Towards Coarse-graining of Active Chromatin

The 46 human DNA molecules (chromosomes), totaling two meters in length, are packed in a fluid environment of cell nucleus of about ten micrometers in diameter. If we increase the scale by a factor of 105 it is like two hundred kilometers of fishing line crammed in a car trunk. For biological functionality of this long fiber of chromatin (DNA with attached proteins) the packing must exhibit a certain order. Polymer physics can give us hints on how this spatial order arises and is maintained in time. Although we know that chromosomes are not circular, their observed internal structure and territorial behavior is very similar to long non-concatenated ring polymers at high density found computationally. The spatial organization is for both the ring model and the chromatin the consequence of the uncrossability of the long fibers. While rings are modeled uncrossable at all times, the chromosomes in the limited space simply don`t have enough time in a cell`s life to mix properly, and therefore each occupies its own territory. This illustrates how a simplified (coarse- grained) model can help us understand what is the essential feature in the organization of a complex system. In this project, we aim at learning more governing physical mechanisms behind the chromatin organization using such coarse-grained models. With computer simulations guided by analytical theory we will address its two aspects. Firstly, we look at rings of different sizes representing the different chromosomes and ask whether the pure effect of size, variety, or in combination with confinement can cause their preferential relative and absolute positioning within the nucleus that is observed in living cells. Theoretical studies on short rings indicate that typically a smaller ring squeezes in a bigger one which causes a size-positioning correlation. Secondly, we explore fundamental self-organizing properties of active particles in the presence of surrounding fluid. The active particles consume energy from the surroundings and convert it into their own motion, much like molecular motors that pull on chromatin segments in living cells. It has been shown that a mixture of active and normal (passive) particles without the fluid leads to a spontaneous self-organization of mostly active and passive domains. The chromatin also exhibits this active-passive separation, however, it is surrounded with fluid which affects the segregation process. In this part, we develop a novel simulation technique based on machine learning that allows for efficient hydrodynamic simulations, which would be otherwise costly. Finally, we join the two previous topics and investigate the effect of activity of polymer ring segments on their global organization and internal structure. This study provides a deeper understanding of chromatin large-scale structure, which affects the cell function and ultimately also our lives. Moreover, it yields new results for prospective novel highly elastic materials based on ring polymer solutions and has the potential to uncover fundamental physical laws of living matter.

The 46 human DNA molecules (chromosomes), totaling two meters in length are packed in a cell nucleus of about ten micrometers in diameter. If we increase the scale by a factor of 100.000, it is like two hundred kilometers of fishing line crammed in a car trunk. For biological functionality of this long fiber of chromatin (DNA with attached proteins), the packing must be somehow ordered. Polymer physics can give us hints on how this spatial order arises and is maintained in time. In this project we aimed at exploring the physical mechanism governing chromatin organization using simplified (coarse-grained) models. With computer simulations guided by analytical theory, we addressed two aspects: 1) the fact that the long molecules cannot cross and 2) the effects of molecular motors that pull on chromatin segments. We have found that the combination of these two ingredients not only captures some of the main features of chromatin organization and motion, but can also lead to a previously unknown state of polymeric matter - the active topological glass. The chromosomes contain loops that cannot cross, which prevents them from mixing, and thereby each chromosome occupies its own territory. Additionally, In living cells, there exist molecular motors that pull on some chromatin segments on the expense of energy. It has been shown that a mixture of such actively driven and passive (non-driven) polymers leads to a spontaneous self-organization of mostly active and passive domains. The chromatin also exhibits this active-passive separation, but it has been unknown how is it consistent with the organization arising from the non-crossability and what is the impact on the motion. Although the rings (loops) cannot cross, they can thread each other, meaning one ring piercing through the eye of another ring, thereby constraining each other's motion. We have investigated how frequently such threading happens on rings containing the active segments. We have found the activated rings thread and entangle so extensively that they practically cannot move past each other, similarly to chromosomes. This novel state of matter resembles ordinary glassy materials, because it appears solid, but is very distinct microscopically. Our simulations show some similarities in the motion and organization with the nuclei of living cells, but whether the DNA under living conditions could be in the state of the active topological glass, remains an open question. More detailed properties of this material remain to be uncovered, but it is already exciting, not only from the fundamental physics point of view, but also on account of the potential applications such as creating an artificial fluid material with reversible vitrification upon activation, which can be achieved by molecular motors or external stimuli.