Computational Study of Actin: Mechanics of Actin Filaments, Rheology of Actin Networks and Build up of Force in Contractile Actin Assemblies

The actin cytoskeleton is the scaffolding structure of eukaryotic cells, providing them with structural integrity, resistance to deformation and remodeling. It is mostly composed of: actin filaments (F-actin), cross-linking proteins, and molecular motors. The actin filament is a semiflexible polymer with the geometry of a right-handed double helix and whose mechanical performance depends on the bound ligands (i.e., ATP/ADP nucleotides and Ca2+/Mg2+ cations); cross-linking proteins comprise a family of actin binding proteins with molecular weight from 20 to 300 kDa that mediate the organization of F-actins into orthogonal networks or parallel bundles; myosin II molecular motors are ATP-dependent motor proteins comprising multiple myosin heads that collectively generate force dipoles on pairs of actin filaments with opposite polarities leading to organization of the actin network into various contractile assemblies, including stress fibers, random polarity bundles and the contractile ring. The characteristics of the various elements of the cytoskeleton, including the mechanics and length of F-actin, the density of molecular motors and the concentration of crosslinking proteins, have a direct effect on the morphology and rheology of the actin cytoskeleton and on the dynamics and steady state properties of its assemblies. Although various experimental and computational studies have been conducted, the interplay between the various elements in the actin cytoskeleton is still poorly understood and the use of one single technique is not sufficient to elucidate phenomena at different scales of complexity. In this thesis, we employed different computational methods, spanning temporal and spatial scales from nanoseconds to seconds and from angstroms to micrometers, in order to investigate the effects of various ligands on the mechanics of the actin filaments, the origin of the rheology of passively crosslinked actin networks in different conditions of filament and crosslinks mechanical properties, and the dynamics and steady state properties of contractile arc-shaped actin bundles. After reviewing the state of art in studying actin filaments, actin networks and contractile assemblies (Chapter 1), we captured the effects of nucleotides and cations on the mechanics of the single filaments (Chapter 2) using a combination of molecular dynamics (MD) simulations, elastic network modeling (ENM) and normal mode analysis (NMA). We found that specific groups of residues on the external surface of the actin monomers are responsible for strengthening (or weakening) longitudinal and lateral interactions and lead to enhanced (or reduced) filament rigidity. We incorporated our data regarding the mechanical properties of the filaments in the different conditions of bound cations and/or nucleotides into a 3D minimal model system mimicking an actin network composed of actin filaments and static crosslinking proteins (Chapter 3). While the network was passive, with no molecular motors, it was thermally activated. We investigated the regime of strain-stiffening, focusing on the interplay between the bending/stretching stiffness of the filaments and the bending/stretching rigidity of the crosslinking proteins (Chapter 4). Strain-stiffening was characterized by a first linear regime, followed by a nonlinear phase. We found that in the first linear regime, the deformation was mostly accommodated by crosslinking proteins, while the actin filaments deformed by bending, while in the nonlinear phase, actin filaments stretched out and the contribution from cross-linkers decreased proportionally with increasing deformation. Thermal fluctuations were manifested only at low deformation. By varying the actin concentration and the average length of the actin filaments (Chapter 5), the elastic shear modulus changed exponentially and reflected the degree of network percolation. We also characterized the contraction of the crosslinked actin network introducing into the passive network elements mimicking molecular motors and varying the rigidity of the surrounding boundaries (Chapter 6). We elucidated the relation between motor kinetics and level of contractile force. On soft substrates, motors stalled owing to occupancy of available binding, generating low contractile force and dense networks; on rigid substrates, motors stopped walking due to reaching of the stalling force, generating high contraction and sparse networks. Furthermore, we simulated the condensation of a homogeneous actin filament network into a contractile bundle resembling the dimensions and the level of axial force of an actin arc, typically found in the lamellipodium/lamella region of migrating cells (Chapter 7). We characterized the morphology of the arc-shaped bundle at the steady state and its build up of force along the longitudinal axis at different filament lengths, densities of motors and crosslinkers. We identified combinations of crosslinks/motors concentrations determining the transitions between a contractile network and an arc and between formation of an arc and a contractile sheet. By systematically varying the average length of the actin filaments, we also identified a threshold length of the filaments equal to 2 µm, below which the contraction of the network into a compact contractile assembly could not occur. Last, we discuss the future developments of this study (Chapter 8) and possible extensions of the computational approach adopted

Computational Study of Actin: Mechanics of Actin Filaments, Rheology of Actin Networks and Build up of Force in Contractile Actin Assemblies

The actin cytoskeleton is the scaffolding structure of eukaryotic cells, providing them with structural integrity, resistance to deformation and remodeling. It is mostly composed of: actin filaments (F-actin), cross-linking proteins, and molecular motors. The actin filament is a semiflexible polymer with the geometry of a right-handed double helix and whose mechanical performance depends on the bound ligands (i.e., ATP/ADP nucleotides and Ca2+/Mg2+ cations); cross-linking proteins comprise a family of actin binding proteins with molecular weight from 20 to 300 kDa that mediate the organization of F-actins into orthogonal networks or parallel bundles; myosin II molecular motors are ATP-dependent motor proteins comprising multiple myosin heads that collectively generate force dipoles on pairs of actin filaments with opposite polarities leading to organization of the actin network into various contractile assemblies, including stress fibers, random polarity bundles and the contractile ring. The characteristics of the various elements of the cytoskeleton, including the mechanics and length of F-actin, the density of molecular motors and the concentration of crosslinking proteins, have a direct effect on the morphology and rheology of the actin cytoskeleton and on the dynamics and steady state properties of its assemblies. Although various experimental and computational studies have been conducted, the interplay between the various elements in the actin cytoskeleton is still poorly understood and the use of one single technique is not sufficient to elucidate phenomena at different scales of complexity. In this thesis, we employed different computational methods, spanning temporal and spatial scales from nanoseconds to seconds and from angstroms to micrometers, in order to investigate the effects of various ligands on the mechanics of the actin filaments, the origin of the rheology of passively crosslinked actin networks in different conditions of filament and crosslinks mechanical properties, and the dynamics and steady state properties of contractile arc-shaped actin bundles. After reviewing the state of art in studying actin filaments, actin networks and contractile assemblies (Chapter 1), we captured the effects of nucleotides and cations on the mechanics of the single filaments (Chapter 2) using a combination of molecular dynamics (MD) simulations, elastic network modeling (ENM) and normal mode analysis (NMA). We found that specific groups of residues on the external surface of the actin monomers are responsible for strengthening (or weakening) longitudinal and lateral interactions and lead to enhanced (or reduced) filament rigidity. We incorporated our data regarding the mechanical properties of the filaments in the different conditions of bound cations and/or nucleotides into a 3D minimal model system mimicking an actin network composed of actin filaments and static crosslinking proteins (Chapter 3). While the network was passive, with no molecular motors, it was thermally activated. We investigated the regime of strain-stiffening, focusing on the interplay between the bending/stretching stiffness of the filaments and the bending/stretching rigidity of the crosslinking proteins (Chapter 4). Strain-stiffening was characterized by a first linear regime, followed by a nonlinear phase. We found that in the first linear regime, the deformation was mostly accommodated by crosslinking proteins, while the actin filaments deformed by bending, while in the nonlinear phase, actin filaments stretched out and the contribution from cross-linkers decreased proportionally with increasing deformation. Thermal fluctuations were manifested only at low deformation. By varying the actin concentration and the average length of the actin filaments (Chapter 5), the elastic shear modulus changed exponentially and reflected the degree of network percolation. We also characterized the contraction of the crosslinked actin network introducing into the passive network elements mimicking molecular motors and varying the rigidity of the surrounding boundaries (Chapter 6). We elucidated the relation between motor kinetics and level of contractile force. On soft substrates, motors stalled owing to occupancy of available binding, generating low contractile force and dense networks; on rigid substrates, motors stopped walking due to reaching of the stalling force, generating high contraction and sparse networks. Furthermore, we simulated the condensation of a homogeneous actin filament network into a contractile bundle resembling the dimensions and the level of axial force of an actin arc, typically found in the lamellipodium/lamella region of migrating cells (Chapter 7). We characterized the morphology of the arc-shaped bundle at the steady state and its build up of force along the longitudinal axis at different filament lengths, densities of motors and crosslinkers. We identified combinations of crosslinks/motors concentrations determining the transitions between a contractile network and an arc and between formation of an arc and a contractile sheet. By systematically varying the average length of the actin filaments, we also identified a threshold length of the filaments equal to 2 µm, below which the contraction of the network into a compact contractile assembly could not occur. Last, we discuss the future developments of this study (Chapter 8) and possible extensions of the computational approach adopte

Caratterizzazione meccanica di proteine citoscheletriche

Il citoscheletro delle cellule eucariote è formato principalmente da tre tipi di filamenti proteici: microtubuli, filamenti di actina e filamenti intermedi. I più numerosi sono i filamenti di actina, che costituiscono la corteccia cellulare, e i microtubuli, che circondano il nucleo. Le funzioni di questi filamenti sono sia di tipo strutturale, che di tipo funzionale e vanno dal mantenimento della forma della cellula al trasporto intracellulare, ai motori molecolari. I filamenti di actina presentano una struttura a doppia elica, con diametro complessivo di circa 6 nm, mentre i microtubuli mostano la geometria di un cilindro cavo, con diametro medio dell'ordine dei 20 nm. Sia i microtubuli, che i filamenti di actina mostrano un comportamento meccanico altamente dinamico, dovuto ai continui fenomeni di polimerizzazione/depolimerizzazione. Inotre, il tipo di attività in cui i microtubuli e i filamenti di actina sono coinvolti richiedono che essi posseggano proprietà meccaniche adeguate. Alcune osservazioni sperimentali hanno mostrato una relazione tra la variazione di lunghezza di questi filamenti proteici e le loro caratteristiche mecchaniche, mostrando che la rigidezza a flessione di flamenti di actina diminuisce con l'accorciamento della catena. Tuttavia, questi risultati non sono stati confermati da studi computazioni. Uno strudio sistematico delle variazioni delle proprietà meccaniche dei filamenti di actina e dei microtubuli in funzione della lunghezza al controno (che corrisponde alla lunghezza del filamento) non è ancora stato condotto. Inoltre, gli studi effettuati fino ad oggi, non hanno messo a confronto le proprietà meccaniche specifiche delle due strutture proteiche. L'obiettivo del presente studio è fornire una descrizione quantitativa della relzione tra le proprietà meccaniche e la lunghezza al contorno dei filamenti di actina e dei microtubuli, mettendone a confronto il diverso comportamento meccanic

Multiscale impact of nucleotides and cations on the conformational equilibrium, elasticity and rheology of actin filaments and crosslinked networks

Cells are able to respond to mechanical forces and deformations. The actin cytoskeleton, a highly dynamic scaffolding structure, plays an important role in cell mechano-sensing. Thus, understanding rheological behaviors of the actin cytoskeleton is critical for delineating mechanical behaviors of cells. The actin cytoskeleton consists of interconnected actin filaments (F-actin) that form via self-assembly of actin monomers. It has been shown that molecular changes of the monomer subunits impact the rigidity of F-actin. However, it remains inconclusive whether or not the molecular changes can propagate to the network level and thus alter the rheological properties of actin networks. Here, we focus on how cation binding and nucleotide state tune the molecular conformation and rigidity of F-actin and a representative rheological behavior of actin networks, strain-stiffening. We employ a multiscale approach by combining established computational techniques: molecular dynamics, normal mode analysis and Brownian dynamics. Our findings indicate that different combinations of nucleotide (ATP, ADP or ADP-Pi) and cation (Mg[superscript 2+] or Ca[superscript 2+] at one or multiple sites) binding change the molecular conformation of F-actin by varying inter- and intra-strand interactions which bridge adjacent subunits between and within F-actin helical strands. This is reflected in the rigidity of actin filaments against bending and stretching. We found that differences in extension and bending rigidity of F-actin induced by cation binding to the low-, intermediate- and high-affinity sites vary the strain-stiffening response of actin networks crosslinked by rigid crosslinkers, such as scruin, whereas they minimally impact the strain-stiffening response when compliant crosslinkers, such as filamin A or α-actinin, are used

Multiscale Modelling of entire Microtubules and Actin Microfilaments

4th International Conference on the Mechanics of Biomaterials and Tissues Marriott Waikola Beach Resort and Spa, Hawai’i, USA, 11-14 December 201