Mechanism Of Pattern Formation Research Articles

Automatic design of gene regulatory mechanisms for spatial pattern formation

Gene regulatory mechanisms (GRMs) control the formation of spatial and temporal expression patterns that can serve as regulatory signals for the development of complex shapes. Synthetic developmental biology aims to engineer such genetic circuits for understanding and producing desired multicellular spatial patterns. However, designing synthetic GRMs for complex, multi-dimensional spatial patterns is a current challenge due to the nonlinear interactions and feedback loops in genetic circuits. Here we present a methodology to automatically design GRMs that can produce any given two-dimensional spatial pattern. The proposed approach uses two orthogonal morphogen gradients acting as positional information signals in a multicellular tissue area or culture, which constitutes a continuous field of engineered cells implementing the same designed GRM. To efficiently design both the circuit network and the interaction mechanisms—including the number of genes necessary for the formation of the target spatial pattern—we developed an automated algorithm based on high-performance evolutionary computation. The tolerance of the algorithm can be configured to design GRMs that are either simple to produce approximate patterns or complex to produce precise patterns. We demonstrate the approach by automatically designing GRMs that can produce a diverse set of synthetic spatial expression patterns by interpreting just two orthogonal morphogen gradients. The proposed framework offers a versatile approach to systematically design and discover complex genetic circuits producing spatial patterns.

Droplet dynamics affecting the shape of patterns formed spontaneously by transforming UV-curable emulsions

Forming large pitch and depth patterns spontaneously based on a bottom–up approach is a challenging task but with great industrial value. It is possible to spontaneously form an uneven (concave–convex) patterns with submillimeter-to-millimeter-scale pitches and depths by the direct pattern exposure of a UV-curable oil-in-water (O/W) emulsion liquid film. UV irradiation generates a latent pattern of a cured particle aggregation in the liquid film, and an uneven structure is spontaneously formed during the subsequent drying process. This process does not require any printing and embossing plates or development process. In this report, we presented an example of unevenness formation with a maximum pattern depth of approximately 0.4 mm and a maximum pitch width of 5 mm. The patterns formed by this method have raised edges in the exposed areas and fogging in unexposed areas. The pattern shapes become conspicuous under overexposure conditions, but the formation mechanism has not yet been understood in detail and needs to be investigated. In this study, we focused on the exposure process and clarified the mechanism of pattern formation by analyzing the dynamics of emulsion droplets in the medium by an in situ microscopy observation method. As a result, we found that the fogging was mainly caused by light leakage from the exposed area, and the raised pattern edges were caused by droplets transported from the unexposed area to the exposed area. Furthermore, the convection caused by the heat generated from polymerization is a determining factor affecting all these phenomena. By controlling the pattern shape related to convection utilizing direct projection exposure, we showed an example of eliminating raised pattern edges with a height difference of approximately 0.1 mm. By devising and selecting exposure methods, we can expand the range of design applications such as interior decorative patterns.

Consistent temporal behaviors over a non-Newtonian/Newtonian two-phase flow

The temporal behaviors of non-Newtonian/Newtonian two-phase flows are closely tied to flow pattern formation mechanisms, influenced significantly by the non-Newtonian index, and exhibiting nonlinear rheological characteristics. The nonlinear behavior of fluid flow cannot be directly inferred from the rheological models, making their temporal characteristics difficult to predict. This limitation hinders the development of a unified analytical approach and consistent results, confining researches to case-by-case studies. In this study, sets of digital microfluidics experiments, along with continuous-discrete phase-interchanging schemes, yielded 72 datasets under various non-Newtonian fluid solution configurations, micro-channel structures, and multiple Carreau-related models. Among these datasets, we identified consistent temporal behaviors featuring non-Newtonian flow patterns in digital microfluidics. Generally, selecting the most appropriate model to accurately represent the flow characteristics of non-Newtonian fluids is case-dependent. Nonetheless, there exists a generally applicable description of the flow behavior that is not affected by specific rheological model. This discovery is of significant importance for understanding the common behavioral characteristics of non-Newtonian fluids.

Self-enhanced mobility enables vortex pattern formation in living matter.

Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation1-4, purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa5 and bacteria6. Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 104-105 motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length7-9. Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems10 near the boundary of fluid- and solid-like behaviours11-17.

Pattern selection mechanism from the equilibrium point and limit cycle.

The outbreak of infectious diseases often exhibits periodicity, and this periodic behavior can be mathematically represented as a limit cycle. However, the periodic behavior has rarely been considered in demonstrating the cluster phenomenon of infection induced by diffusion (the instability modes) in the SIR model. We investigate the emergence of Turing instability from a stable equilibrium and a limit cycle to illustrate the dynamical and biological mechanisms of pattern formation. We identify the Hopf bifurcation to demonstrate the existence of a stable limit cycle using First Lyapunov coefficient in our spatiotemporal diffusion-driven SIR model. The competition between different instability modes induces different types of patterns and eventually spot patterns emerge as stable patterns. We investigate the impact of susceptible, infected, and recovered individuals on the type of patterns. Interestingly, these instability modes play a vital role in selecting the pattern formations, which is directly related to the number of observed spot patterns. Subsequently, we explain the dynamical and biological mechanisms of spot patterns to develop an effective epidemic prevention strategy.

Minimal reaction schemes for pattern formation.

We link continuum models of reaction-diffusion systems that exhibit diffusion-driven instability to constraints on the particle-scale interactions underpinning this instability. While innumerable biological, chemical and physical patterns have been studied through the lens of Alan Turing's reaction-diffusion pattern-forming mechanism, the connections between models of pattern formation and the nature of the particle interactions generating them have been relatively understudied in comparison with the substantial efforts that have been focused on understanding proposed continuum systems. To derive the necessary reactant combinations for the most parsimonious reaction schemes, we analyse the emergent continuum models in terms of possible generating elementary reaction schemes. This analysis results in the complete list of such schemes containing the fewest reactions; these are the simplest possible hypothetical mass-action models for a pattern-forming system of two interacting species.

Artificial cell system as a tool for investigating pattern formation mechanisms of intracellular reaction-diffusion waves

Artificial cell system as a tool for investigating pattern formation mechanisms of intracellular reaction-diffusion waves

A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains

In this study, we present theoretical considerations of, and analyse, the effects of circular geometry on the stability analysis of semi-linear parabolic PDEs of reaction–diffusion type with linear cross-diffusion for a two-component system on circular domains. The highlights of our theoretical and computational findings are: (i) By employing linear stability analysis for a two-component reaction–diffusion system with linear cross-diffusion on circular disc domains, we derive necessary and sufficient conditions for the system to exhibit cross-diffusion driven-instability, dependent on the length scale of the geometry. These analytical studies involve cross-diffusion and circular geometry to unravel analytical conditions for the full computational classification of the parameter spaces that allow the system to exhibit Turing, Hopf and transcritical patterns. (ii) We compute parameter spaces on which patterns are formed only due to linear cross-diffusion as well as due to a critical domain length. These spaces do not exist in the absence of cross-diffusion nor when the conditions on the domain length are violated. (iii) To support our theoretical findings, finite element simulations illustrating the formation of spot patterns on circular domains are presented. Model parameter values are selected from parameter spaces that are induced by cross-diffusion, thereby supporting linear cross-diffusion coupled with reaction–diffusion theory as a candidate mechanism for pattern formation. (iv) A by-product of this study, is that an activator-depleted reaction–diffusion system with linear cross-diffusion on circular domains, appears to favour the formation of spot patterns for most of the parameter values chosen. Such patterns are reminiscent of those observed on stingrays, which form on approximately circular domains during growth development.

Dynamical Pattern Formation without Self-Attraction in Quorum-Sensing Active Matter: The Interplay between Nonreciprocity and Motility.

We study a minimal model involving two species of particles interacting via quorum-sensing rules. Combining simulations of the microscopic model and linear stability analysis of the associated coarse-grained field theory, we identify a mechanism for dynamical pattern formation that does not rely on the standard route of intraspecies effective attractive interactions. Instead, our results reveal a highly dynamical phase of chasing bands induced only by the combined effects of self-propulsion and nonreciprocity in the interspecies couplings. Turning on self-attraction, we find that the system may phase separate into a macroscopic domain of such chaotic chasing bands coexisting with a dilute gas. We show that the chaotic dynamics of bands at the interfaces of this phase-separated phase results in anomalously slow coarsening.

Self-organized submicron structures in photoresist films by UV-laser irradiation at water-confined conditions

A new kind of self-organized pattern formation process has been found during laser irradiation of polymer films in water confinement just below the laser ablation threshold, resulting in a randomly oriented pattern with a period of about 475 nm. The morphology, orientation, period, and amplitude of these patterns are inconsistent with both laser-induced periodic surface structures that typically consist of linear grooves with periods smaller the laser wavelength and wrinkling patterns that feature a much larger period and appear at layered systems. Excimer laser (λ = 248 nm, tp = 25 ns) exposure of 650 nm thick photoresist films on silicon wafers cause the growth of irregular submicron patterns. The pattern morphology that is examined with imaging techniques is correlated to processing parameters. The amplitude of these laser-induced self-organized (LISE) submicron structures are strengthened with pulse number and laser fluence. The experimental results are discussed together with simulations of laser heating the photoresist film in water confinement. The proposed pattern formation mechanism of such laser-induced self-organized submicron structures at temporal excitation of a confined polymer surface comprises the formation of an oriented roughness based on LIPSS that are developed to wrinkled structures due to the transient formation of a soft subsurface area that provides conditions for wrinkling of the water cooled, stiff polymer surface by laser-induced stress fields. Size, amplitude, and morphology of the LISE pattern provide good properties for applications in such fields as wetting, friction, optics, and bioactivity.

Transcriptome analysis provides insights into the mechanism of carapace stripe formation in two closely related Marsupenaeus species

Marsupenaeus japonicus has two types of phenotypic differences that are mainly reflected in the stripe pattern of the carapace. However, the underlying mechanism regulating the stripe patterns is not clear. In the present study, we first observed the composition of pigment cells and detected the contents of different carotenoids in the carapace of M. japonicus. We clearly observed the setae structure on the carapace. There were red pigment cells in the stripe pattern and yellow pigment cells in the other parts. Both red pigment cells and yellow pigment cells showed dendritic morphology. In the carapace, the content of astaxanthin was the highest, significantly (P < 0.05) higher than that of other carotenoids. Some differentially expressed genes between two pattern types of M. japonicus, may be associated with the body color formation, such as crustacyanin (CRCN), apolipoprotein D (ApoD), tubulin alpha-1 chain, cuticle protein, and ABC transporter, which were verified by quantitative PCR experiments. The amino acid composition and secondary structure of CRCN A2, CRCN C1, and ApoD were significantly different. The results of this study will help to elucidate the molecular mechanism of the differential pattern formation of M. japonicus and provide a reference for further exploration of the formation mechanism of crustacean color.

Identification of small-sized intrachromosomal segments at the ends of INV-DUP-DEL patterns.

The mechanism of chromosomal rearrangement associated with inverted-duplication-deletion (INV-DUP-DEL) pattern formation has been investigated by many researchers, and several possible mechanisms have been proposed. Currently, fold-back and subsequent dicentric chromosome formation has been established as non-recurrent INV-DUP-DEL pattern formation mechanisms. In the present study, we analyzed the breakpoint junctions of INV-DUP-DEL patterns in five patients using long-read whole-genome sequencing and detected 2.2-6.1 kb copy-neutral regions in all five patients. At the end of the INV-DUP-DEL, two patients exhibited chromosomal translocations, which are recognized as telomere capture, and one patient showed direct telomere healing. The remaining two patients had additional small-sized intrachromosomal segments at the end of the derivative chromosomes. These findings have not been previously reported but they may only be explained by the presence of telomere capture breakage. Further investigations are required to better understand the mechanisms underlying this finding.

Free energy dissipation enhances spatial accuracy and robustness of self-positioned Turing pattern in small biochemical systems.

Accurate and robust spatial orders are ubiquitous in living systems. In 1952, Turing proposed a general mechanism for pattern formation exemplified by a reaction-diffusion model with two chemical species in a large system. However, in small biological systems such as a cell, the existence of multiple Turing patterns and strong noise can lower the spatial order. Recently, a modified reaction-diffusion model with an additional chemical species is shown to stabilize the Turing pattern. Here, we study non-equilibrium thermodynamics of this three-species reaction-diffusion model to understand the relationship between energy cost and the performance of self-positioning. By using computational and analytical approaches, we show that beyond the onset of pattern formation the positioning error decreases as energy dissipation increases. In a finite system, we find that a specific Turing pattern exists only within a finite range of total molecule number. Energy dissipation broadens this range, which enhances the robustness of Turing pattern against molecule number fluctuations in living cells. The generality of these results is verified in a realistic model of the Muk system underlying DNA segregation in Escherichia coli, and testable predictions are made for the dependence of the accuracy and robustness of the spatial pattern on the ATP/ADP ratio.

Pattern forming mechanisms of color vision.

While our understanding of the way single neurons process chromatic stimuli in the early visual pathway has advanced significantly in recent years, we do not yet know how these cells interact to form stable representations of hue. Drawing on physiological studies, we offer a dynamical model of how the primary visual cortex tunes for color, hinged on intracortical interactions and emergent network effects. After detailing the evolution of network activity through analytical and numerical approaches, we discuss the effects of the model's cortical parameters on the selectivity of the tuning curves. In particular, we explore the role of the model's thresholding nonlinearity in enhancing hue selectivity by expanding the region of stability, allowing for the precise encoding of chromatic stimuli in early vision. Finally, in the absence of a stimulus, the model is capable of explaining hallucinatory color perception via a Turing-like mechanism of biological pattern formation.

Analyzing the effect of cell rearrangement on Delta-Notch pattern formation.

The Delta-Notch system plays a vital role in many areas of biology and typically forms a salt and pepper pattern in which cells strongly expressing Delta and cells strongly expressing Notch are alternately aligned via lateral inhibition. In this study, we consider cell rearrangement events, such as cell mixing and proliferation, that alter the spatial structure itself and affect the pattern dynamics. We model cell rearrangement events by a Poisson process and analyze the model while preserving the discrete properties of the spatial structure. We investigate the effects of the intermittent perturbations arising from these cell rearrangement events on the discrete spatial structure itself in the context of pattern formation and by using an analytical approach, coupled with numerical simulation. We find that the homogeneous expression pattern is stabilized if the frequency of cell rearrangement events is sufficiently large. We analytically obtain the balanced frequencies of the cell rearrangement events where the decrease of the pattern amplitude, as a result of cell rearrangement, is balanced by the increase in amplitude due to the Delta-Notch interaction dynamics. Our framework, while applied here to the specific case of the Delta-Notch system, is applicable more widely to other pattern formation mechanisms.

Field emission angular distribution from single molecules

We demonstrate that the field emission from a single molecule at the apex of a metallic tip exhibits a well-defined angular distribution pattern (field emission angular distribution, FAD) with a spherical harmonics shape, regardless of the species of the molecule. From carefully controlled simultaneous measurements of the emission pattern, the emission current and emission energy, we deduced the formation mechanism of the FAD pattern in which the electron from the metallic tip resonantly tunnels into vacuum via a molecule-induced state situated at the Fermi level of the tip. The characteristic FAD patterns were consistent with the Fourier transform of the superatom molecular orbitals (SAMOs). Thus, the present method is unique for real-time imaging of the SAMOs, or the low-lying Rydberg states, of single molecules.

Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data.

The rapid increase of population and settlement structures in the Global South during recent decades has motivated the development of suitable models to describe their formation and evolution. Such settlement formation has been previously suggested to be dynamically driven by simple pattern-forming mechanisms. Here, we explore the use of a data-driven white-box approach, called SINDy, to discover differential equationmodels directly from available spatiotemporal demographic data for three representative regions of the Global South. We show that the current resolution and observation time of the available data are insufficient to uncover relevant pattern-forming mechanisms in settlement development. Using synthetic data generated with a generic pattern-forming model, the Allen-Cahn equation, we characterize what the requirements are for spatial and temporal resolution, as well as observation time, to successfully identify possible model system equations. Overall, the study provides a theoretical framework for the analysis of large-scale geographical and/or ecological systems, and it motivates further improvements in optimization approaches and data collection.

Stability and Pattern Formation in a General Class of Reaction-Diffusion-Advection System

In this paper, we systematically study two-species reaction-diffusion-advection system with linear cross-diffusion and cross-advection. Firstly, we provide sufficient conditions for cross-diffusion, self-advection and cross-advection driven instability, which implies that cross-diffusion, self-advection and cross-advection can give rise to pattern formation for the same diffusion coefficients. Secondly, we focuses on a class of general reaction-diffusion-advection system. By investigating the linearized stability of the constant equilibrium solution, we prove that the self-diffusion and self-advection terms have no effect on the stabilization of the constant steady state, the linear cross terms favor the destabilization of the constant steady state and mechanism of pattern formation. Furthermore, the theoretical results are applied to predator-prey and water-vegetation systems with cross-diffusion and cross-advection.

A Formation Mechanism of Spatial Distribution Pattern of Industrial Clusters under Flow Space

This study focuses on analyzing the spatial distribution pattern and formation mechanisms of urban industrial clusters and aims to address the mismatch between industrial clusters and resource distribution. Firstly, the spatial distribution pattern of industrial clusters is analyzed using the kernel density estimation approach. Subsequently, a multi-layered model of interactive driving factors is constructed to analyze the functional types within the multi-layered network space. Lastly, a spatial weighted regression analysis model, considering the intensity of flow space, is developed to explore the intrinsic formation mechanisms of industrial agglomeration. The experimental results indicate the following: (1) There is a trend of industrial agglomeration in the Yangtze River Delta region, primarily concentrated in cities such as Shanghai, Nanjing, Hefei, Jinhua, and Taizhou. (2) The impact of spatial interaction factors on industrial agglomeration development is significant, and the analysis of interaction networks reflects the strength of interactive influencing factors to a certain extent. (3) The regression analysis model, which incorporates interactive information considering flow space intensity, better aligns with the study of the actual mechanisms behind industrial agglomeration in physical space.

Inhibitory SMAD6 interferes with BMP-dependent generation of muscle progenitor cells and perturbs proximodistal pattern of murine limb muscles.

The mechanism of pattern formation during limb muscle development remains poorly understood. The canonical view holds that naïve limb muscle progenitor cells (MPCs) invade a pre-established pattern of muscle connective tissue, thereby forming individual muscles. Here, we show that early murine embryonic limb MPCs highly accumulate pSMAD1/5/9, demonstrating active signaling of bone morphogenetic proteins (BMP) in these cells. Overexpression of inhibitory human SMAD6 (huSMAD6) in limb MPCs abrogated BMP signaling, impaired their migration and proliferation, and accelerated myogenic lineage progression. Fewer primary myofibers developed, causing an aberrant proximodistal muscle pattern. Patterning was not disturbed when huSMAD6 was overexpressed in differentiated muscle, implying that the proximodistal muscle pattern depends on BMP-mediated expansion of MPCs before their differentiation. We show that limb MPCs differentially express Hox genes, and Hox-expressing MPCs displayed active BMP signaling. huSMAD6 overexpression caused loss of HOXA11 in early limb MPCs. In conclusion, our data show that BMP signaling controls expansion of embryonic limb MPCs as a prerequisite for establishing the proximodistal muscle pattern, a process that involves expression of Hox genes.