry on the wave pattern of 3D-printed hydrogels, and the autonomous motion of hydrogels. Overall, these results open the door for future research on BZ reaction systems with low-toxicity. Furthermore, they contribute to the creation of new 3D locomotive hydrogels and to the development of realistic 3D models that could mimic Nature more efficiently.. However, cecal microbiome and antioxidative capacity were not affected after 42 d. Finally, 2 consecutive experiments were conducted to evaluate the effect of XPC and AviCare on measures of intestinal health in Cobb 500 male broilers and mixed-sex Pekin ducks exposed to cyclic heat stress during the last 14 d of growth. In both experiments yeast fermentate attenuated the negative effects of heat stress on villus length and villus/crypt ratio but not goblet cell density. Yeast fermentate also affected metabolism but did not improve electrolyte balance. In conclusion, adding yeast fermentate to the feed or drinking water reduced stress susceptibility by reducing glucocorticoid production, supported intestinal cell survival during cyclic heat stress, and modulated inflammatory processes in poultry exposed to rearing stress but not cyclic heat stress

The Evolution of Reaction-diffusion Controllers for Minimally Cognitive Agents

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A concise review of microfluidic particle manipulation methods

Particle manipulation is often required in many applications such as bioanalysis, disease diagnostics, drug delivery and self-cleaning surfaces. The fast progress in micro- and nano-engineering has contributed to the rapid development of a variety of technologies to manipulate particles including more established methods based on microfluidics, as well as recently proposed innovative methods that still are in the initial phases of development, based on self-driven microbots and artificial cilia. Here, we review these techniques with respect to their operation principles and main applications. We summarize the shortcomings and give perspectives on the future development of particle manipulation techniques. Rather than offering an in-depth, detailed, and complete account of all the methods, this review aims to provide a broad but concise overview that helps to understand the overall progress and current status of the diverse particle manipulation methods. The two novel developments, self-driven microbots and artificial cilia-based manipulation, are highlighted in more detail

Chitosan-based electroconductive inks without chemical reaction for cost-effective and versatile 3D printing for electromagnetic interference (EMI) shielding and strain-sensing applications

The burgeoning interest in biopolymer 3D printing arises from its capacity to meticulously engineer tailored, intricate structures, driven by the intrinsic benefits of biopolymers—renewability, chemical functionality, and biosafety. Nevertheless, the accessibility of economical and versatile 3D-printable biopolymer-based inks remains highly constrained. This study introduces an electroconductive ink for direct-ink-writing (DIW) 3D printing, distinguished by its straightforward preparation and commendable printability and material properties. The ink relies on chitosan as a binder, carbon fibers (CF) a low-cost electroactive filler, and silk fibroin (SF) a structural stabilizer. Freeform 3D printing manifests designated patterns of electroconductive strips embedded in an elastomer, actualizing effective strain sensors. The ink's high printability is demonstrated by printing complex geometries with porous, hollow, and overhanging structures without chemical or photoinitiated reactions or support baths. The composite is lightweight (density 0.29 ± 0.01 g/cm3), electroconductive (2.64 ± 0.06 S/cm), and inexpensive (20 USD/kg), with tensile strength of 20.77 ± 0.60 MPa and Young's modulus of 3.92 ± 0.06 GPa. 3D-printed structures exhibited outstanding electromagnetic interference (EMI) shielding effectiveness of 30–31 dB, with shielding of &gt;99.9 % incident electromagnetic waves, showcasing significant electronic application potential. Thus, this study presents a novel, easily prepared, and highly effective biopolymer-based ink poised to advance the landscape of 3D printing technologies.</p