The nucleus is an organelle found in most eukaryotic cells, the exception being red blood cells. In animal cells it is both the largest and stiffest organelle and is easily identifiable by light microscopy. The average mammalian nucleus has a diameter of ~6µm and occupies about 10% of the total cell volume.
The primary functions of the nucleus are to store the cell’s DNA, maintain its integrity, and facilitate its transcription and replication. The nuclear contents, which include the genetic material and the many proteins required for its processing, are enclosed within a double membrane known as the nuclear envelope, but remain functionally connected to the cytoplasm via nuclear pores. It is through these pores that RNA can be transported to the cytoplasm for further processing.
The nucleus is composed of several substructures and highly dynamic intra-nuclear regions. At its periphery, the nucleus possesses a double lipid bilayer that serves to separate the nuclear contents from the cytoplasm. This membrane is continuous with the rough endoplasmic reticulum, and as such, is studded with ribosomes. Since the membrane is impermeable to most molecules, traffic between the nucleus and cytoplasm is mediated though nuclear pores (reviewed in ). These pores, which enable the selective transport of water soluble molecules through the nuclear membrane are themselves composed of a large number of proteins (several hundred in mammals). Although many larger biomolecules, including proteins and RNA, are unable to passively diffuse through these pores they may be actively transported in conjunction with importin/karyopherin proteins and the RanGTP family of small GTPases. Adjacent to the nuclear membrane is a network of intermediate filaments known as the nuclear lamina. This layer is mainly composed of lamin proteins and primarily provides mechanical strength to the nucleus (reviewed in ).
Deeper inside the nucleus resides the DNA, which usually exists in the form of interphase chromosomes. Being an extremely long molecule (~2 meters for mammals) DNA must be packaged extensively to fit inside the relatively small space of the nucleus. This is achieved via an energy dependent process that involves numerous proteins and ultimately gives rise to a structure known as chromatin.
Despite the importance of DNA packaging, it is equally important that the DNA sequence remains accessible to repair and transcription machinery. This accessibility is highly dependent on the extent of compaction and this is reflected in the two types of chromatin that exist in the nucleus; euchromatin and heterochromatin (reviewed in ). Euchromatin is less compact than heterochromatin and is more transcriptionally active.
Another prominent structure found in the nucleus is the nucleolus. This is often seen as a distinctly dense body and is sometimes referred to as a sub-organelle (reviewed in ), although it is not bound by membrane. The nucleolus is enriched with tandem repeats of rDNA (regions of DNA that encode rRNA or ribosomal RNA). The major role of the nucleolus therefore, is the synthesis of rRNA and the assembly of ribosomes – the protein synthesis machinery of the cell.
Along with these major structural and functional components of the nucleus, dozens of additional smaller assemblies are often observed. These include cajal bodies, promyelocytic leukemia bodies, nuclear speckles, etc (reviewed in ). While the functions of these structures remain unclear, their presence clearly indicates a high level of functional compartmentalization and organization within the nucleus.
As an integral part of cellular behavior, cells are sensitive to matrix rigidity, local geometry and stress or strain applied by external factors . In recent years, it has been established that an extensive network of protein assembly couples the cytoskeleton to the nucleus  (reviewed in ) and that condensation forces of the chromatin balance cytoskeletal forces resulting in a prestressed nuclear organization . Hence, besides remodeling cytoskeletal filaments, the forces generated within the cell and that experienced at distant cell surface sites converge to the nucleus. This can happen either by physical transmission along the linked cytoskeleton  (reviewed in ) or by chemical signaling, where transcription regulators get transported to the nucleus upon activation  (reviewed in ). These mechanosignals have a significant impact on the mechanical properties of the nucleus such as shape and rigidity (reviewed in  ) through modification of the scaffolding proteins at the nuclear envelope and interior.
The double-membrane envelope, the non-random organization of chromatin and the nuclear scaffold proteins, all contribute to the rigidity of the nucleus  (reviewed in ). Nevertheless, its shape and size vary considerably between different cell types and organisms. Various tensile and compressive elements modulate the nuclear envelope, ultimately dictating the overall nuclear size, rigidity and morphology. For example, change in cell size also affects nuclear size in most differentiated cells. Maintenance of a certain volume ratio between the cell and nucleus (karyoplasmic ratio) is critical for transcription regulation .
With the cytoskeleton providing an outward pull and chromatin compaction providing an inward force, the nucleus can be envisioned as an elastic structure maintained in a stretched state due to force balance. Any perturbation to this homeostasis causes disorder in the system due to shrinkage or bulging of the nucleus, thus impairing its functional landscape. DNA processing and gene expression programs are affected due to alterations in cytoskeleton, nucleoskeleton and genome compaction   (reviewed in ). In other words, the nucleus can be regarded as a load bearing organelle that can physically transmit mechanical cues  and a plethora of cellular traits, such as shape, motility, differentiation and development.
Similar to the concept of long distance force propagation along cytoskeleton based on the tensegrity model, the prestressed nuclear state due to intracellular force balance enables mechanotransduction  . Both the nuclear envelope and nuclear interior contribute to its mechanical properties.
Several studies on nuclear mechanical properties have convincingly established that the nucleus is about 3-10 times stiffer than the surrounding cytoplasm depending on cell type . Nuclear stiffness is mainly attributed to lamins A and lamins C, that form a network underneath the nuclear envelope termed ‘nuclear lamina’ . Their role is very evident in the case of stem cells, where lamin A is absent. Hence their nuclei are highly fragile, while upon differentiation (whereby lamin A is being expressed) they stiffen and resist deformation .
Further, the plasticity of stem cell nucleus is attributed to enhanced collisions between chromosome interfaces due to lack of spatial organization. Differentiated cells reveal precise cell-type specific positional coordinates for each chromosome through physical anchoring to other chromosomes or scaffolding proteins  . Such well-defined interfaces are brought about by the orderly assembly of nuclear structural proteins upon activation of gene expression programs  .
Microrheology studies have also demonstrated a higher viscoelastic modulus for the nucleoplasm relative to cytoplasm, arising primarily due to the heterogeneous chromatin organization . The nuclear envelope behaves like an elastic sac with gel-like viscous contents . The importance of nuclear mechanics is reflected in many disease conditions.
Cytoskeletal filaments bridge the nucleus to the plasma membrane, which in turn is anchored at sub-cellular sites to extracellular substrates via a plethora of proteins that form focal adhesions (FAs). FAs are points of cross-talk between transmembrane integrin receptors and the cytoplasmic filaments and thus are key sites for both biochemical and mechanotransduction pathways (reviewed in ). Linkage can be direct or via various adaptor proteins, providing structural support to both cellular and nuclear structures (reviewed in )
While actin filaments and microtubules constantly undergo remodeling by a contractile mechanism and dynamic instability respectively  domain proteins and the microtubule associated motor protein, dynein, thus providing structural integrity to the nucleus. From inside, the nuclear lamins and chromatin are anchored to the inner nuclear membrane through adaptor transmembrane SUN (Sad1p, UNC-84) proteins, which in turn are connected to KASH proteins . Hence, though physically separated by the nuclear membrane (~50nm), the cytoplasm and nucleoplasm are linked by these evolutionarily conserved proteins, that mediate force transmission. Together these proteins are known as the Linker of Nucleoskeleton and Cytoskeleton (LINC) complex, . The localization of KASH domain proteins like nesprin at outer nuclear envelope is affected by depletion of SUNs, which in turn depend on nuclear lamins . These links are emerging to be pivotal in various physiological processes including cell migration and cytoskeletal integrity. Together, this network helps the cell cope with mechanical stress .
Work by Mazumder et al. ascertained the active involvement of cytoskeletal forces in determining nuclear morphology. Change in nuclear size upon perturbation of actomyosin and microtubules affirmed their roles in exerting tensile and compressive forces respectively on the nucleus, correlating with their functions in the cellular context  , .
Furthermore, the ‘perinuclear cap’, which is composed of contractile actin bundles that bridge focal adhesions on either side of the nucleus, has been shown to tightly regulate the nuclear geometry . These bundles pass apically to form a dome covering the top of the nucleus and are connected to the nucleus through the LINC complexes. They are completely absent in pluripotent cells whereas during differentiation, their formation accompanies expression and assembly of lamin A/C as well as the LINC complexes on the nuclear envelope . As a result, the nuclear height and shape are under their control, suggesting a role in mediating mechanosensitive processes such as motility and polarization .
Besides nuclear morphology, cytoplasmic forces also govern nuclear positioning in the cell by regulating the translational and rotational dynamics  . Positioning is accomplished by the physical connection by nuclear envelope proteins SUN-KASH-lma1 between centromeric heterochromatin regions and the microtubule network . With the centromere providing tensional force on the microtubules that undergo dynamic instability, dynein motors mediate the rotation . Actin links via SUN-nesprin are implicated in force transduction for nuclear movement during cell migration . Regulation of nuclear position and orientation is critical in many cellular processes such as migration, cell division, polarization, fertilization and differentiation .
The nucleoskeleton is a complex network comprising several mechanical structures that provide structural integrity and stability to the nucleus. They form an elastic shell at the nuclear periphery and scaffolds for localized stiffness in the viscoelastic interior; both of which are thought to serve as platforms for different genome functions (reviewed in ). However, the underlying mechanisms are not well understood.
At the nuclear envelope, lamins A/lamins C form a meshwork of interconnected rods manifesting stiffness to the otherwise floppy nucleus   while in the interior they are involved in the DNA processing that include transcription control during G1-S phase transition of cell cycle and chromatin remodeling during replication  (reviewed in ). B-type lamins play fundamental roles in transcription and cellular signaling during processes such as cell migration .
The nuclear lamina, which is a region that lies between the inner nuclear membrane and the peripheral chromatin, is composed of a compressed lamin layer along with an array of adaptor proteins (reviewed in ). These proteins include emerin, MAN-1, HP-1 (Heterochromatin binding protein) and ]LAP2 (Lamin associated peptide) (reviewed in ). They stabilize the membrane-protein interactions and have several other binding partners, implying a role in mechanosignaling . The average elastic modulus of the nuclear lamina is measured as 25mN/m in Xenopus oocyte nuclei suggesting its potential as a molecular shock absorber . Besides this, the lamina also associates with heterochromatin and several transcriptional repressors, indicative of its role in epigenetic control at the nuclear periphery as well (reviewed in ).
In addition, accessory structural proteins such as titin and spectrin aid in organizing lamins. They provide resilience to stretch by simultaneously binding lamins, chromatin and adaptor proteins to form stable multi-protein complexes  (reviewed in ). Spectrin is also implicated in DNA repair mechanisms .
Nuclear actin, which is believed to support the overall nucleoskeleton by stabilizing protein complexes, is made of very short filaments that bind emerin at the envelope . These are also seen in the nuclear interior and implicated in chromatin remodeling as well as dynamics of mRNA (reviewed in ).
Packaging of approximately a meter-long DNA duplex within the elastic nucleus determines its spatial 3D architecture and the genomic accessibility of tissue-specific transcriptional programs. Apart from several biochemical processes, there are various forces at play in the chromatin organization, that in turn affect nuclear functions (reviewed in ). DNA micromanipulation experiments reveal that it has a persistent length of ~50nm and hence in an entropic configuration will have a radius of gyration ~300um due to electrostatic repelling as a consequence of its negative charge . However, compaction of this flexible polymer inside a much smaller nucleus (~10-50um) is possible only because of the positively charged histones and other non-histone proteins that enable condensation, by stabilizing the electrostatic interactions .