The interphase mammalian chromosome as a structural system based on tensegrity

Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

1 2 3 4 5 6 7 8 9 10 11 12 13 Q2 14 15 Q1 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

Contents lists available at ScienceDirect

Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/yjtbi

The interphase mammalian chromosome as a structural system based on tensegrity Armando Aranda-Anzaldo n Laboratorio de Biología Molecular y Neurociencias, Facultad de Medicina, Universidad Autónoma del Estado de México, Paseo Tollocan y Jesús Carranza s/n, Toluca, 50180 Edo. Méx., México

H I G H L I G H T S








Entropy promotes primary condensation of DNA in the interphase nucleus. Dissipation of torsional stress determines the organization of chromosomal DNA. Each chromosome is organized in supercoiled loops anchored to the nuclear matrix (NM). The interactions DNA–NM preserve the molecular integrity of chromosomal DNA. The interphase organization of chromosomal DNA is based on structural tensegrity.

art ic l e i nf o

a b s t r a c t

Article history: Received 8 August 2015 Received in revised form 11 December 2015 Accepted 4 January 2016

Each mammalian chromosome is constituted by a DNA fiber of macroscopic length that needs to be fitted in a microscopic nucleus. The DNA fiber is subjected at physiological temperature to random thermal bending and looping that must be constrained so as achieve structural stability thus avoiding spontaneous rupturing of the fiber. Standard textbooks assume that chromatin proteins are primarily responsible for the packaging of DNA and so of its protection against spontaneous breakage. Yet the dynamic nature of the interactions between chromatin proteins and DNA is unlikely to provide the necessary long-term structural stability for the chromosomal DNA. On the other hand, longstanding evidence indicates that stable interactions between DNA and constituents of a nuclear compartment commonly known as the nuclear matrix organize the chromosomal DNA as a series of topologically constrained, supercoiled loops during interphase. This results in a primary level of DNA condensation and packaging within the nucleus, as well as in protection against spontaneous DNA breakage, independently of chromatin proteins which nevertheless increase and dynamically modulate the degree of DNA packaging and its role in the regulation of DNA function. Thus current evidence, presented hereunder, supports a model for the organization of the interphase chromosome as resilient system that satisfies the principles of structural tensegrity. & 2016 Published by Elsevier Ltd.

Keywords: DNA loops DNA topology Entropy Nuclear matrix Nuclear higher-order structure

1. Introduction The current evidence indicates that the interior of the cell nucleus is a highly structured milieu where macromolecular complexes and chromatin, constituted by genomic DNA and closely associated proteins, interact according to a spatiotemporal order resulting in the fundamental nuclear processes of DNA replication and transcription. Known mammalian-genome sizes reported in picograms of DNA (Bachmann, 1972; Gregory, 2015) allow the estimation of total nuclear DNA length. Therefore, a n

Tel.: þ 52 722 2702899x222. E-mail addresses: [email protected], [email protected]

typical diploid, somatic cell of a mammal contains some two meters of nuclear DNA split and organized into chromosomes according to a species-specific karyotype. The size and so the DNA content per chromosome is rather variable but a given mammalian chromosome is defined by a single DNA molecule whose length may be in the centimeters range and yet it needs to be accommodated within the microscopic volume of the typical nucleus (o10 mm diameter). Any fiber-like polymer, such as DNA, in suspension at room temperature spontaneously adopts a highlyprobable, randomly coiled configuration with higher entropy than the unlikely extended configuration (Neumann, 1977). Moreover, the translation of a randomly-coiled molecule through the surrounding medium generates a viscous drag that increases the torsional stress along the molecule (Nelson, 1999). Thus continual

http://dx.doi.org/10.1016/j.jtbi.2016.01.005 0022-5193/& 2016 Published by Elsevier Ltd.

Please cite this article as: Aranda-Anzaldo, A., The interphase mammalian chromosome as a structural system based on tensegrity. J. Theor. Biol. (2016), http://dx.doi.org/10.1016/j.jtbi.2016.01.005i

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

A. Aranda-Anzaldo / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

motion of chromosome-length DNA in a thermal environment may cause random breakage as well as untwisting of the antiparallel strands. Therefore, a key question is what structural organization of the chromosome during interphase prevents the spontaneous breakage of chromosomal DNA while allowing the packaging of such a lengthy molecule within the nucleus. The mainstream opinion, presented in standard textbooks, assumes without proof that the interaction between DNA and chromatin proteins such as histones, that result in the nucleosomal organization typical of chromatin, is enough for explaining both the packaging of chromosomal DNA within the nucleus and the protection of DNA against spontaneous breakage or untwisting. However, the known turnover dynamics of chromatin proteins, their binding affinity as well as their structural mode of binding to DNA (Deal et al., 2010; Chereji and Morozov, 2015; Hemmerich et al., 2011) are not consistent with such proteins having a primary role in preserving the structural integrity of chromosomal DNA or providing the primary level of packaging of DNA within the nucleus. Hereunder an alternative model for the organization of mammalian chromosomes during interphase is presented. In this conceptual model, the empirically-demonstrated set of stable interactions of chromosomal DNA with non-chromatin proteins belonging to the underlying nuclear compartment known as the nuclear matrix (NM), is considered as the necessary and fundamental condition for achieving the long-term structural stability of chromosomal DNA as well as its primary level of packaging within the cell nucleus, thus precluding its spontaneous untwisting and/ or breakage during interphase. According to this view packaging of chromosomal DNA is further increased but not fundamentally sustained by the rather dynamic interactions between DNA and chromatin proteins. The following Sections 2–9 present the evidence that supports the model (presented in Section 10). This conceptual model is presented with the aim of encouraging further research that may settle the question of the structural organization of the mammalian chromosome during interphase.

2. The problem of structural stress in DNA DNA is prone to undergo structural stress along its length resulting on the one hand from the mutual repulsion of the negative charges of the phosphodiester bonds along the antiparallel sugar backbones (Bates and Maxwell, 2005; p. 45) and the “breathing” hydrogen bonds between base pairs (FrankKamenetskii and Prakash, 2014; von Hippel et al., 2013) whose stability depends on maintaining a time-averaged critical distance of roughly 1.8 Å between the interacting atoms (Wu et al, 2001). On the other hand, since the two DNA strands are twisted around the axis of the molecule approximately once every 10.5 base pairs and the atomic bond lengths and angles of the covalently-joined polynucleotide backbones pose a physical limit to the degree of twisting, any increase or reduction in the degree of twisting results in torsional stress (Nelson, 1999). The structural stress in DNA might be dissipated by suspending the hydrogen-bonding between complementary base pairs in such a way that the bases rotate away from the internal DNA axis (base flipping) but this would break apart the double helix (Giudice et al, 2003; van Aalten et al, 1999). Thus the physiological solution to the problem posed by the intrinsic structural stress in DNA implies the necessary preservation of the double helical structure.

3. The problem of spontaneous bending and looping in DNA As any lengthy polymer DNA possesses a persistence length (P ) a measure of its stiffness. The persistence length of DNA is highly

dependent on the specific sequence of base pairs (bp) along a DNA 67 68 tract since hydrogen bonding is a major contributor to DNA per69 sistence length (Travers, 2004). The Kuhn length, equal to 2P, 70 corresponds to the length of the hypothetical segments of a given 71 polymer that can be considered as freely jointed with each other 72 and so they can randomly orient in any direction independent of 73 the directions taken by the other segments, and so the spatial 74 conformation of the molecule can only be described statistically as 75 a three-dimensional random walk. Thus for random-sequence 76 DNA the Kuhn length is in the order of 300 bp or 100 nm, this 77 makes DNA one of the stiffest known natural polymers (Peters and 78 Maher, 2010; Teif and Bohinc, 2011). Nevertheless such a Kuhn 79 length is very short when compared with the typical length of 80 chromosomal DNA in mammals, which means that multiple ran81 dom bending and looping of chromosome-length DNA at physio82 logical temperature is unavoidable (Fig. 1), since the contraction of Q3 83 a lengthy polymer into a random-coiled state is a classical example 84 of an entropy-driven process (Neumann, 1977). 85 DNA base pairs continuously break apart and open at the milli86 second timescale (Frank-Kamenetskii and Prakash, 2014; Nikolova et 87 al., 2013). Therefore continuous but random bending and looping at 88 physiological temperature may cause base-pair opening (Vologodskii 89 90 and Frank-Kamenetskii, 2013) creating “bubbles” of denatured DNA 91 (von Hippel et al., 2013). The spontaneous unzipping (untwisting and 92 opening) of the double helix could lead to wholesale destabilization of 93 the molecule depending on the magnitude of the unzipping and 94 the local and large scale dynamics of the DNA molecule. Moreover, 95 DNA is polymorphic and heterogeneous in sequence and so stiffness or 96 flexibility varies continuously along the fiber. The thermally induced 97 loops along the lengthy chromosomal DNA may fluctuate continuously 98 eventually leading to rupturing at locally-weak points along the 99 molecule (Fig. 1). For example, where Hoogsteen-type base pairing 100 (which is less stable than classical Watson–Crick base pairing) 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 Fig. 1. A long but extended DNA fiber in suspension (A) corresponds to a low 124 entropy and highly unlikely state at physiological temperature (37 °C). Indeed, the 125 lengthy DNA fiber spontaneously adopts a highly-probable, randomly coiled con126 figuration with higher entropy than the extended configuration (B). Moreover, DNA 127 is polymorphic and heterogeneous in sequence, therefore local stiffness and flexibility varies continuously along the fiber. For example, local change in the pattern 128 of hydrogen bonding and base stacking energy of a given base pair step may create 129 an intrinsic weak point (red dot) where the fiber could break (C) as a consequence 130 of continued, unconstrained thermally-induced bending and deformation (D).(For 131 interpretation of the reference to color in this figure legend, the reader is referred 132 to the web version of this article.)

Please cite this article as: Aranda-Anzaldo, A., The interphase mammalian chromosome as a structural system based on tensegrity. J. Theor. Biol. (2016), http://dx.doi.org/10.1016/j.jtbi.2016.01.005i

A. Aranda-Anzaldo / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

spontaneously occurs at a rate of 0.1–1.0% of total base pairs (Nikolova et al., 2011; Vologodskii and Frank-Kamenetskii, 2013).

4. DNA condensation DNA is a highly charged molecule since the phosphate backbone of the strands carries one negative charge per nucleotide. Thus any compaction of DNA requires the swamping of an enormous electrostatic barrier and so counterions are necessary for reducing (screening) the electrostatic repulsion between adjacent tracts of DNA (Lipfert et al., 2014). In the nucleus the highlynegatively charged DNA coexists with a significant concentration of positively charged counterions which range from monovalent to polyvalent such as polyamines and positively charged proteins. In presence of the standard solution concentration of 0.15–0.2 M NaCl the repulsive forces between the antiparallel DNA strands and between adjacent segments of a continuous double helix are fully screened so that the effective diameter of naked DNA is 5 nm instead of 2 nm (Bednar et al., 1994; Rybenkov et al., 1993]. This counterion-induced DNA condensation is a primary factor for achieving the tight packing of DNA within the nucleus.

3

As it has been noticed, a classical observation that has stood the test of time is the formation of a DNA halo around the residual nuclear substructure resulting from extracting the nucleus with high salt and non-ionic detergent (Fig. 3), a procedure that eliminates the whole set of chromatin proteins (Woodcock and Ghosh 2010). The halos were shown to consist of negatively-supercoiled naked DNA loops stably anchored to the residual compartment known as the nuclear matrix (Cook et al., 1976; Razin, 2001; RotiRoti et al., 1993). Thus implying that the removal of chromatin proteins by high salt, that screens the weak ionic interactions between the positively charged histones and the negatively charged DNA, reveals DNA supercoils that are constrained

5. Supercoiling in nuclear DNA Another fundamental factor for achieving DNA condensation is supercoiling that spontaneously occurs in presence of physiological counterion concentrations when DNA is topologically constrained so that it has no freely rotating ends (Bates and Maxwell, 2005; p. 146; Mirkin, 2001; Teif and Bohinc, 2011]. This naturally occurs in the covalently-joined DNA circle of the typical bacterial chromosome. In the case of the mammalian chromosomes it is well established that the telomeres at the ends of each chromosome are attached to the nuclear lamina that forms the inner wall of the cell nucleus so that in fact no freely-rotating DNA ends exist (Luderus et al., 1996). Moreover, by looping and supercoiling along its axis a lengthy DNA molecule may achieve an important degree of condensation and also dissipate the torsional stress without compromising its molecular integrity but provided that the spontaneously formed loops become stabilized and so remain supercoiled by attaching or anchoring to other stuff (Bates and Maxwell, 2005; p. 26; Kramer and Sinden, 1997; Mirkin, 2001) that may reduce the bending and looping dynamics of the lengthy DNA fiber at physiological temperature as shown in Fig. 2. The linking number (Lk) is a fundamental topological property of DNA and corresponds to the number of times that one strand, arbitrarily taken as the reference edge of an imaginary surface, is crossed by the other strand. Lko correspond to the ideal Lk of a relaxed circular DNA and such a value depends on the DNA contour length in bp. DNA that is underwound compared to the relaxed DNA of an equivalent contour length has a  Lk, this results in compensatory negative supercoiling in which the DNA helix winds around its central imaginary axis. In nature most DNA is underwound and so negatively supercoiled, this situation is regarded as thermodynamically favorable because negativelysupercoiled DNA is easier to “melt” thus being rather permissive for the local strand separation necessary for replication or transcription and it also creates favorable high-energy conformations that facilitate DNA binding by functional proteins (Bates and Maxwell, 2005; p. 75; Mirkin, 2001). Two main configurations of DNA supercoiling exist: toroidal (also known as solenoidal) supercoiling in which DNA wraps around other stuff such as proteins (the case of histones) and plectonemic or interwound supercoiling which occurs in naked DNA. The last one is the primary form in vivo (Bates and Maxwell, 2005; p. 41).

Fig. 2. Within the cell nucleus the thermally induced DNA loops may be stabilized and remain supercoiled by attaching or anchoring to discrete conglomerates of structural proteins and other elements (green dots) provided that such interactions are of higher affinity and so longer-lasting than those between DNA and chromatin proteins (A). The increase in the number of DNA attachments per unit-length of DNA leads to formation of further DNA loops and so to a more thorough dissipation of the structural stress along the fiber (B). (For interpretation of the reference to color in this figure legend, the reader is reffered to the web version of this article.)

Fig. 3. Nuclear halo preparations, also known as nucleoids, that result from extracting the cell nucleus with high salt and non-ionic detergent that eliminate the nuclear envelope, the nucleoplasm and all chromatin proteins. The residual nuclear compartment or substructure known as the nuclear matrix (NM) is clearly visible in the phase contrast micrographs on the left. The fluorescent dye ethidium bromide intercalates between the rungs of base pairs of the naked chromosomal DNA that remains anchored to the NM (middle) and provokes the unwinding of the formerly supercoiled loops. The result of this is a halo of DNA that surrounds the NM (right). The diameter of the halo is directly proportional to the average size of the DNA loops (Razin et al., 1995). In the upper panel a typical nucleoid form an 80 day rat hepatocyte displays a large DNA halo while in the lower panel a typical nucleoid from an 80 day post-mitotic rat neuron displays a smaller DNA halo, evidence of a larger number of shorter on average DNA loops anchored to the NM in the neuronal nucleus by comparison to those anchored to the NM in the hepatocyte nucleus (Alva-Medina et al., 2010), since both nuclei hold the same quantity of DNA. Size bar¼ 15 mm (photos courtesy of Evangelina Silva-Santiago M.D.).

Please cite this article as: Aranda-Anzaldo, A., The interphase mammalian chromosome as a structural system based on tensegrity. J. Theor. Biol. (2016), http://dx.doi.org/10.1016/j.jtbi.2016.01.005i

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

A. Aranda-Anzaldo / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

(absorbed or hidden) by the wrapping of DNA around the histone octamers (Fig. 3). Indeed, it has been shown that the wrapping of DNA around the core particle of each nucleosome absorbs one negative supercoil (Worcel et al., 1981). Thus it must be remarked that in chromatin DNA wraps around the core histone octamer present in each nucleosome and so this constrains but never by itself creates the negative supercoiling. Moreover, efficient reconstitution of the nucleosomal organization in vitro only occurs when the core histone octamers are incubated with negatively supercoiled DNA but not with linearized DNA (Pfaffle and Jackson, 1990; Patterton and von Holt, 1993) implying that preexisting negative supercoiling is necessary for efficient nucleosome assembly. Otherwise chromatin assembly would be very costly as it would require large amounts of metabolic energy to occur (Lusser and Kadonaga, 2004). Therefore the nucleosomal organization of chromatin is neither the cause nor necessary for achieving stable DNA supercoiling. Thus when histones and other chromatin proteins are extracted the formerly constrained but now naked DNA loops bound to the nuclear matrix spontaneously shift from the toroidal to the plectonemic configuration (Fig. 3). Yet the Lk remains the same as before provided that the looped DNA remains unbroken (Fig. 4). The subdivision of chromosomal DNA in topologicallyindependent supercoiled looped domains bound to elements

Fig. 4. A naked DNA loop bound at its base to structural elements of the nuclear matrix (green) spontaneously assumes a supercoiled, plectonemic (interwound) configuration (Bates and Maxwell, 2005). However, when the supercoiled DNA wraps around other stuff such as nucleosome core particles (blue dots) the supercoils become constrained (absorbed) (Worcel et al., 1981) and the loop adopts a toroidal configuration (Bates and Maxwell, 2005) that significantly increases the DNA packaging ratio. Yet, as shown in Fig. 3, removal of the loosely bound core particles by exposure to high salt releases the hidden supercoils and so the loop returns to the basic plectonemic configuration on the left. In both situations the Lk ( in this case  4) remains the same. (For interpretation of the reference to color in this figure legend, the reader is reffered to the web version of this article.)

of the NM and so akin to covalently closed DNA circles, contributes to the fundamental packaging of DNA within the nucleus and also to the wholesale stability of the chromosome since any particular domain may undergo extensive structural modifications as a result of functional transactions or local damage but without affecting the adjacent looped domains (Roti-Roti et al., 1993; Mirkin, 2001). Moreover, from the functional perspective it is remarkable that stable DNA looping may contribute to the efficient interaction between DNA and regulatory proteins such as transcription factors, since in stretched DNA the protein search for its specific binding site occurs by one-dimensional diffusion along the DNA chain or by random binding-unbinding-rebinding that results in local short hops along DNA. However, protein rebinding in a contiguously looped DNA is likely to occur in a segment that is linearly remote but close by in 3D space to the previous site of random binding. The result is a dramatic enhancement of the targetsequence search rate by regulatory proteins (Lomholt et al., 2009), thus increasing the efficiency of gene regulation.

6. Entropy and nuclear organization Entropic processes occur in colloidal suspensions such as the nucleoplasm leading to depletion effects so that small particles induce the segregation or compartmentalization of bigger ones. Such depletion effects within the nucleus explain in part the largescale organization of chromosomes and chromatin (Finan et al., 2011; Hancock, 2014). Moreover, molecular modeling has shown that the presence of loops in the structure of chromatin leads to a strong increase in the repulsive interactions between chromosomes and that increasing the number of loops per chromosome decreases the probability of chromosome overlapping or intermingling (Bohn and Heermann, 2011). Thus entropy-driven looping of chromosomal DNA contributes to the efficient segregation of chromosomes within the nucleus. Nevertheless, given that the nucleotide sequence, size, mass and charge of the individual chromosomes is largely the same, as well as the overall composition of the nucleoplasm, in all cell types of a given mammal, these facts predict that chromosome location and distribution within the nucleus must be either quite similar or completely random in all cells. Yet there is strong evidence that during interphase individual chromosomes occupy well-defined discrete territories not intermingling among them, despite their relatively decondensed state by comparison with their mitotic form (Meaburn and Misteli, 2007). Also, interphase chromosomes show a significant preference for having specific nearest-neighbors according to cell type (Parada et al., 2004) and their arrangement within the nucleus changes during cell differentiation despite the fact that chromosome size and mass remain constant (Meaburn and Misteli, 2007). Moreover, the specific radial positions of chromosome centromeres remain unchanged despite experimental depletion of most chromatin (Petrova et al., 2005) indicating that the repulsive electrostatic interactions between chromosomes and the entropy-driven phase separation (mediated by colloidal depletion effects) are not enough for explaining the actual tissue-specific positioning of chromosomes during interphase. Molecular modeling suggests that a pure chromatin network is rather viscous and so the self-diffusion of such a network is too rapid to keep molecules trapped. Yet actual experiments with tracer molecules indicate a long-time trapping regime for the diffusing tracers suggesting that the nucleus actually contains an elastic network that cannot be constituted by a purely diffusive chromatin fiber since long-time trapping requires a stiffer network. This can be achieved by the crosslinking of chromatin to

Please cite this article as: Aranda-Anzaldo, A., The interphase mammalian chromosome as a structural system based on tensegrity. J. Theor. Biol. (2016), http://dx.doi.org/10.1016/j.jtbi.2016.01.005i

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

A. Aranda-Anzaldo / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

other stuff that stabilizes the formation of chromatin loops (Fritsch and Langowski, 2011). This implies the existence of an underlying stiffer macromolecular network that may account for the actual high elasticity of the cell nucleus and that affects the folding of interphase chromosomes. The experimental decondensation of interphase chromatin induced by protease treatment of isolated nuclei leads to entropic expansion of chromatin and the eventual rupture of the nuclear envelope and the underlying nuclear lamina (the protein layer that covers the nucleoplasmic side of the nuclear envelope). The kinetics of chromatin expansion and data from micro-rheological experiments using atomic force microscopy indicate that the entropic swelling of chromatin is only partially explained by the removal of nucleosomal histones and so the excess pressure driving the expansion is the result of eliminating a standing pre-stress operating upon chromatin due to its anchoring to an internal but resilient protein scaffold (Mazumder et al., 2008). Therefore, anchoring of chromatin to a scaffold compartment is necessary for preserving the structural integrity of the nucleus by establishing a counterbalance against the outward entropic forces generated by DNA behavior as a massive semiflexible polymer, since the inward forces arising from histone tail– tail interactions are not enough for that purpose.

7. The nuclear matrix Currently, the nuclear matrix (NM) is operationally defined as the substructure or compartment that results from extracting the nucleus with high salt and non-ionic detergent after extensive digestion of chromatin with DNase I (Engelke et al., 2014; Tsutsui et al., 2005). Classical reports suggested that the NM is a cage-like network of fibers that permeates the nuclear interior (Capco et al., 1982) such a network originally observed in fixed preparations after removal of chromatin has been also observed in unfixed preparations in which the chromatin has been removed under isotonic conditions (Wan et al., 1999). Furthermore, electron spectroscopic imaging reveals the presence of a protein network inside the nucleus of non-extracted cells (Hendzel et al., 1999) and there is a large number of experimental reports of NM observations (Nickerson, 2001; Zbarsky, 1998). However, for years there has been controversy about whether such a NM is an artifact resulting from precipitation of proteins after the extracting procedure (Martelli et al., 2002). The “artifact by precipitation” argument could hold when considering the use of ammonium sulfate in NM extraction (Capco et al., 1982; Fey et al., 1986), as this salt is known for its “salting-out” effects that promote protein precipitation. However the same argument goes against established knowledge when applied to the use of sodium chloride (Berezney and Coffey, 1974; 1977; Cook et al., 1976; Zbarsky, 1998), which is by far the salt most commonly used for NM extraction. Indeed, a simple inspection of the classical Hofmeister series that orders ions in terms of their ability to affect the solubility of proteins, shows that Na þ and Cl  are right in the middle of the series, thus neither ion displays significant “salting-out” or “salting-in” effects on proteins (Baldwin, 1996; Zhang and Cremer 2006). On the other hand, the notion of the NM as a rigid protein network that permeates the nuclear interior goes against the evidence for a relatively high diffusion rate of several proteins associated with the NM. Thus, it has been suggested that the NM is not a static cage-like structure but a relatively dynamic compartment (Nickerson, 2001; Tsutsui et al., 2005) a notion that ties in with the current consensus indicating that there is a nucleoskeleton integrated as a highly dynamic network of protein networks that includes many proteins considered to be classical components of the NM (Simon and Wilson, 2011).

5

67 State of the art proteomics coupled with sophisticated computer68 based analysis of data has been applied to preparations corresponding 69 to the three most widely used methods for extracting and obtaining 70 the NM. This work revealed the presence of a core NM proteome 71 corresponding to 272 proteins. The high correlation of the results 72 obtained with the three different extraction procedures argues against 73 the notion that the NM is an artifact or a randomly generated structure (Engeleke et al., 2014). However, analysis by electron-microscopic Q4 74 75 tomography of the NM resulting from the extraction with 2 M NaCl 76 (the most common NM-extraction method) reveals the presence of 77 several local scaffolding platforms within the nucleus instead of a 78 continuous meshwork spanning the entire nuclear volume (Engeleke 79 et al., 2014). This finding is consistent with the notion of a rather 80 dynamical NM instead of a cage-like structure. 81 82 8. The nuclear higher-order structure 83 84 DNA interacts with the NM through nucleotide sequences of 85 variable length known as matrix attachment or matrix addressed 86 regions (MARs). However in mammalian chromosomes there is no 87 consensus sequence that defines such MARs although they are 88 relatively rich in A–T and repetitive sequences besides mapping to 89 regions where DNA has propensity for bending, kinking or melting 90 (Ottaviani et al., 2008). In situ the MARs have been operationally 91 classified into constitutive-structural that resist extraction with 92 high salt and facultative-transient that do not resist such an 93 extraction. Therefore the resulting DNA loops can also be regarded 94 either as structural or facultative (Elcock and Bridger, 2008; Maya95 Mendoza et al., 2003; Razin, 2001). The high salt-resistant MARs 96 are also known as true loop anchorage regions (LARs) and define a 97 fundamental nuclear higher-order structure (NHOS) consisting of 98 structural DNA loops anchored to the NM (Aranda-Anzaldo, 2009). 99 It must be stressed that such NHOS is largely independent of the 100 nucleosomal organization and chromatin proteins as well as of 101 regulatory proteins (such as transcription factors) that may tran102 siently interact with DNA, since high salt extraction removes all 103 these proteins (Verheijen et al., 1986) and yet the NHOS remains. 104 Thus, currently it is not possible to establish a clear correlation 105 between the structural DNA loops constituting the NHOS and the 106 many and diverse chromatin loops determined by 3C (chromo107 some conformation capture) and related assays such as Hi-C that 108 depend on the artificial and indiscriminate cross-linking of nuclear 109 DNA with any sort of DNA bound proteins and whose many 110 caveats are a current matter of discussion (Gavrilov et al., 2013; 111 O’Sullivan et al., 2013; Williamson et al., 2014). Despite the iden112 tification of some tissue-specific MAR-binding proteins (Ottaviani 113 et al., 2008; Tsustsui et al., 2005) the lack of consensus sequence 114 for MARs coupled to the evidence that there are hundreds if not 115 thousands of potential MARs along a given chromosome (Boulikas, 116 1995; Hakes and Berezney, 1991; Maya-Mendoza et al., 2005) 117 suggest that most DNA–NM interactions do not depend on direct 118 readouts between specific nucleotides and specific aminoacids of 119 specialized DNA-binding proteins but more likely result from 120 indirect readouts that might depend on both the local and overall 121 topology of the interacting partners (Koudelka et al., 2006; 122 Yamasaki et al., 2012; Zhang et al., 2004). This is not an unheard 123 124 phenomenon since well known chromatin proteins such as those 125 belonging to the high-mobility group display affinity for bent or 126 distorted DNA independently of the local nucleotide composition 127 (Thomas, 2001). On the other hand, recent evidence indicates that 128 long non-coding RNAs (lncRNAs) are involved in the interactions 129 between DNA and NM proteins acting as a third party that either 130 organizes or mediates such interactions (Hacisuleyman et al., 131 2014; Hall et al., 2014; Nakagawa and Hirano, 2014; Nozawa and 132 Gilbert, 2014). These observations are consistent with the fact that

Please cite this article as: Aranda-Anzaldo, A., The interphase mammalian chromosome as a structural system based on tensegrity. J. Theor. Biol. (2016), http://dx.doi.org/10.1016/j.jtbi.2016.01.005i

A. Aranda-Anzaldo / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

standard NM preparations reveal a residual network composed of heterogeneous nuclear ribonucleoproteins (hnRNPs) and that a significant subset of nuclear RNAs resists the most radical extraction procedures, thus remaining as stable components of the NM (Fey et al., 1986; Nickerson, 2001). The experimental evidence indicates that the NHOS defined by the average pattern of structural DNA–NM interactions is cell typespecific (Rivera-Mulia and Aranda-Anzaldo, 2010; Trevilla-García and Aranda-Anzaldo, 2011, 2012). Thus considering that in a given species each chromosome DNA sequence is common to all cell types, the differential responsible for this cell type-specificity of the NHOS must lay on the properties of the NM as there is ample evidence of diverse cell type-specific NM proteins (Dent et al., 2010; Stuurman et al., 1990) that may constitute alternative options for DNA–NM interactions. Moreover, the highly-packed constitutive heterochromatin decays with time into less condensed states (Macieira-Coelho, 1995; Villeponteau, 1997) so that formerly hidden DNA sequences become exposed and so able to interact with the NM, thus contributing to the modification of the NHOS in time.

9. Mitotic chromosome structure In fully condensed mitotic chromosomes it has been observed the presence of a residual protein-rich scaffold after removal of chromatin proteins and digestion of DNA (Adolph et al., 1977). Moreover, classical electron micrographs show that histonedepleted metaphase chromosomes consist of a core scaffold that retains the overall shape of the metaphase chromosome surrounded by a dense halo of DNA loops anchored to the scaffold (Paulson and Laemmli, 1977). The size range of such DNA loops is quite similar to that reported for unwound DNA loops attached to the NM in interphase (Jackson et al., 1990). Thus early models for mitotic chromosome structure suggested a system of chromatin loops interconnected by a non-histone protein scaffold (Marsden and Laemmli, 1979). Later experiments indicated that the nonchromatin proteins that constitute the scaffold are not connected forming a continuous structure but rather they act as cross-linking nodes for DNA which is the actual linker that connects the chromosome-scaffold proteins together (Maniotis et al., 1997; Poirier and Marko, 2002; Sun et al., 2011). Recent results coupled to mathematical modeling suggest that the mitotic chromosome is organized as a linear compressed array of rather irregular consecutive loops (Naumova et al., 2013), although the size range of such loops (80–120 kb) is consistent with the average loop size reported for interphase chromosomes (Jackson et al., 1990). An important question is what happens with the chromosome scaffold during interphase and the obvious suggestion is that there must be similarity if not complete identity between the scaffold and the NM (Nickerson, 2001). Yet it is remarkable that there is only scattered evidence but no systematic characterization to date linking the chromosome scaffold with the NM (Sheval and Polyakov, 2006). For example, the enzyme topoisomerase II is an intrinsic component of the NM (Berrios et al., 1985) and it is also a standard component of the mitotic chromosome scaffold (Earnshaw et al., 1985) and plays a structural role in mitotic chromosomes that is independent of its enzymatic activities (Bojanowski et al., 1998).

10. A tensegrity model for the interphase chromosome structure Tensegrity (tensional-integrity) is an architecturalengineering principle that guides the building of structures in

67 which discontinuous compression elements balance the force 68 generated by continuous tension elements thus reaching a 69 structural equilibrium that is largely independent of gravity 70 (Galli et al., 2005; Ingber et al., 2014). In a tensegrity structure 71 the bulky compression elements are minimized as the force is 72 distributed to slender or lightweight tension elements resulting 73 in a highly-stable but not massive structure. A notable property 74 of tensegrity structures is the presence of isometric tension or 75 pre-stress that leads to a configuration that minimizes the 76 stored elastic energy of the whole structure (Galli et al., 2005). 77 Therefore, tensegrity structures require pre-stress of their 78 structural components for maintaining their integrity. Tensegr79 ity structures belong to the class of so-called underconstrained 80 structures that resist external loads by changing the spacing or 81 orientation of their structural components (Volokh and Vilnay, 82 83 1997). Currently there is ample evidence that tensegrity oper84 ates in the structural organization of cells and that tensegrity is 85 fundamental for understanding mechano-transduction within 86 and among cells (Ingber et al., 2014). In solid tissues a con87 tinuous system of mechano-transduction couples the extra88 cellular matrix with the cytoskeleton and the cell nucleus (Wang 89 et al., 2009). Indeed, the cell can be modeled as a vector field in 90 which the mechanically coupled cytoskeleton-nucleoskeleton is 91 the transducer of mechanical information (Aranda-Anzaldo, 92 1989). Such a model predicts that changes in cell shape result in 93 changes in the network of mechanical interactions leading to 94 modifications in the nuclear higher-order structure. Experi95 mental proof of principle of this has been provided by showing 96 that induction of stable change in cellular shape leads to change 97 in nuclear shape and modification of structural DNA loops 98 99 (Martínez-Ramos et al., 2005). Classical cable-and-strut tensegrity structures, such as the 100 101 well-known sculptures by Kenneth Snelson that can be easily 102 browsed through the internet, display a stability that depends on 103 continuous tension and discontinuous compression, since the 104 tensile load-bearing cables pull on both ends of the struts and put 105 them under compression while the struts push out and tense the 106 cables leading to the presence of tensile pre-stress. Thus an 107 interphase organization in which the bulk chromosomal DNA is 108 subdivided into supercoiled looped domains anchored to nodes of 109 internal scaffold/NM ribonucleoproteins, while the corresponding 110 telomeric regions are anchored to the peripheral nuclear lamina, 111 displays all the basic features of a tensegrity structural system in 112 which the DNA plays the cable role while the nodes of NM con113 stituents play the role of the compressible struts (Fig. 5). Indeed, 114 experimental evidence that massive perturbation of the super115 coiling present in the structural DNA loops leads to wholesale Q5116 117 fragmentation of the NM (Maya-Mendoza et al., 2005; Alva118 Medina et al., 2011) is consistent with the notion that interphase 119 chromosomes correspond to tensegrity structures since the 120 induction of tearing forces by forced unwinding of the DNA loops 121 affects the stability of the proteinaceous NM. Moreover, the 122 attachment of the whole set of chromosome telomeres to the 123 peripheral lamina component of the NM (Luderus et al., 1996) 124 guarantees that the resulting structural organization is balanced 125 by both internal (nodes of NM-constituents) and external ele126 ments (peripheral nuclear lamina) leading to minimization of the 127 stored elastic energy of the whole set of chromosomes, and this 128 shields the nucleus against the massive outward entropic forces 129 that an unconstrained chromatin might generate (Mazumder et al., 130 2008) and that otherwise may cause spontaneous disintegration of 131 132 the nucleus.

Please cite this article as: Aranda-Anzaldo, A., The interphase mammalian chromosome as a structural system based on tensegrity. J. Theor. Biol. (2016), http://dx.doi.org/10.1016/j.jtbi.2016.01.005i

A. Aranda-Anzaldo / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

Fig. 5. In the interphase nucleus the chromosome telomeres are bound to the nuclear lamina component of the NM (violet rectangles) that underlies the inner membrane of the nuclear envelope (Luderus et al., 1996), while supercoiled loops of chromosomal DNA are bound to rather heterogeneously-sized conglomerates of ribonucleoproteins of the internal NM (green dots) (Cook et al., 1976; Jackson et al., 1990; Razin et al., 1995; Razin, 2001; Roti-Roti et al., 1993) constituting a tensegrity structural system in which DNA is the continuous tension element and the NM contributes the discontinuous compression elements (A). Both quantitative and qualitative changes in NM composition during cell differentiation lead to the actualization of further DNA–NM interactions (Alva-Medina et al., 2011; MayaMendoza et al., 2005; Dent et al., 2010) resulting in a larger number of shorter and more homogeneously sized DNA loops per unit length of chromosomal DNA (B). (For interpretation of the reference to color in this figure legend, the reader is reffered to the web version of this article.)

7

(supercoiled loops) results in the dissipation, by compartmentalization into multiple discrete units, of the torsional stress along the DNA molecule and so the stress energy is more homogeneously distributed within the nucleus. This phenomenon satisfies the second law of thermodynamics. Indeed, the paradoxical emergence of structure in open systems (such as the cell) able to export entropy to the surroundings is not a contradiction but a confirmation of the second law of thermodynamics (Ebeling, 2005). It seems that cell differentiation is coupled to a structural process within the nucleus that relentlessly evolves from a dynamic but asymmetric state towards a stable and symmetric attractor depending on thermodynamic constraints (Alva-Medina et al., 2011; Maya-Mendoza et al., 2005). This entropy-driven process (that results in the presence of supercoiled DNA loops anchored to constituents of the NM) is the primary factor leading to DNA condensation and packaging within the nucleus, while the interaction of DNA with chromatin proteins increases the degree of DNA packaging but also contributes to the dynamic regulation of genome functions. The organization of interphase chromosomes as tensegrity structures that collectively contribute to the nuclear higher-order structure allows the individual chromosomes to participate in local structural transactions, associated with normal genome functions such as replication or transcription, while preserving a basic chromosomal organization that is resilient and so non-permissive to wholesale perturbation and disorganization.

Acknowledgments 11. Conclusion The existence of metazoan chromosomes constituted by very lengthy DNA molecules poses, from the functional and structural perspective, the problem of how to avoid the spontaneous breakage of such molecules carriers of genetic information. The experimental evidence shows that chromosomal DNA spontaneously organizes into DNA loops that become stabilized and supercoiled by anchoring to clusters (nodes) of ribonucleoproteins from the internal NM (Alva-Medina et al., 2011; Cook et al., 1976; Maya-Mendoza et al., 2005; Razin, 2001; Roti-Roti et al., 1993). Yet the nodes become interconnected by the linker DNA, that it is also linked to the peripheral nuclear lamina (Luderus et al., 1996). Thus the nuclear higher-order structure, defined by the set of structural DNA–NM interactions, constitutes an integral structural system linking elements of the internal and peripheral NM. The trend is for such interactions to increase on average in time resulting in a larger number of shorter and more homogeneously sized DNA loops until most if not all torsional stress has been dissipated (Alva-Medina et al., 2011; Maya-Mendoza et al., 2005). This fact correlates with quantitative changes in the NM composition (Fig. 5) due to cell differentiation and aging (Alva-Medina et al., 2011; Maya-Mendoza et al., 2005). Indeed, the experimental evidence indicates that the supercoiled DNA loops are less numerous and more heterogeneous in size in cells preserving a proliferating potential, while such loops become more numerous and more homogeneous in size in terminally differentiated cells (AlvaMedina et al., 2010; Maya-Mendoza et al., 2005). The result is a higher stability of the nuclear higher-order structure in fully differentiated, post-mitotic cells, which has been suggested to represent the non-genetic structural basis of their post-mitotic condition (Aranda-Anzaldo 2012; Aranda-Anzaldo et al., 2014) considering that the post-mitotic state appears to be independent of specific gene functions since so far there are not known gene mutations able to revert it (Rakic, 2006). The entropy-driven trend for subdividing the lengthy metazoan chromosome into numerous independent topological domains

I thank the members of the Laboratorio de Biología Molecular y Neurociencias for helpful discussions. This work was sponsored by CONACYT-México Grant 176794. CONACYT had no role in the writing or preparation of this work for publication. The author declares no conflict of interest.

References Adolph, K.W., Cheng, S.M., Paulson, J.R., Laemmli, U.K., 1977. Isolation of a protein scaffold from mitotic HeLa cell chromosomes. Proc. Natl. Acad. Sci. USA 74, 4937–4941. Alva-Medina, J., MAR, Dent, Aranda-Anzaldo, A., 2010. Aged and post-mitotic cells share a very stable higher-order structure in the cell nucleus in vivo. Biogerontology 11, 703–716. Alva-Medina, J., Maya-Mendoza, A., MAR, Dent, Aranda-Anzaldo, A., 2011. Continued stabilization of the nuclear higher-order structure of post-mitotic neurons in vivo. PLoS One 6 (6), e21360. Aranda-Anzaldo, A., 1989. On the role of chromatin higher-order structure and mechanical interactions in the regulation of gene expression. Speculat. Sci. Technol., 163–176. Aranda-Anzaldo, A., 2009. A structural basis for cellular senescence. Aging 1, 598–607. Aranda-Anzaldo, A., 2012. The postmitotic state in neurons correlates with a stable nuclear higher-order structure. Commun. Integr. Biol. 5, 134–139. Aranda-Anzaldo, A., Dent, M.A.R., Gómez-Martínez, A., 2014. The higher-order structure in the cell nucleus as the structural basis of the postmitotic state. Prog. Biophys. Mol. Biol. 114, 137–145. Bachmann, K., 1972. Genome size in mammals. Chromosoma 37, 85–93. Baldwin, R.L., 1996. How Hofmeister ion interactions affect protein stability. Biophys. J. 71, 20156–20206. Bates, A.D., Maxwell, A., 2005. DNA Topology, 2nd ed. Oxford University Press, Oxford, U.K. Bednar, J., Furrer, P., Stasiak, A., Dubochet, J., Egelman, E.H., Bates, A.D., 1994. The twist, writhe and overall shape of supercoiled DNA change during counterioninduced transition from a loosely to a tightly interwound superhelix. Possible implications for DNA structure in vivo. J. Mol. Biol. 235, 825–847. Berezney, R., Coffey, D.S., 1974. Identification of a nuclear protein matrix. Biochem. Biophys. Res. Commun. 60, 1410–1417. Berezney, R., Coffey, D.S., 1977. Nuclear matrix, isolation and characterization of a framework structure from rat liver nuclei. J. Cell Biol. 73, 616–637. Berrios, M., Osheroff, N., Fisher, P.A., 1985. In situ localization of DNA topoisomerase II, a major polypeptide component of the Drosophila nuclear matrix fraction. Proc. Natl. Acad. Sci. USA 82, 4142–4146.

Please cite this article as: Aranda-Anzaldo, A., The interphase mammalian chromosome as a structural system based on tensegrity. J. Theor. Biol. (2016), http://dx.doi.org/10.1016/j.jtbi.2016.01.005i

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 Q6 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

A. Aranda-Anzaldo / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Bohn, M., Heermann, D., 2011. Repulsive forces between looping chromosomes induce entropy-driven segregation. PLoS One 6 (1), e14428. Bojanowski, K., Maniotis, A.J., Plisov, S., Larsen, A.K., Ingber, D.E., 1998. DNA topoisomerase II can drive changes in higher order chromosome architecture without enzymatically modifying DNA. J. Cell Biochem. 69, 127–142. Boulikas, T., 1995. Chromatin domains and prediction of MAR sequences. Int. Rev. Cytol. 162A, 279–388. Capco, D.G., Wan, K.M., Penman, S., 1982. The nuclear matrix: three-dimensional architecture and protein composition. Cell 29, 847–858. Chereji, R.V., Morozov, A.V., 2015. Functional roles of nucleosome stability and dynamics. Brief. Funct. Genom. 14, 50–60. Cook, P.R., Brazell, I., Jost, E., 1976. Characterization of nuclear structures containing superhelical. DNA J. Cell Sci. 22, 303–324. Deal, R.B., Henikoff, J.G., Henikoff, S., 2010. Genome-wide kinetics of nucleosome turnover determined by metabolic labeling of histones. Science 328, 1161–1164. Dent, M.A.R., Segura-Anaya, E., Alva-Medina, J., Aranda-Anzaldo, A., 2010. NeuN/ Fox3 is an intrinsic component of the neuronal nuclear matrix. FEBS Lett. 584, 2767–2771. Earnshaw, W.C., Halligan, B., Cooke, C.A., Heck, M.M., Liu, L.F., 1985. Topoisomerase II is a structural component of mitotic chromosome scaffolds. J. Cell Biol. 100, 1706–1715. Ebeling, W., 2005. Thermodynamics, past, present and future. In: Adv. Solid State Phys. B. Kramer (ed); 45: 3-14. Elcock, L.S., Bridger, J.M., 2008. Exploring the effects of a dysfunctional nuclear matrix. Biochem. Soc. Trans. 36, 1378–1383. Engelke, R., Riede, J., Hegermann, J., Wuerch, A., Eimer, S., Dengjel, J., Mittler, G., 2014. The quantitative nuclear matrix proteome as a biochemical snapshot of nuclear organization. J. Proteome Res. 13, 3940–3956. Fey, E.G., Krochmalnic, G., Penman, S., 1986. The non-chromatin substructures of the nucleus: the ribonucleoprotein (RNP)-containing and RNP-depleted matrices analyzed by sequential fractionation and resinless section electron microscopy. J. Cell Biol. 102, 1654–1665. Finan, K., Cook, P.R., Marenduzzo, D., 2011. Non-specific (entropic) forces as major determinants of the structure of mammalian chromosomes. Chromosome Res. 19, 53–61. Frank-Kamenetskii, M.D., Prakash, S., 2014. Fluctutations in the double helix: a critical review. Phys. Life Rev. 11, 153–170. Fritsch, C.C., Langowski, J., 2011. Chromosome dynamics, molecular crowding and diffusion in the interface nucleus: a MonteCarlo lattice simulation study. Chromosome Res. 19, 63–81. Galli, C., Guizazardi, S., Passeri, G., Macaluso, G.M., Scandroglio, R., 2005. Life on the wire: on tensegrity and force balance in cells. Acta Bio. Med. 76, 5–12. Gavrilov., A.A., Golov, A.K., Razin, S.V., 2013. Actual ligation frequencies in the chromosome conformation capture procedure. PLoS One 8 (3), e60403. Giudice, E., Várnai, P., Lavery, R., 2003. Base pair opening within B DNA: free energy pathways for GC and AT pairs from umbrella sampling simulations. Nucleic Acids Res. 31, 1434–1443. Gregory, T.R., 2015. Animal genome size database. 〈http://www.genomesize.com〉. Hacisuleyman, E., Goff, L.A., Trapnell, C., Willimas, A., Henao-Mejia, J., Sun, L., McClanahan, P., Hendrickson, D.G., Sauvageau, M., Kelly, D.R., Morse, M., Engreitz, J., Lander, E.S., Guttman, M., Lodish, H.F., Flavell, R., Raj, A., Rinn, J.L., 2014. Topological organization of multi-chromosomal regions by Firre. Nat. Struct. Mol. Biol. 21, 198–206. Hakes, D.J., Berezney, R., 1991. DNA binding properties of the nuclear matrix and individual nuclear matrix proteins. J. Biol. Chem. 266, 1113–11140. Hall, L.L., Carone, D.M., Gomez, A.V., Kolpa, H.J., Byron, M., Metha, N., Fackelmayer, M.O., Lawrence, J.B., 2014. Stable C0T-1 repeat RNA is abundant and is associated with euchromatic interphase chromosomes. Cell 156, 907–919. Hancock, R., 2014. The crowded nucleus. Int. Rev. Cell Mol. Biol. 307, 15–26. Hemmerich, P., Schimiedeberg, L., Dieckmann, S., 2011. Dynamic as well as stable protein interactions contribute to genome functiona and maintenance. Chromosome Res. 19, 131–151. Hendzel, M.J., Boisvert, F., Bazett-Jones, D.P., 1999. Direct visualization of a protein nuclear architecture. Mol. Biol. Cell 10, 20151–22062. Ingber, D.E., Wang, N., Stamenovic, D., 2014. Tenesgrity, cellular biophysics and the mechanics of living systems. Rep. Prog. Phys. 77 (4), 046603. Jackson, D.A., Dickinson, P., Cook, P.R., 1990. The size of chromatin loops in HeLa cells. EMBO J. 9, 567–571. Koudelka, G.B., Mauro, S.A., Ciubotaru, M., 2006. Indirect readout of DNA sequence by proteins: the roles of DNA sequence-dependent intrinsic and extrinsic forces. Prog. Nucleic Acid. Res. Mol. Biol. 81, 143–177. Kramer, P.R., Sinden, R.R., 1997. Measurement of unrestrained negative supercoiling and topological domain size in living human cells. Biochemistry 36, 3151–3158. Lipfert, J., Doniach, S., Das, R., Herschlag, D., 2014. Understanding nucleic acid-ions interactions. Ann. Rev. Biochem. 83, 813–841. Lomholt, M.A., van den Broek, B., Kalisch, S.-M.J., Wuite, G.J.L., Metzler, R., 2009. Facilitated diffusion with DNA coiling. Proc. Natl. Acad. Sci. USA 106, 8204–8208. Luderus, M.E., van Steensel, B., Chong, L., Sibon, O.C., Cremers, F.F., de Lange, T., 1996. Structure, subnuclear localization and nuclear matrix association of the mammalian telomeric complex. J. Cell Biol. 135, 867–881. Lusser, A., Kadonaga, J.T., 2004. Strategies for the reconstitution of chromatin. Nat. Methods 1, 19–26. Macieira-Coelho, A., 1995. The last mitoses of the human fibroblast proliferative lifespan, physiopathologic implications. Mech. Ageing Dev. 82, 91–104.

Maniotis, A.J., Bojanowski, K., Ingber, D.E., 1997. Mechanical continuity and reversible chromosome disassembly within intact genomes removed from living cells. J. Cell Biochem. 65, 114–130. Marsden, M.P., Laemmli, U.K., 1979. Metaphase chromosome structure: evidence of a radial loop model. Cell 17, 849–858. Martelli, A.M., Falcieri, E., Zweyer, M., Bortul, R., Tabellini, G., Cappellini, A., Cocco, L., Manzoli, L., 2002. The controversial nuclear matrix: a balanced point of view. Histol. Histopathol. 17, 1193–11205. Martínez-Ramos, I., Maya-Mendoza, A., Gariglio, P., Aranda-Anzaldo, A., 2005. A global but stable change in HeLa cell morphology induces reorganization of DNA structural loop domains within the cell nucleus. J. Cell Biochem. 96, 79–88. Maya-Mendoza, A., Hernández-Muñoz, R., Gariglio, P., Aranda-Anzaldo, A., 2003. Gene positional changes relative to the nuclear substructure correlate with the proliferating status of hepatocytes during liver regeneration. Nucleic Acids Res. 31, 6168–6179. Maya-Mendoza, A., Hernández-Muñoz, R., Gariglio, P., Aranda-Anzaldo, A., 2005. Natural ageing in the rat liver correlates with progressive stabilisation of DNAnuclear matrix interactions and withdrawal of genes from the nuclear substructure. Mech. Ageing Dev. 126, 767–782. Mazumder, A., Roopa, T., Basu, A., Mahadevan, L., Shivashankar, G.V., 2008. Dynamics of chromatin decondensation reveals the structural integrity of a mechanically prestressed nucleus. Biophys. J. 95, 3028–3035. Meaburn, K.J., Misteli, T., 2007. Chromosome territories. Nature 445, 379–381. Mirkin, S.M., 2001. DNA topology: fundamentals. eLS. Nakagawa, S., Hirano, T., 2014. Gathering around Firre. Nat. Struct. Mol. Biol. 21, 207–208. Naumova, N., Imakaev, M., Fudenberg, G., Zhan, Y., Lajoie, B.R., Mirny, L.A., Dekker, J., 2013. Organization of the mitotic chromosome. Science 342, 948–953. Nelson, P., 1999. Transport of torsional stress in DNA. Proc. Natl. Acad. Sci. USA 96, 14342–14347. Neumann, R.M., 1977. The entropy of a single Gaussian macromolecule in a noninteracting solvent. J. Chem. Phys. 66, 870–871. Nickerson, J.A., 2001. Experimental observations of a nuclear matrix. J. Cell Sci. 114, 463–474. Nikolova, E.N., Kim, E., Wise, A.A., O’Brien, P.J., Andricioaei, I., Al-Hashimi, H.M., 2011. Transient Hoogsteen base pairs in canonical duplex DNA. Nature 470, 498–502. Nikolova, E.N., Zhou, H., Gottardo, F.L., Alvey, H.S., Kimsey, I.J., Al-Hashimi, H.M., 2013. A historical account of Hoogsteen base pairs in DNA. Biopolymers 99, 955–968. Nozawa, R.-S., Gilbert, N., 2014. Interphase chromatin LINEd with RNA. Cell 156, 864–865. O’Sullivan, J.M., Hendy, M.D., Pichugina, T., Wake, G.C., Langowski, J., 2013. The statistical mechanics of chromosome conformation capture. Nucleus 4, 390–398. Ottaviani, D., Lever, E., Takousis, P., Sheer, D., 2008. Anchoring the genome. Genome Biol. 9 (1), 201. Parada, L.F., McQueen, P.G., Misteli, T., 2004. Tissue-specific spatial organization of genomes. Genome Biol. 5, R44. Patterton, H.G., von Holt, C., 1993. Negative supercoiling and nucleosome cores. I. The effect of negative supercoiling on the efficiency of nucleosome core formation in vitro. J. Mol. Biol. 229, 623–636. Paulson, J.R., Laemmli, U.K., 1977. The structure of histone-depleted metaphase chromosomes. Cell 12, 817–828. Peters III, J.P., Maher, L.J., 2010. DNA curvature and flexibility in vitro and in vivo. Q. Rev. Biophys. 43, 23–63. Petrova, N.V., Iarovaia, O.V., Verbovoy, V.A., Razin, S.V., 2005. Specific radial positions of centromeres of human chromosomes X, 1 and 19 remain unchanged in chromatin-depleted nuclei of primary human fibroblasts: evidence for the organizing role of the nuclear matrix. J. Cell Biochem. 96, 850–857. Pfaffle, P., Jackson, V., 1990. Studies on rates of nucleosome formation with DNA under stress. J. Biol. Chem. 265 16821–1689. Poirier, M., Marko, J.F., 2002. Mitotic chromosomes are chromatin networks without a mechanically contiguous protein scaffold. Proc. Natl. Acad. Sci. USA 99, 15393–15397. Rakic, P., 2006. Neuroscience: no more cortical neurons for you. Science 313, 928–929. Razin, S.V., 2001. The nuclear matrix and chromosomal DNA loops: is there any correlation between partitioning of the genome into loops and functional domains? Cell Mol. Biol. Lett. 6, 59–69. Razin, S.V., GromovaII, S.V., Iarovaia, O.V., 1995. Specificity and functional significance of DNA interactions with the nuclear matrix: new approaches to clarify the old questions. Int. Rev. Cytol. 162B, 405–448. Rivera-Mulia, J.C., Aranda-Anzaldo, A., 2010. Determination of the in vivo structural DNA loop organization in the genomic region of the rat albumin locus by means of a topological approach. DNA Res. 17, 23–35. Roti-Roti, J.L., Wright, W.D., Taylor, Y.C., 1993. DNA loop structure and radiation response. Adv. Radiat. Biol. 17, 227–259. Rybenkov, V.V., Cozzarelli, N.R., Vologodskii, A.V., 1993. Probability of DNA knotting and the effective diameter of the DNA double helix. Proc. Natl. Acad. Sci. USA 90, 5307–5311. Sheval, E.V., Polyakov, V.Y., 2006. Visualization of the chromosome scaffold and intermediates of loop domain compaction in extracted mitotic cells. Cell Biol. Int. 30, 1028–1040. Simon, D.N., Wilson, K.L., 2011. The nucleoskeleton as a genome-associated dynamic network of networks. Nat. Rev. Mol. Cell Biol. 12, 695–708.

Please cite this article as: Aranda-Anzaldo, A., The interphase mammalian chromosome as a structural system based on tensegrity. J. Theor. Biol. (2016), http://dx.doi.org/10.1016/j.jtbi.2016.01.005i

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

A. Aranda-Anzaldo / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

Stuurman, N., Meijne, A.M.L., van Der Pol, A.J., de Jong, L., van Driel, R., van Renswoude, J., 1990. The nuclear matrix from cells of different origin. J. Biol. Chem. 265, 5460–5465. Sun, M., Kawamura, R., Marko, J.F., 2011. Micromechanics of human mitotic chromosomes. Phys. Biol. 8, 015003. Teif, V.B., Bohinc, K., 2011. Condensed DNA; condensing the concepts. Prog. Biophys. Mol. Biol. 105, 208–222. Thomas, J.O., 2001. HMG1 and 2: architectural DNA-binding proteins. Biochem. Soc. Trans. 29, 395–401. Travers, A.A., 2004. The structural basis of DNA flexibility. Phil. Trans. R. Soc. Lond. A 362, 1423–1438. Trevilla-García, C., Aranda-Anzaldo, A., 2011. Cell-type-specific organization of nuclear DNA into structural looped domains. J. Cell Biochem. 112, 531–540. Trevilla-García, C., Aranda-Anzaldo, A., 2012. The organization of a large transcriptional unit (Fyn) into structural DNA loops is cell-type specific and independent of transcription. Gene 493, 1–8. Tsutsui, K.M., Sano, K., Tsutsui, K., 2005. Dynamic view of the nuclear matrix. Acta Med. Okayama 59, 113–120. van Aalten, D.M.F., Erlanson, D.A., Verdine, G.L., Joshua-Tor, L., 1999. A structural snapshot of base-pair opening of DNA. Proc. Natl. Acad. Sci. USA 96, 11809–11814. Verheijen, R., Kuijpers, H., Vooijs, P., van Venrooij, Ramaekers, F., 1986. Protein composition of nuclear matrix preparations from HeLa cells: an immunochemical approach. J. Cell Sci. 80, 103–122. Villeponteau, B., 1997. The heterochromatin loss model of aging. Exp. Gerontol. 32, 383–394. Vologodskii, A., Frank-Kamenetskii, M.D., 2013. Strong bending of the DNA double helix. Nucleic Acids Res. 41, 6785–6792. Volokh, K.Y., Vilnay, O., 1997. Natural, kinematic and elastic displacements of underconstrained structures. Int. J. Solids Struct. 34, 911–930.

9

von Hippel, P.H., Johnson, N.P., Marcus, A.H., 2013. Fifty years of DNA breathing: reflections on old and new approaches. Biopolymers 99, 923–954. Wan, K.M., Nickerson, J.A., Krockmalinc, G., Penman, S., 1999. The nuclear matrix prepared by amine modification. Proc. Natl. Acad. Sci. USA 96, 933–938. Wang, N., Tytell, J.D., Ingber, D.E., 2009. Mechanotransduction at a distance: mechanically coupling the extracellular matrix and the nucleus. Nat. Rev. Mol. Cell Biol. 10, 75–82. Williamson, I., Berlivet, S., Eskeland, R., Boyle, S., Illingworth, R.S., Paquette, D., Dostie, J., Bickmore, W.A., 2014. Spatial genome organization: contrasting views from chromosome conformation capture and in situ hybridization. Genes. Dev. 28, 2778–2791. Woodcock, C.L., Ghosh, R.P., 2010. Chromatin higher-order structure and dynamics. Cold Spring Harb. Perspect. Biol. 2, a000596. Worcel, A., Strogatz, S., Riley, D., 1981. Structure of chromatin and the linking number of DNA. Proc. Natl. Acad. Sci. USA 78, 1461–1465. Wu, Z., Ono., A., Kainosho, M., Bax, A., 2001. H…N hydrogen bond lengths in double stranded DNA from internucleotide dipolar couplings. J. Biomol. NMR 19, 361–365. Yamasaki, S., Terada, T., Kono, H., Shimizu, K., Sarai, A.A., 2012. New method for evaluating the specificity of indirect readout in protein-DNA recognition. Nucleic Acids Res. 40, e129. Zbarsky, I.B., 1998. On the history of nuclear matrix manifestation. Cell Res. 8, 99–103. Zhang, Y., Xi, Z., Hegde, R.S., Shakked, Z., Crothers, D.M., 2004. Predicting indirect readout effects in protein–DNA interactions. Proc. Natl. Acad. Sci. USA. 101, 8337–8341. Zhang, Y., Cremer, P.S., 2006. Interactions between macromolecules and ions: the Hofmeister series. Curr. Opin. Chem. Biol. 10, 658–663.

Please cite this article as: Aranda-Anzaldo, A., The interphase mammalian chromosome as a structural system based on tensegrity. J. Theor. Biol. (2016), http://dx.doi.org/10.1016/j.jtbi.2016.01.005i

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132