Modeling DNA damage occurrence during constricted migration

A simple model has been developed to explain the DNA damage occurs during constricted migration. This model assumes a dynamic equilibrium of DNA damage and repair process with a constant damaging rate and a varied repair rate due to mis-localization of DNA repair factors caused by both segregation (squeezing sponge model) and NE rupture during constricted migration (Bennett et al., 2017).

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A simple elastic-fluid model of the nucleus provides insight into the physics of protein squeeze-out. The nucleus is treated as a two-part system with an elastic component (chromatin) immersed in a fluid component containing mobile nuclear proteins (Bennett et al., 2017). In an undeformed nucleus, the volume fraction ϕ of solid-phase chromatin is ϕ₀~ 67% (Bancaud et al., 2009), so the free volume for diffusion of mobile factors is (1 - ϕ₀) ~ 33%. However, when the nucleus is constricted, the solid volume fraction changes with radial nuclear deformation Λr:

𝜙 = 𝜙0_⁄Λ𝑟2−𝛼_{, (1)}

where 𝛼 is related to the Poisson ratio of the nucleus. According to Eq. 1, the local density of chromatin inside a 3 µm pore/pipette increases to ϕ_constricted ~ 85%, leaving a free volume fraction of just (1 - ϕ_constricted) ~ 15% for the mobile protein fluid. It follows that mobile factors inside the constriction should be (1 - ϕ_constricted) (1 - ⁄ ϕ₀)≃ 15% / 33% ≃ 50% as abundant as mobile factors in an unperturbed nucleus in theory (Bennett et al., 2017). Comparing to real numbers in micropipette aspiration experiments, as the nucleus is entering the confinement, DNA repair factors are squeezed out from the DNA (Fig 1.4). Smaller confinement in general causes more segregation (Fig 1.4). When the confinement is ~3µm in diameter, protein segregation tends to be ~50% independent of protein sizes (Fig 1.4). Therefore, this model prediction agrees well with the above- described experiments showing depletion of diffusible nuclear proteins from confining pores and micropipettes (Irianto et al., 2016b).

Depletion of nuclear proteins—in particular, repair proteins—is expected to physically inhibit the DNA damage response. In short, DNA breaks constantly form by various means, such as replication and oxidative stress. Normally, these routine lesions are repaired by dedicated factors (e.g. ATM, BRCA1, etc.) such that the breakage and repair rates reach a steady state. In the simple elastic-fluid model of the nucleus, described above, it is assumed that breaks are repaired when repair factors bind to them. Hence, the concentration of unbound breaks cU and concentration of bound breaks cB evolve over time as breaks form and repair factors bind and unbind. The change

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over time in cU is essentially the rate per unit volume at which unrepaired breaks arise (kb(ϕ)) minus the rate per unit volume at which repair factors adsorb to those breaks:

𝑑𝑐_𝑈

𝑑𝑡 = 𝑘𝑏(𝜙) − 𝑘ads𝑐𝑈(𝑡)[𝑐𝑟(1 − 𝜙) − 𝑐𝐵(𝑡)], (2)

where k_ads is the rate constant for adsorption of repair factors to break sites, and 𝑐𝑟 is the constant concentration of repair factors. A similar rate equation describes the evolution of cB:

𝑑𝑐𝐵

𝑑𝑡 = 𝑘ads𝑐𝑈(𝑡)[𝑐𝑟(1 − 𝜙) − 𝑐𝐵(𝑡)] − 𝑘des𝑐𝐵(𝑡), (3)

with kdes being the desorption rate of repair factors from break sites (Bennett et al., 2017).

The total DNA damage D in the nucleus is calculated by solving Eqs. 2 and 3 for the unbound break density cU, and then integrating cU over the whole volume of the chromatin Vchrom,

as follows:

𝐷(𝑡) = ∫ 𝑑𝑉𝑐𝑈(𝑡) ≈ 𝑐𝑈(𝑡)𝑉chrom= 𝑐𝑈(𝑡) 𝑉nucl𝜙0

𝜙

𝑉chrom , (4)

where Vnucl is nuclear volume. Altogether, this model shows that radial deformation of the nucleus

Λr, as occurs during pore migration and micropipette aspiration, reduces the fluid volume fraction

1 - ϕ_constricted inside the constriction (Eq. 1). As a result, there is less space for free diffusion of mobile proteins, so these proteins are severely depleted from the pore/pipette, where chromatin is densest. As long as repair factors are thus segregated away from chromatin, normally occurring DNA breaks cannot be efficiently repaired, and unbound breaks (i.e. breaks not bound by repair factors) accumulate (Eq. 2,3). Excess unbound breaks mean excess DNA damage (Eq. 4) (Bennett et al., 2017). Although the model suggests low level of DNA repair can still occur in the constriction, experimental results are still lacking to prove such concept.

Migration-induced mis-localization of crucial DNA repair proteins occurs not only through mobile protein segregation, but also through rupture of the NE (NE), which causes mobile proteins to leak into the cytoplasm over many hours (Irianto et al., 2017; Xia et al., 2018b). A simple

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hydrodynamic theory suggests that NE rupture happens when the internal pressure in the nucleus rises due to compressive forces exerted on the nucleoplasm during constricted migration. In regions of the NE where no external forces are applied, such as the (high-curvature) leading tip of the nucleus, this increased internal pressure is balanced by an increase in the NE surface tension σ, per the Young-Laplace equation:

∆𝑝 = 2𝜎𝐶, (5)

where the Laplace pressure ∆p is the pressure difference across the NE, and C = 1 R⁄ c is the mean

NE curvature. Formation of a hole in the nuclear lamina lowers the membrane bending energy and disrupts this force balance (Eq. 5), leading possibly to fluid outflow from the nucleus. Such outflow locally inflates the NE around the lamina hole, producing a bleb that can burst to allow exchange of nucleo-cytoplasmic contents and even chromatin herniation (Deviri et al., 2017). By this mechanism, DNA repair proteins frequently mis-localize to the cytoplasm during constricted migration, which, again, physically inhibits routine DNA damage repair over the hours-long migration process.