Status
Completed

Period
19 September 2021 – 01 October 2021

Applicant
Dr. Valerio Sorichetti

Home Institution
Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Saclay

Host Contact
Dr. Davide Michieletto

Host Institution
School of Physics and Astronomy, University of Edinburgh

Aim of the mission

The main purpose of this STSM was to start a scientific collaboration between the Applicant and the Host on the following themes: (1) Rheology and kinetics of “living” polymers. (2) Microrheology of
topological polymer nanocomposites (TPNCs – see below) in which the polymeric matrix is either a melt of “chimeric” polymers or a topological gel (e.g. Olympic gel).

• Rheology and Kinetics of Living Polymers: “Living” polymers can change their architecture over time [1]. These macromolecules exhibit exotic rheological behaviours which are appealing for next-generation self-healing and responsive materials and completely defy classic polymer theories. In particular, we are interested in systems of polymer strands that can undergo either ligation (two strands joining each other) or cyclization (a single strand forming a ring) in an irreversible manner. These systems have been shown to display a time-dependent viscosity, due to the increase of the average chain length and to the formation of rings [1]. The Host lab is currently studying these systems via molecular dynamics simulations and experimentally with lambda-DNA strands functionalized with reactive groups. Since the applicant has extensive experience in theory and modeling of polymer ligation, the first objective of the STSM was to start a collaboration on this topic. The Host and the Applicant have started a collaboration to explain the Host experiments on DNA. This is relevant for EUTOPIA objectives in WG2 and WG4 such as “Exploration of the relationship between topology and functions of DNA and chromatin in various biological contexts” and “Characterize the rheological, transport, and mechanical properties of systems at point 2, so to control them by tuning external conditions (e.g. confinement)”.
• Topological Polymer Nanocomposites: Polymer nanocomposites (PNCs) are materials in which a small volume fraction of nanoparticles (NPs) is added to a polymeric matrix, greatly improving its mechanical/thermal/optical/transport properties [2]. Until today, most studies on PNCs have focused on systems of linear polymers, and PNCs with topologically non-trivial polymers, such as ring and “chimeric” (combination of linear and rings [3]) polymers, i.e., TPNCs, remains largely unexplored. The study of these systems is especially timely thanks to the facile realisation of topological polymers using DNA nanotechnology, such as DNA origami [4]. The study of TPNCs perfectly aligns with the scope of EUTOPIA in particular with objectives of WG2 “Expand the scope of present self-assembling techniques by identifying novel designable topologies”. We also note that ring polymer melts have been argued to capture important aspects of genome organisation in the cell nucleus [5]. We thus argue that this STSM will lead to novel developments relevant for WG4 “Development of systematic coarse-grain strategies for DNA and chromatin, with particular emphasis on computational models capable of matching between different resolutions in space and time” and “Explore the interplay of active and passive mechanisms controlling the entanglement of chromatin, and nucleic acids in general, within the crowded nuclear environment”. The embedding of NPs in TPNCs has a twofold purpose: It can be used to enhance the properties of the polymeric matrix, but it also allow us to study the rheological and elastic properties of TPNCs using nano- and microrheology [6, 7]. This approach can thus be used to study the rheological and elastic properties of melts of chimeric polymers and also of topological gels, such as Olympic gels. Thiscan contribute to the objectives of CA17139, and in particular of WG2 “Shed light on the onset and evolution of entanglement in networks of polymers, for different concentrations, bending rigidity and molecular interlocking (e.g. Olympic gels of ring polymers, woven micromaterials)” and “Characterize the rheological, transport, and mechanical properties of systems at point 2, so to control them by tuning external conditions”. The Host and the Applicant also plan to develop novel techniques to experimentally assemble Olympic gels, that could be first tested in silico and successively realized experimentally in the Host lab. This aligns with WG2 objective “Expand the scope of present self-assembling techniques by identifying novel designable topologies”.

References
[1] D. Michieletto, “Non-equilibrium living polymers,” Entropy, vol. 22, no. 10, p. 1130, 2020.
[2] K. I. Winey and R. A. Vaia, “Polymer nanocomposites,” MRS Bull., vol. 32, no. 4, pp. 314–322, 2007.
[3] A. Rosa, J. Smrek, M. S. Turner, and D. Michieletto, “Threading-induced dynamical transition in tadpole-shaped polymers,” ACS Macro Lett., vol. 9, no. 5, pp. 743–748, 2020.
[4] P. W. Rothemund, “Folding dna to create nanoscale shapes and patterns,” Nature, vol. 440, no. 7082, pp. 297–302, 2006.
[5] J. D. Halverson, J. Smrek, K. Kremer, and A. Grosberg, “From a melt of rings to chromosome territories: the role of topological constraints in genome folding,” Rep. Prog. Phys., vol. 77, p. 022601, 2014.
[6] T. Ge, G. S. Grest, and M. Rubinstein, “Nanorheology of entangled polymer melts,” Phys. Rev. Lett., vol. 120, no. 5, p. 057801, 2018.
[7] T. G. Mason, “Estimating the viscoelastic moduli of complex fluids using the generalized stokes – einstein equation,” Rheo. Acta, vol. 39, no. 4, pp. 371–378, 2000.
[8] V. Sorichetti, V. Hugouvieux, and W. Kob, “Structure and dynamics of a polymer–nanoparticle composite: Effect of nanoparticle size and volume fraction,” Macromolecules, vol. 51, no. 14, pp. 5375–5391, 2018.
[9] V. Sorichetti, V. Hugouvieux, and W. Kob, “Dynamics of nanoparticles in polydisperse polymer networks: from free diffusion to hopping,” Macromolecules, vol. 54, no. 18, p. 8575–8589, 2021.
[10] F. Sciortino, C. De Michele, and J. F. Douglas, “Growth of equilibrium polymers under non-equilibrium conditions,” J. Phys. Condens. Matter, vol. 20, no. 15, p. 155101, 2008.
[11] A. L. Garcia, C. Van Den Broeck, M. Aertsens, and R. Serneels, “A monte carlo simulation of coagulation,” Physica A: Statistical Mechanics and its Applications, vol. 143, no. 3, pp. 535–546, 1987.
[12] B. A. Krajina, A. Zhu, S. C. Heilshorn, and A. J. Spakowitz, “Active dna olympic hydrogels driven by topoisomerase activity,” Phys. Rev. Lett., vol. 121, no. 14, p. 148001, 2018.
[13] G. Pickett, “Dna-origami technique for olympic gels,” EPL, vol. 76, no. 4, p. 616, 2006.
[14] E. Raphaël, C. Gay, and P. De Gennes, “Progressive construction of an “olympic” gel,” J. Stat. Phys., vol. 89, no. 1, pp. 111–118, 1997.

Summary of the Results
The Host and the Applicant have met on a daily basis times and the Applicant had the opportunity to extensively interact with the Host group thereby expanding his knowledge of DNA systems. At the same time, the Applicant has shared his expertise in self-assembling polymers. He has been mostly involved in a project involving the ligation of lambda-DNA moleucles using an ATP-consuming enzyme. Since the Applicant is currently working on a project on the polymerization kinetics of semiflexible biopolymers (intermediate filaments), he has the experience on the theoretical/simulation techniques to describe such processes. Moreover, he has extensive expertise on simulations of nano- and microrheology [8, 9], which can be used in both simulations and experiments to study the rheological properties of these systems. The Host and the Applicant have discussed the relevance of Smoluchowski coagulation equation approach and proposed to add terms capturing cyclization of the DNA molecules to explain the currently puzzling experimental results. In particular, the Applicant proposed a theoretical approach to predict how the mean length of the DNA strands increases with time, and how to address the influence of ring formation. As a consequence of our interaction, the Host has gained a deeper knowledge of scaling theories that are applicable to polymerising systems of polymers while the Applicant has learnt how it is possible to experimentally realise such systems. Finally, the Applicant gave a Condensed Matter Seminar on “Diffusion of Nanoparticles in Polydisperse Polymer Networks”, in which the results of a recently published paper [9] were presented. He also discussed and exchanged ideas with academic members of the department (Prof. A. Morozov, Prof. D. Marenduzzo). Moreover, he took part to weekly group meetings in the Host group and to joint group meetings with the group of Prof. D. Marenduzzo.

• Theoretical and computational tools do describe DNA ligation/cyclization The Applicant and the Host identified which theoretical and computational tools are more suitable to study ligation and cyclization processes in systems of functionalized DNA strands. In particular,the Applicant proposed to model this process using the Smoluchowski coagulation equation [10], and to include the formation of rings as a “sink” term in said equation. By knowing the reaction rates for ligation and cyclization, and in particular how these reaction rates depend on the chains’ lengths, it is possible to numerically solve the Smoluchowski equation using methods such as Direct Simulation Monte Carlo [11] or by directly solving the system of ordinary differential equations. The Applicant and the Host group also discussed possible methods to model living polymers using molecular dynamics simulations. They concluded that the experimental system can be simulated using molecular dynamics (MD) as bead-spring polymers which move according to a Langevin equation. The latter will make it so each monomer will feel an “implicit” solvent, however hydrodynamic interactions are neglected. The ligation/cyclization events can then by simulated by including a certain number of bond-creation Monte Carlo steps in the molecular dynamics simulation.
• Simulation methods for topological polymer nanocomposites (TPNCs) The Applicant and the Host discussed methods to computationally study TPNCs. Knowledge exchange between the Host (expert in simulations of topologically complex polymers) and the Applicant (expert in simulation of polymer nanocomposites) was fundamental to this end. It was established that the best model to simulate TPNCs is a coarse-grained one, in which the polymers are modeled as bead-spring chains and the NPs as soft spheres. The interaction between polymers and NPs will be modeled using a horizontally shifted Lennard-Jones potential, which allows to change the NP size while keeping its size constant and it is standard in simulations of PNCs [8, 9]. Finally, it was discussed how to use microrheology to connect the dynamics of the NPs to the bulk rheological and elastic properties of the polymeric matrix.
• In silico assembly and microrheology of Olympic gels The Applicant and the Host identified possible methods to self-assemble Olympic gels in silico. The objective is first assemble the gels, and then to embed NPs in order to use microrheology to study the elastic properties of the gels, which will in general depend on the assembly procedure. Inspired by the available literature [12, 13, 14], three possible methods to self-assemble Olympic gels were identified, and their respective advantages and shortcomings were discussed and carefully evaluated.

Dissemination
The Host and the Applicant agreed to write a paper as a result of the ongoing collaboration on the ligation/cyclization project, also involving the current supervisor of the Applicant (Dr. Martin Lenz,
University of Paris-Saclay and CNRS, Orsay, France). The preprint of the work is available on ArXiv

Runaway Transition in Irreversible Polymer Condensation with Cyclisation ( https://arxiv.org/abs/2210.14010 )