Self-organization in and on biological spheres

Three biological settings involving self-organization performed by the Turing-Child field inside a sphere and on its surface are considered. In the first setting the interior of a sphere made up of cells communicating via gap junctions is considered. It is suggested that the Turing-Child self-organization is the cause of radial polarization, the first differentiation of an early mammalian embryo. In the second setting, the Turing example of gastrulation of a hollow cellular sphere is considered. It is shown that Child's experimental patterns are predicted and explained by the Turing-Child theory. The third setting is the interior of a biological cell, and it is suggested that it is the self-organization of the Turing-Child field that causes the formation of the mitotic spindle.     

整体大于部分之和: 生态自组织斑图及其涌现属性

近30年来, 自组织理论已经发展成为解释生态系统呈现规则空间格局的有效理论。伴随着生态系统自发有序空间格局的生成, 自组织过程产生一系列的涌现属性, 这些特征对生态系统功能至关重要。在此, 我们将介绍这一正蓬勃发展的研究领域的主要理论进展。首先, 叙述了自组织这一概念的发展历程与定义, 详细阐述了自组织理论的两个经典理论框架: 图灵原理与相分离原理。然后, 根据几个典型的生态自组织研究案例, 描述了图灵原理与相分离原理在不同生态系统中的具体数学模型表达形式。接着, 分别阐述了图灵原理的涌现属性对生态系统功能以及相分离原理的涌现属性对细胞功能的作用。最后, 从多尺度自组织斑图、瞬态斑图和生物个体行为自组织3个方面对未来生态自组织理论发展方向进行了探讨。自组织研究在生态学与生物学研究中方兴未艾, 希望更多的学者在未来关注与参与该领域的发展。     

Self-organization in and on biological spheres

Three biological settings involving self-organization performed by the Turing-Child field inside a sphere and on its surface are considered. In the first setting the interior of a sphere made up of cells communicating via gap junctions is considered. It is suggested that the Turing-Child self-organization is the cause of radial polarization, the first differentiation of an early mammalian embryo. In the second setting, the Turing example of gastrulation of a hollow cellular sphere is considered. It is shown that Child's experimental patterns are predicted and explained by the Turing-Child theory. The third setting is the interior of a biological cell, and it is suggested that it is the self-organization of the Turing-Child field that causes the formation of the mitotic spindle.     

Self-organization in biological systems

Biological systems are considered that are capable of dynamic self-organization, i.e., spontaneous emergence of spatio-temporal order with the formation of various spatio-temporal patterns. A cell is involved in the organization of ontogenesis of all stages. Embryonic cells exhibit coordinated social behavior and generate ordered morphological patterns displaying variability and equifinality of development. Physical and topological patterns are essential for biological systems as an imperative that restricts and directs biological morphogenesis. Biological self-organization is directed and fixed by natural selection during which selection of the most sustainable, flexible, modular systems capable of adaptive self-organization occurs.     

EPH/EPHRIN regulates cellular organization by actomyosin contractility effects on cell contacts

EPH/EPHRIN signaling is essential to many aspects of tissue self-organization and morphogenesis, but little is known about how EPH/EPHRIN signaling regulates cell mechanics during these processes. Here, we use a series of approaches to examine how EPH/EPHRIN signaling drives cellular self-organization. Contact angle measurements reveal that EPH/EPHRIN signaling decreases the stability of heterotypic cell:cell contacts through increased cortical actomyosin contractility. We find that EPH/EPHRIN-driven cell segregation depends on actomyosin contractility but occurs independently of directed cell migration and without changes in cell adhesion. Atomic force microscopy and live cell imaging of myosin localization support that EPH/EPHRIN signaling results in increased cortical tension. Interestingly, actomyosin contractility also nonautonomously drives increased EPHB2:EPHB2 homotypic contacts. Finally, we demonstrate that changes in tissue organization are driven by minimization of heterotypic contacts through actomyosin contractility in cell aggregates and by mouse genetics experiments. These data elucidate the biomechanical mechanisms driving EPH/EPHRIN-based cell segregation wherein differences in interfacial tension, regulated by actomyosin contractility, govern cellular self-organization.     

A Mechanochemical Model Explains Interactions between Cortical Microtubules in Plants

Microtubules anchored to the two-dimensional cortex of plant cells collide through plus-end polymerization. Collisions can result in rapid depolymerization, directional plus-end entrainment, or crossover. These interactions are believed to give rise to cellwide self-organization of plant cortical microtubules arrays, which is required for proper cell wall growth. Although the cell-wide self-organization has been well studied, less emphasis has been placed on explaining the interactions mechanistically from the molecular scale. Here we present a model for microtubule-cortex anchoring and collision-based interactions between microtubules, based on a competition between cross-linker bonding, microtubule bending, and microtubule polymerization. Our model predicts a higher probability of entrainment at smaller collision angles and at longer unanchored lengths of plus-ends. This model addresses observed differences between collision resolutions in various cell types, including Arabidopsis cells and Tobacco cells.     

Involvement of protein kinases in self-organization of the rhythm of protein synthesis by direct cell-cell communication

Primary cultures of rat hepatocytes grown on slides were studied in serum-free medium. Ultradian protein synthesis rhythm was used as a marker of synchronization of individual oscillations, resulting in the formation of a common rhythm of the cell population, i.e. cell-cell self-organization. Dense synchronous and sparse non-synchronous cultures were used to estimate effect of protein kinase activity on the kinetics of protein synthesis. Treatment of dense cultures with the inhibitors H7 (40 microM) or H8 (25 microM) resulted in a loss of the protein synthesis rhythm, a suppression of the cell-cell self-organization. Stimulation of protein kinase activity with either 0.5 or 1.0 microM phorbol 12-miristate-13-acetate (PMA) or 10 microM forskolin caused the appearance of the synthetic rhythm in non-synchronous sparse cultures under otherwise normal conditions. Inhibition of protein kinase activity with H7 resulted in signal factors, such as gangliosides and phenylephrine, failing to initiate this rhythm in sparse cultures. Activation of protein kinase activity with PMA shifted the phase pattern of the protein synthesis rhythm. Thus, according to our previous and the new data, protein kinase activity and consequently protein phosphorylation is the crucial step of sequence of processes resulting in synchronization during self-organization of cells in producing a common rhythm in the population. The general pathway can be presented as follows: signaling of gangliosides or other calcium agonists-->efflux of calcium ion from intracellular stores, with elevation of calcium concentration in the cytoplasm-->activation of protein kinases-->protein phosphorylation-->synchronization of individual oscillations in protein synthesis rates-->induction of a common rhythm throughout this population. The data have been discussed concerning similarity of the direct cell-cell communication and the cell self-organization in cultures and in organism.     

Mechanisms of Self-Organization of Cortical Microtubules in Plants Revealed by Computational Simulations

Microtubules confined to the two-dimensional cortex of elongating plant cells must form a parallel yet dispersed array transverse to the elongation axis for proper cell wall expansion. Some of these microtubules exhibit free minus-ends, leading to migration at the cortex by hybrid treadmilling. Collisions between microtubules can result in plus-end entrainment (“zippering”) or rapid depolymerization. Here, we present a computational model of cortical microtubule organization. We find that plus-end entrainment leads to self-organization of microtubules into parallel arrays, whereas catastrophe-inducing collisions do not. Catastrophe-inducing boundaries (e.g., upper and lower cross-walls) can tune the orientation of an ordered array to a direction transverse to elongation. We also find that changes in dynamic instability parameters, such as in mor1-1 mutants, can impede self-organization, in agreement with experimental data. Increased entrainment, as seen in clasp-1 mutants, conserves self-organization, but delays its onset and fails to demonstrate increased ordering. We find that branched nucleation at acute angles off existing microtubules results in distinctive sparse arrays and infer either that microtubule-independent or coparallel nucleation must dominate. Our simulations lead to several testable predictions, including the effects of reduced microtubule severing in katanin mutants.     

Steps Towards the Formation of A Protocell: The Possible Role of Short Peptides

The paper deals with molecular self-organization leading to formation of a protocell. Plausible steps towards a protocell include: polymerization of peptides and oligonucleotides on mineral surfaces; coevolution of peptides and oligonucleotides with formation of collectively autocatalytic sets; self-organization of short peptides into vesicles; entrapment of the peptide/oligonucleotide systems in mixed peptide and simple amphiphile membranes; and formation of functioning protocells with metabolism and cell division. The established propensity of short peptides to self-ordering and to formation of vesicles makes this sequence plausible. We further suggest that evolution of a protocell produced cellular ancestors of viruses as well as ancestors of cellular organisms.     

Membrane Binding of MinE Allows for a Comprehensive Description of Min-Protein Pattern Formation

The rod-shaped bacterium Escherichia coli selects the cell center as site of division with the help of the proteins MinC, MinD, and MinE. This protein system collectively oscillates between the two cell poles by alternately binding to the membrane in one of the two cell halves. This dynamic behavior, which emerges from the interaction of the ATPase MinD and its activator MinE on the cell membrane, has become a paradigm for protein self-organization. Recently, it has been found that not only the binding of MinD to the membrane, but also interactions of MinE with the membrane contribute to Min-protein self-organization. Here, we show that by accounting for this finding in a computational model, we can comprehensively describe all observed Min-protein patterns in vivo and in vitro. Furthermore, by varying the system''s geometry, our computations predict patterns that have not yet been reported. We confirm these predictions experimentally.     

A Cell-Based Model of Extracellular-Matrix-Guided Endothelial Cell Migration During Angiogenesis

Angiogenesis, the formation of new blood vessels sprouting from existing ones, occurs in several situations like wound healing, tissue remodeling, and near growing tumors. Under hypoxic conditions, tumor cells secrete growth factors, including VEGF. VEGF activates endothelial cells (ECs) in nearby vessels, leading to the migration of ECs out of the vessel and the formation of growing sprouts. A key process in angiogenesis is cellular self-organization, and previous modeling studies have identified mechanisms for producing networks and sprouts. Most theoretical studies of cellular self-organization during angiogenesis have ignored the interactions of ECs with the extra-cellular matrix (ECM), the jelly or hard materials that cells live in. Apart from providing structural support to cells, the ECM may play a key role in the coordination of cellular motility during angiogenesis. For example, by modifying the ECM, ECs can affect the motility of other ECs, long after they have left. Here, we present an explorative study of the cellular self-organization resulting from such ECM-coordinated cell migration. We show that a set of biologically-motivated, cell behavioral rules, including chemotaxis, haptotaxis, haptokinesis, and ECM-guided proliferation suffice for forming sprouts and branching vascular trees.     

Cytoskeleton: microtubules born on the run

The organization of microtubules into large arrays determines cell morphology and structure. Recent work in the fission yeast describes a novel mechanism for microtubule self-organization in the absence of centrosomes; this mechanism may function in a variety of cell types found in diverse organisms.     

Pattern formation on the combs of honeybees: increasing fitness by coupling self-organization with templates

Biological patterns are often constructed via a combination of mechanisms including self-organization, templates and recipes. Our understanding of self-organization is becoming increasingly clear, yet how multiple mechanisms work together and what selective advantage they confer over simpler mechanisms is poorly understood. Honeybee (Apis mellifera) combs exhibit a pattern of brood at the bottom, pollen in a band next to it and honey at the top. This study constructs an agent-based model, derived from experimental studies, to determine both how self-organization interacts with two templates and to elucidate a selective basis for the use of multiple mechanisms. The vertical pattern of honey and brood is shown to be dependent on a gravity-based template, while the pollen band is shown to form via the interaction of a queen-based template and self-organization. The study suggests that the selective basis for this complex mechanism may be that colonies have higher growth rates when multiple mechanisms are used as opposed to self-organization alone. As self-organization is used in many contexts in which the addition of supplemental mechanisms could be advantageous, this result may be of general significance to many biological systems.     

Historical and conceptual background of self-organization by reactive processes

Order, form, pattern and organization are properties central to much living matter. The physicochemical processes by which an initially homogeneous solution of reacting chemicals or biochemicals might self-organize is hence a question of fundamental biological importance. In most cases, solutions of reacting chemicals in a test-tube do not self-organize. Because of this, for many years, it was not thought possible that reactive processes could result in self-organization. However, progressively over the last hundred years, it has been shown that this is not always the case, and under certain conditions, the combination of reaction with molecular diffusion can lead to macroscopic self-organization. In 'complex' systems comprised of populations of strongly coupled elements, new 'emergent' properties, such as self-organization, arise by way of the dynamics of the system. Self-organizing reaction-diffusion systems form a specific type of complex system. Here, I will give a personal overview of the conceptual and historical background to this approach with an emphasis on biological self-organization.     

Mathematical theory on formation of category detecting nerve cells

The nerve cells are believed to have such ability of self-organization that, given a number of input patterns, each cell tunes itself to become responsive to only one of the patterns, or to one subset of patterns having some features in common. The detectors of patterns or pattern subsets are formed in this manner. A simple but plausible mechanism of self-organization is proposed based on the two hypotheses: 1) Synaptic modification process is non-linear, activated when the output of a cell is positive. 2) Not only excitatory but also inhibitory synapses are modifiable. A rigorous mathematical analysis is given to elucidate the characteristics of modifiable synapses to form these detectors. The present model fits well most of the experiments on the developmental plasticity of the visual cortex such as the formation of orientation detecting cells, monocular and alternate monocular deprivation in normal and abnormal environments.     

The uniqueness of biological self-organization: challenging the Darwinian paradigm

Here we discuss the challenge posed by self-organization to the Darwinian conception of evolution. As we point out, natural selection can only be the major creative agency in evolution if all or most of the adaptive complexity manifest in living organisms is built up over many generations by the cumulative selection of naturally occurring small, random mutations or variants, i.e., additive, incremental steps over an extended period of time. Biological self-organization—witnessed classically in the folding of a protein, or in the formation of the cell membrane—is a fundamentally different means of generating complexity. We agree that self-organizing systems may be fine-tuned by selection and that self-organization may be therefore considered a complementary mechanism to natural selection as a causal agency in the evolution of life. But we argue that if self-organization proves to be a common mechanism for the generation of adaptive order from the molecular to the organismic level, then this will greatly undermine the Darwinian claim that natural selection is the major creative agency in evolution. We also point out that although complex self-organizing systems are easy to create in the electronic realm of cellular automata, to date translating in silico simulations into real material structures that self-organize into complex forms from local interactions between their constituents has not proved easy. This suggests that self-organizing systems analogous to those utilized by biological systems are at least rare and may indeed represent, as pre-Darwinists believed, a unique ascending hierarchy of natural forms. Such a unique adaptive hierarchy would pose another major challenge to the current Darwinian view of evolution, as it would mean the basic forms of life are necessary features of the order of nature and that the major pathways of evolution are determined by physical law, or more specifically by the self-organizing properties of biomatter, rather than natural selection.     

Understanding self-organization of ecosystems under disturbance using a microcosm study

It is a key to success of ecological engineering to understand self-organization of a target ecosystem. Self-organizing patterns of ecosystems, however, become complicated due to a wide range of disturbance regimes in nature. We investigated how disturbances influence self-organization of ecosystems from energetic perspectives using 14 freshwater aquatic microcosms transplanted from lakes in Florida. We observed five different disturbance-productivity relationships from the microcosm tests and these variable relationships were attributed to the different initial states of the microcosms under the same input sequence of test plans and disturbance regimes. Through processes of self-organization, as the microcosms matured with time, resistance increased and resilience decreased. The microcosm study provided insights regarding restoration and management of ecosystems including the insight that initial seeds for restoration of an ecosystem should be carefully selected in consideration of typical disturbance regimes of the region. It is also suggested that consideration or manipulation of disturbance regimes in each successional stage is sometimes needed for maximum productivity or a designated goal of a restoration project because self-organizing patterns that result under disturbances vary depending on a system's maturity.     

Modulated Self-Organization in Complex Amphiphilic Systems

Abstract

We discuss novel simulation methods for 3D pattern formation in complex amphiphilic systems. The focus is on the supra-molecular or mesoscopic level. The building blocks consist of sequences of dissimilar monomers, connected in copolymer chain molecules. Internal factors such as composition and architecture of the polymers, but also external factors such as applied shear, embedded reactions and level of confinement control the self-organization phenomena. Specific examples include dynamical pattern formation in polymer surfactant solution, reactive polymer blends and surface directed structure formation in block copolymer liquids. The approach lives in a twilight zone between scientific disciplines. The ambitious goal is the invention of methods for the rational design of truly complex bio-mimicking materials, in which we combine principles from chemical engineering, physics, chemistry and biology. The keyword is self-organization, of course. But do not be mistaken: autonomous self-organization leads to trouble, modulated self-organization leads to beauty.     

On the role of gravity and positional information in embryological axis formation and tissue compartmentalization

The idea that gravity affects dorso-ventral polarization in anouran development contrasts with the theories of self-organization through reaction-diffusion processes. As a result of a literature study we discuss the role of gravity in embryological axis formation and speculate on an influence of gravity on tissue compartmentalization. The involvement of compartmentalization in tissue homeostasis is discussed in the light of the recent progress in mammalian cell culture studies.