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Recent super-resolution imaging technologies enable tracing chromatin conformation with nanometer-scale precision at the single-cell level. They revealed, for example, that human chromosomes fold into a complex three-dimensional structure within the cell nucleus that is essential to establish biological activities, such as the regulation of the genes. Yet, to decode from imaging data the molecular mechanisms that shape the structure of the genome, quantitative methods are required. In this review, we consider models of polymer physics of chromosome folding that we benchmark against multiplexed FISH data available in human loci in IMR90 fibroblast cells. By combining polymer theory, numerical simulations and machine learning strategies, the predictions of the models are validated at the single-cell level, showing that chromosome structure is controlled by the interplay of distinct physical processes, such as active loop-extrusion and thermodynamic phase-separation.

Within cell nuclei, several biophysical processes occur in order to allow the correct activities of the genome such as transcription and gene regulation. To quantitatively investigate such processes, polymer physics models have been developed to unveil the molecular mechanisms underlying genome functions. Among these, phase-separation plays a key role since it controls gene activity and shapes chromatin spatial structure. In this paper, we review some recent experimental and theoretical progress in the field and show that polymer physics in synergy with numerical simulations can be helpful for several purposes, including the study of molecular condensates, gene-enhancer dynamics, and the three-dimensional reconstruction of real genomic regions.

Starting from Goethe. Currently, there exists no discipline whose specific boundaries could be defined as MORPHOLOGY. Nevertheless, it is possible to trace out its history in ample terms and to define its scope broadly by understanding it as the place where the semantics of FORMS are defined and where they are connected to a reference IMAGE. The central link in the field of MORPHOLOGY is FORM-IMAGE, and it refers to those dynamics of the FORM and to the DYNAMIC SYSTEMS that have taken hold in late modernity and that continue to grow today.

Vladimir Yakovlevich Propp was born in St. Petersburg on April 17, 1895 and died in Leningrad on August 22, 1970. Despite remaining in the same city, the events of history caused those places, over the course of (his) time, to take on a whole new meaning and a very different flavor. Of course, to a folklorist like Propp, used to reflecting on the distance of millennia, those seventy-five years will have been nothing. Though the fact remains that the monumental epochal shifts he witnessed (the Russian Revolution and the long cultural and political Soviet regime that followed) feature heavily in his brilliant work.

In the continuous model of a solid object, which is ideally considered composed of such material points that each one of them is surrounded by a dense neighbourhood fully occupied by other points, the deformation is a variation carried out by a transformation, which does not preserve isometry. Deformations differ from displacements caused by rigid motions. For a closed boundary curve in the three-dimensional space, Plateau wondered what surfaces would minimize the potential surface energy. Deformation was held to underlie the evolution of biological forms, described by the “Cartesian transformations”, or the interpolation function of landmarks covariation over a thin-plate spline, the perception of depth, plastic arts, and art expression.

Complex and in many ways enlightening, the history of this concept presents the succession of an eighteenth-century phase in which the descriptive and structural meaning prevails, and of an nineteenth-twentieth-century phase in which, vice versa, the concept is charged with highly negative evaluative meanings, to the point of becoming salient in Nazi ideology as the indicator of an anti-model to be annihilated in the name of a totalitarian program connoted at the same time and alternatively in a biological-racial and artistic-stylistic sense.

Representation is a primitive notion of many philosophical theories and of cognitive science. It is assumed as an intuitively understandable label assigned to the functions by which a biological or an artificial agent takes part in the world in an epistemological or a behavioral manner. It is employed to define the conditions for the semantic individuation of the states of the agent. The notion of representation was introduced systematically in the Scholastics’ view of cognition. In modern philosophy, the term is often used as a verb. Representation becomes the function of a class of mental states. In contemporary philosophy, the debate over the semantic individuation of states is intertwined with biology and cognitive science.

The concept of evidence is implied by distinct kinds of cognitive and reasoning processes carried out in ordinary experience or in specialized domains of knowledge, like science, philosophy, logic and mathematics. Theories have been developed along three orthogonal axes. Along the first axis, theories are located according to their view on evidence as a necessary and sufficient condition for knowledge. Along the second axis, theories are located according to the cognitive characterization of evidence. On the third axis, theories are distinguished by the individuation of the bearers of evidence.

Phenomenology and ontology. In the Goethean project of MORPHOLOGY, some basic theoretical LINES can be seen which have not ceased to profoundly influence the further development of methodological reflection on living FORMS and their becoming, on the relationships between FORM and IMAGE, and not least on the configurations of knowledge in the light of the decisive encounter with FORM and IMAGE.

Form constancy denotes the appearance of the invariant shape of objects in the environment, notwithstanding the variability due to changes of the viewpoint, caused by subjects movement, to objects displacement, to illumination, lightness, color, and texture whose variation can affect the internal and external boundaries of the surfaces that fall in the simultaneous or successive views of solid objects. In early psychology of perception, shape invariance was called form constancy to highlight the perceptual ability to derive something constant from the changing forms of the multiple views of objects. Shape is an attribute of 2D surfaces and 3D objects, which are invariant across the transformations in the coordinate system of the viewer. The perception of shape can be decomposed in viewer-centered and object-centered factors.

Aristotle’s rhetoric inscribes the discourse on PATHOS within a powerful systematic framework, destined to permanently influence the historical debate, as it identifies in the form of argumentation the structure of a technical elaboration of the elements involved in the persuasive discourse.

Although the expression πλαστική τέχνη [plastic art] has Greek origins, the derivative term “plasticity” enters the European languages only in the Modern Age. The term has a double meaning: it indicates, at the same time, the art of manipulating a ductile substance and the ability to transform oneself to recreate formal qualities in response to external events (positive meaning of plasticity) or to cancel pre-existing formal configurations, originating morphological novelties (negative meaning of plasticity). For this reason, the birthplace of plasticity is the domain of art but the term is used with different connotations also in the morphological, physicochemical and medical fields.

No concept in ecology has been more variously defined or more universally confused than ‘niche’.

Since its earliest attestations, the Greek word συμμετρία (composed of συν [together] and μετρία [measure]) oscillates between two different meanings, linked to a static and to a dynamic conception.

The contour is the locus at which the parts of opaque solid objects appear to form an edge because it corresponds for the viewer to the projection of the rim, namely the curve that divides the surfaces into visible and invisible parts. The rim between the visible front and the invisible rear side is projected onto the contour that is the envelope of all the curves of equal depth. Although the rim and the contour run into depth, they are distinct concepts that regard the object-centred and the viewer-centred description. The outline is the boundary of the surface delimited by the contour, which fills a spatial region. Rubin (1921) discovered the property that allows the contour and the outline playing a crucial role in perception by studying the figure–ground phenomenon. The geometrical and perceptual properties of the contour and the outline support the perception and the production of pictures.

The term derives from the Greek word μεταμόρφωσις (composed of μετα, prefix indicating the transformation, and μορφή, “form”) and has two closely related meanings.

The first issue of Word, the Journal of the Linguistic Circle of New York, published in April 1945 by Roman Jakobson and André Martinet, both exiles living in the USA, features one of the first articles by Claude Lévi-Strauss (1958) (L’analyse structurale en linguistique et en anthropologie) and the last essay by Ernst Cassirer (2002) (Structuralism in Modern Linguistics), who died a few weeks before its publi cation. This is the official birth of structuralism, a term seemingly coined by the author of Philosophie der symbolischen Formen in his posthumous essay with its testimonial quality.

A graph is any abstract object that consists of vertices and edges. This entry presents the main attributes of vertices and edges.

The word “pattern” is a very complex term. Generally, it refers to “an arrange- ment that reveals an order, or design, which is meaningful” (cf. Thaker 1999: 427). But a quick look at many of its different domains of application (e.g. theoretical biology, mathematics, aesthetics, linguistics, etc., etc.) proves that “pattern” has a semantic potential richer than one usually expressed by such a definition. For instance, in the framework of the so-called combinatorics on words (cf. at least Lothaire 2012), a pattern is “a word over an alphabet of variables and is meant to describe some kind of repetitive structures” (cf. Rampersard 2017: 98). Therefore, in this first theoretical approach, “the pattern XX over the single variable X is meant to describe the repetition of the same word twice in succession” (cf. Rampersard 2017: 98).

“Homology is probably the most important concept in comparative biology. It has been treated in different ways, however, and more than one concept of homology is probably defensible” (Minelli 1994: 18); “Homology is one of the terms most widely employed in biology. Together with species, gene and a few others, it is likely to occur in texts devoted to the most diverse biological disciplines, from MORPHOLOGY to systematics to molecular genetics.

The conceptual couple CHARACTER/STATE is an ideal candidate to demonstrate the virtues of a morphological way of proceeding that allows historically distinct disciplinary horizons to dialogue in order to achieve a new disciplinary synthesis (Love 2003) and first of all in order to reach a new morphological lexicon, aware of the traditions of reference and of the mutual advantage arising from the dialogue itself.

We introduce some formal definition of Topological Space in the the framework of the so-called classical mathematics.

The concept of chreod was introduced in 1957 by the English theoretical biologist Conrad Hal Waddington (cf. Waddington: 1957; Galperin: 2008). From a linguistic point of view, the word “chreod” is a neologism, or, more precisely, a compound formed by the combination of two Greek words: the verb chre- (“it is necessary, must”) and the substantive -hodos (“way, road”). Therefore, it means literally “obliged pathway” (cf. Fabris 2018: 252, n. 6). Of course, such an etymology covers only a little bit of the semantic repertoire deployed by chreod. But, it is however true that some aspects of the biology of living systems can be described in these terms. Indeed, at the most general level, the idea of chreod as “obliged pathway” finds a good empirical fit to the morphological development of embryonic tissues. With particular reference to this point, it is common to define a chreod as “an orderly sequence of developmental stages”.

Intuition encompasses questions debated throughout philosophy. This entry treats intuition as a name for cognitive capacities according to the theory in which it is introduced.

The essay analyzes the notion of phenomenon referring to metaphysical, phenomenological and morphological tradition.

Since the first programmatic drafts devoted to MORPHOLOGY, Goethe establishes a very strong connection between the birth of the new science, a dynamic consideration of FORM, and the intent to reach the description of the procedures through which the FORM itself is produced, transformed, and perceived. In fact, the first private entry dedicated to MORPHOLOGY defines it as “Lehre von der Gestalt, der Bildung und Umbildung der organischen Körper”

The term perception denotes the capacity of grasping something that to the common sense belongs to external world, which is the stable and persistent collection of things that are the natural and man-made furniture of the environment. Perception denotes also the capacity of sensing something, like warmth or pain, that is the effect of an external or internal cause localized on or inside one’s own body. Therefore, perception has subjective and objective factors as constituents of its conditions of satisfaction. The activity of perception is describable in terms of the percept, namely the objective constituent of its conditions of satisfaction

SARS-CoV-2 is able to re-structure chromatin organization and alters the epigenomic landscape of the host genome, though the mechanisms that produce such changes are still poorly understood. Here, we investigate with polymer physics chromatin re-organization of the host genome, in space and time upon SARS-CoV-2 viral infection. We show that re-structuring of A/B compartments is well explained by a re-modulation of intra-compartment homotypic affinities, which leads to the weakening of A-A interactions and enhances A-B mixing. At TAD level, re-arrangements are physically described by a general reduction of the loop extrusion activity coupled with an alteration of chromatin phase-separation properties, resulting in more intermingling between different TADs and spread in space of TADs themselves. In addition, the architecture of loci relevant to the antiviral interferon (IFN) response, such as DDX58 or IFIT, results more variable within the 3D single-molecule population of the infected model, suggesting that viral infection leads to a loss of chromatin structural specificity. Analysis of time trajectories of pairwise gene-enhancer and higher-order contacts reveals that such variability derives from a more fluctuating dynamics in infected case, suggesting that SARS-CoV-2 alters gene regulation by impacting the stability of the contact network in time. Overall, our study provides the first polymer-physics based 4D reconstruction of SARS-CoV-2 infected genome with mechanistic insights on the consequent gene mis-regulation.

Extrachromosomal DNAs (ecDNAs) are found in the nucleus of an array of human cancer cells where they can form clusters that were associated to oncogene overexpression, as they carry genes and cis -regulatory elements. Yet, the mechanisms of aggregation and gene amplification beyond copy-number effects remain mostly unclear. Here, we investigate, at the single molecule level, MYC -harboring ecDNAs of COLO320-DM colorectal cancer cells by use of a minimal polymer model of the interactions of ecDNA BRD4 binding sites and BRD4 molecules. We find that BRD4 induces ecDNAs phase separation, resulting in the self-assembly of clusters whose predicted structure is validated against HiChIP data (Hung et al., 2021). Clusters establish in-trans associated contact domains (I-TADs) enriched, beyond copy number, in regulatory contacts among specific ecDNA regions, encompassing its PVT1-MYC fusions but not its other canonical MYC copy. That explains why the fusions originate most of ecDNA MYC transcripts (Hung et al., 2021), and shows that ecDNA clustering per se is important but not sufficient to amplify oncogene expression beyond copy-number, reconciling opposite views on the role of clusters (Hung et al., 2021; Zhu et al., 2021; Purshouse et al. 2022). Regulatory contacts become strongly enriched as soon as half a dozen ecDNAs aggregate, then saturate because of steric hindrance, highlighting that even cells with few ecDNAs can experience pathogenic MYC upregulations. To help drug design and therapeutic applications, with the model we dissect the effects of JQ1, a BET inhibitor. We find that JQ1 reverses ecDNA phase separation hence abolishing I-TADs and extra regulatory contacts, explaining how in COLO320-DM cells it reduces MYC transcription (Hung et al., 2021).