Session C55: Advancing Polymer and Biopolymer Physics though Simulation and Theory I: Biopolymers

Chromosome organization by loop extrusion and phase separation

Inferring principles and mechanisms of 3D organization of chromosomes from Hi-C and imaging data is a challenging biophysical problem. Recently we proposed that an active process loop extrusion by SMC complexes is a universal mechanism responsible for formation of domains in interphase, and chromosome compaction and segregation in metaphase. I will review recent experimental studies that provide strong support to loop extrusion as a universal mechanism of chromosome folding.

These experiments have also showed that spatial segregation of euchromatin and heterochromatin is achieved by a different mechanism. To elucidate mechanisms of this spatial segregation, we examined Hi-C and microscopy for cells with inverted nuclei and conventional nuclear architecture. Polymer model base on these data show that attraction between heterochromatic regions drive the phase separation, while interactions with the lamina central for spatial positioning of phases in the nucleus.

Taken together our results demonstrate two major processes shape chromosome organization through the cell cycle: heterochromatin-driven phase segregation and SMC-driven loop extrusion.   

Modeling interphase chromosomes: Microrheology

The nucleus of eukaryotic cells is one of the most investigated organelle but its complete understanding is far from being reached. Recently considerable efforts have been devoted to experimentally analyze its viscoelastic properties, in particular through microrheology techniques.

We employ molecular dynamics computer simulations comparing experimental data with theoretical models.
Mimicking experiments, we consider a polymeric model representing the crowding of interphase chromosomes [1] containing hundreds of brownian free particles as in [2]. We consider several sizes for particles from the tiny chromatin fiber to the mesh size of the chromatin solution. Tracking the motion of these fictitious nanoprobes we compute dynamical proprieties.

Then we investigate a simple variation of this polymeric model including a set of spring which modifies dramatically the viscoelastic properties. Interestingly, we observed the cage-and-escape dynamics peculiar for short times dynamics of nanoprobes seen in experiments.
We generalize also the model to the situation where active regulatory mechanics are present [3].

[1] A. Rosa, R. Everaers, PLoS Comput Biol., 4(8): e1000153 (2008)
[2] M. Valet, A. Rosa, J Chem Phys., 141, 245101 (2014)
[3] J. Smrek, K. Kremer, Phys. Rev. Lett., 118, 098002 (2017)   

Diffusion of nuclear proteins and its link to 3d chromatin organization

The interaction of proteins with chromatin regulates many cellular functions. Most DNA-binding proteins interact both non-specifically and transiently with many chromatin sites, as well as specifically and more stably with cognate binding sites. These interactions and chromatin structure are important in governing protein dynamics. These questions can be addressed theoretically using diffusion models. I will show how that the dynamics of proteins is determined by the 3d organization of chromatin in the nucleus. The time to find a chromatin target depends on chromatin organization around it, which determines the local association and disassociation rates.

These ideas can be applied to study the dynamics of nuclear proteins and infer from single particle trajectories the geometry of the structures with which they interact.   

All-Atom Molecular Dynamics simulations of the interaction between viral capsid proteins and single-stranded RNA molecules.

We carried out All-Atom Molecular Dynamics (MD) simulations of the interaction between the positively charged tails of viral capsid proteins and negatively charged homopolymeric polyU and polyA RNA molecules. Recent experiments showed that the encapsidation of homopolymeric RNA by viral capsids is sensitively dependent on the nature of the RNA nucleotide (C.Beren, L.Dreesens, K.Liu, C.Knobler and W.Gelbart, Biophys.J. 2017, 339). We found that the degree of base-stacking and helical ordering strongly influences the strength of the electrostatic component of the protein-RNA interaction, and hence the ability of the capsid proteins to package single-stranded RNA molecules. We compare the Potential of Mean Force measured by the MD simulations with the predictions of Poisson-Boltzmann theory for electrostatic interactions.   

Pinning a protein (AQP1) structure by the interacting matrix elements

The effect of temperature on a protein (AQP1) structure by a coarse-grained Monte Carlo simulation shows negative and positive responses in its native and denatured phases respectively. The same protein chain is then immersed in an interactive matrix with constitutive elements (i.e. effective solute particles with size comparable to residue) where an aquatic interactions between the residue and solute can be varied. Local and global physical quantities such as contact map, gyration radius, and structure factor are examined as a function of matrix interaction strength at a range of temperatures. The protein structures, from our preliminary studies, are found to be pinned by the solute, the radius of gyration becomes less sensitive to temperature, and structure factor shows a ramified structure with lower effective dimension than that without solute particles. In-depth analysis will be presented as the data will become available.
  

Protein crystallizing assembly via free and grafted linkers

"Proteins have potential to form numerous lattices due to their highly anisotropic shape. However, the forces required to arrange proteins in a periodic fashion are not understood. In this study we introduce a coarse grained MD simulation approach to study the effects of length and geometry of linkers on the 3 D crystalline assembly of ferritin protein. We find the optimal linker length dependence on the linker to protein ratio beyond which linkers fail to hold the proteins in a crystalline structure. We also study the effect of the length of the grafted linkers on the formation of the protein arrays. In the linker grafted case, we do not find an optimal length suggesting that the grafting of linkers on the protein surface is a better route to yield rich porosity crystalline structures. Our analysis suggests that the emergence of the optimal linker length is rooted at the expense of rotational freedom of the longer linker. The computationally inexpensive method that we present in this study could be useful as the guidelines to understand the assembly of complex molecules."   

Atomistic and Coarse-grained Simulations of Thermoresponsive Biopolymers

This talk focuses on our multi-scale simulation studies on thermoresponsive biopolymers, specifically elastin-like peptides (ELP) and collagen-like peptides (CLP). ELPs are biopolymers that undergo a lower critical solution temperature (LCST)-like phase transition, which means ELPs are soluble below the transition temperature, T_t, and insoluble above T_t. The T_t of ELPs can be tuned via conjugation to other thermoresponsive biomolecules such as CLPs. In our recent work, we used all-atom (AA) and coarse-grained (CG) simulations to elucidate how the guest residue impacts ELP stiffness, its secondary structure formation, and hydrophobicity and thus, the LCST-like transition of ELP and ELP-CLP conjugates. We used the structural data from AA simulations to modify our previous ELP CG model such that it captures the atomistically-informed stiffness while enabling simulations at experimentally relevant length scales. Our new ELP CG model also accounts for the hydrophobicity of the guest residue and its propensity to form compact, secondary structures. Through these modifications, our CG simulations are able to explain the experimental observations in T_t of ELP and ELP-CLP conjugates with W and F as the guest residues.   

Brownian Dynamics Simulation of Single Biomolecules: Contact Formation and Hydrodynamic Radius

The conformational flexibility and dynamics of unfolded peptide chains is of major interest in the context of protein folding. The rate with which amino acids at different positions along the peptide chain meet sets an upper speed limit for protein folding. By using single-molecule photo-induced energy transfer (PET) spectroscopy, we have systematically measured end-to-end and end-to-internal site contact formation rates for several intrinsically disordered protein fragments (10 to 40 amino acids), and have also determined their hydrodynamic radius using dual-focus fluorescence correlation spectroscopy (2fFCS). For interpreting the measured values, we have developed a Brownian dynamics model (a discretized elastic rod in a thermal bath including hydrodynamic interactions) which quantitatively reproduces all measured data surprisingly well while requiring only two fit parameters. The model provides a complete picture of the peptides' dynamics and allows us to translate the experimental rates and radii into molecular properties of the peptides: We find a persistence length of ~0.4 nm and a hydrodynamic radius of ~0.5 nm per amino acid.   

Investigation into multivalently binding polymers

Biology frequently uses multivalent binding interactions to enhance weak, monovalent binding between molecules such as glycoligands and protein receptors. Synthetic glycopolymers have been shown to successfully bind to targets, such as viruses and toxic proteins. This binding indicates that the use of multivalent polymers can be a promising tool for inhibiting target attachment to and subsequent infection of cells. These polymers would act as decoys, suppressing virulence without killing their target and thus minimizing the development of resistance. Many studies have focused on creating multivalent binders with high affinity and high specificity to a single target. In contrast, we investigate how to design polymers that have broad-spectrum binding affinity, so that a single multivalent polymer could be used to inhibit multiple targets. We use a reactive-binding, Brownian dynamics simulation to examine how patterning of heterogeneous binding sites along a polymer chain control binding affinity of a polymer to multiple types of targets. Our results provide direction for designing polymeric inhibitors able to bind multiple targets simultaneously.   

Disorder mediated oligmerization of chromsome translocation proteins of DISC1 gene.

Disrupted-in-Schizophrenia 1 (DISC1) gene is one of the highest
risk factors for neural developent including schizophrenia and other chronic
mental illnesses. Depending on cellualr context DISC1 gene expresses proteins of different length which have markedly differen binding and oligomerization propoensities. Due to highly disorder content the molecular level understanding of DISC1 protein assembly and oligomerization has been missing. We have carried out high throuput molecular dynamics simulations of all DISC1 expressed proteins at the coras grained level to invesigate conformational ensembles and oligmoerization patways of DISC proteins at the level of monomers dimers and various tetrameric combinations. Our findings reveal that disorder content present in DISC1 acts as a graded swithc mediating non-additve binding and oligmerization preferences.   

Characterizing the counterionic cloud of DNA-functionalized nanoparticles with molecular dynamics simulations

DNA-functionalization of proteins allows for cell penetration and self-assembly of protein systems that have the potential for applications in therapeutics and other fields. However, the impacts of the resulting electrostatic interactions associated with the DNA shell and counterionic cloud are still being explored. Here, we use molecular dynamics simulations to examine the stability of a protein’s DNA shell in the presences of DNAse, as it relates to the composition of this counterionic cloud. We use molecular dynamics simulations and a simple thermodynamic model in tandem with SAXS measurements to understand the composition of this cloud under varying salt conditions and protein shapes. This work builds on previous efforts to calculate this composition of this cloud using DFT calculations; detailed molecular dynamics simulations have been used to incorporate multiple species of ion as well as excluded volume effects and correlations.   

Exploring the Structure and Dynamics of Carbohydrate Nanoparticles using Molecular Dynamics Simulations

PhytoSpherix is a carbohydrate-based nanoparticle composed of glucose units joined in a dendritic manner. These particles are of interest as they are a biodegradable and biocompatible nanomaterial. In this work, we present results from all-atom molecular dynamics simulations (GROMACS) of a PhytoSpherix-like particle. The particle is dynamically grown until it contains ~1100 glucose units. Analysis of structural features is conducted as the particle equilibrates to a relaxed state. The complex internal structure is characterized by hydrophobic interactions between chains and water-containing areas in contact with hydrophilic regions of the carbohydrate. Results concerning the dynamics inside of the particle are also examined. This characterization can assist the development of new applications for PhytoSpherix particles.   

Investigating the Structure of Phytoglycogen using Coarse-Grained Simulations

Phytoglycogen is a dendritic nanoparticle composed of repeatedly branching chains of glucose. Despite glucose being a common form of energy storage in plants, many questions still remain about the structure of this naturally occurring particle. In this work, pytoglycogen was modelled with a coarse-grained approach, simplifying each glucose unit to a single particle. A hydrophobic attraction between chains was observed in atomistic simulations and this was modelled in the the coarse-grained simulations with a simple attraction between glucose particles. The strength of this attraction was used as a free parameter to investigate how changing it changes the structure of the particle. The simulated particles with radii similar to those seen in experiment were observed to have a hairy colloid shape, with a dense core and hairs extending out from the core.