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Continuum biomechanics modeling of homologue proteins

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  • 1. Continuum Biomechanics Modeling of Homologue Proteins Jonathan Chang, Regine Labog, Sweta RamachandranAbstract nucleation and further growth of the actin Actin and mreB possess homologous traits protofilament. Once ATP is incorporated into thethat interest scientists who believe that the actin filament, it hydrolyzes immediately and theconservation of protein sequencing suggests a ADP remains in the actin filament until itcommon ancestor. After observing their similaritiesin sequence and structure, we will use COMSOL to depolymerizes and an ATP is sent into thediscover whether or not their biomechanical nucleation site while the previous ADP exits. G-properties account for actins and mreBs differing actin creates filamentous actin (F-actin) when ATP,biological functions. To do so, f-actin and mreB Mg, and K are present. However, above the criticalwere modeled while taking into account f-actins concentration of G-actin, the molecules polymerize.122 degree twist and mreB parallel structure. These Below the critical concentration, the actin filamentsmodels revealed that mreBs maximum depolymerize.displacement was significantly lower than actins.This exponential displacement of actin is due to theg-actins angle when the force was applied and the Actin filaments possess polarity. The positive endlinear displacement of mreB was due to the parallel of G-actin is opposite the cleft holding the ATPapplication of force. By apply forces on the two molecule, which is the negative end. Growth andproteins, we see that the flexibility of actin is polymerization occurs more rapidly in the positivenecessary for actin which must handle multiple end. Though the intermolecular interactions of twofunctions in a eukaryotic cell. However, in bacteria actin molecules is weak, adding a third actinwhere mreBs main function is to provide thestructure for bacteria, it requires a more rigid monomer stabilizes the overall complex. Once thestructural component. Our model accounts for the dimer becomes a trimer, the actin molecules addsstructures of the two proteins which will, in the more monomers and forms a nucleation site.future, help in determining when the two proteins Adding actin filaments or key actin binding proteinsdiverged from their common ancestor. elongates the actin molecules to form a long helical polymer. After the growth period, the polymerIntroduction reaches an equilibrium phase whereActin is a component of the cytoskeletal system depolymerization controls the length of the polymerallowing cell movement and cellular processes. as new monomers are added.Actin filaments are called microfilaments of thin mreBfilaments that undergo constant rearrangement tocreate movement. Actin is a globular protein with Bacillus subtilis mreB is a bacterial, actin-likethe ATP binding site at the center of the molecule. protein that has been shown to perform essentialG-actin is short for globular actin, a short functions in cellular physiology. It affects cellpolypeptide chain made up of 375 amino acids. G- growth, cell shape, chromosome segregation andactin combines with other g-actin monomers to polar localization of proteins, and localization ascreate an actin filament. It serves as a site for helical filaments under the cell membrane. MreB
  • 2. performs dynamic, motor-like movements in the its designated 166 degree twist, the primary designcells and extend along helical tracks in seconds. to incorporate. In COMSOL, we used a 3D, structural, static model. Since we were moreMreB is a bacterial protein considered an actin interested in comparing the difference in responsehomologue based on its similarities in tertiary to loads between actin and MreB, using a transientstructure and conservation in the active sites model was not of interest. With the static model,peptide sequence. MreB has filaments located under one end was fixed and the other end was applied athe cellular membrane to control the width of rod vertical/parallel load. By simplifying the model ofshaped bacteria F-actin to incorporate half the number of subunits for clarity sake, calculated the precise positions andAside from tubulin, the other major component of direction vectors of the subunits was possible whilethe eukaryotic cytoskeleton is F-actin (filamentous the overall structural design was not sacrificed.actin), a relatively thin protein composed of two Edge gaps between subunits was modeled instrands twisted around each other. Actin works in both actin and MreB since separation does naturallycell motility, shape determination, phagocytosis, occur between subunits--the gaps were designed tocytokinsesis, and rearragement of surface be as consistent as possible between the twocomponents. It is 43kDa bi-lobed protein that binds COMSOL models. Two forces that wereATP in a cleft between the two lobes. The mreB determined through literature research to be thegene is associated with prokaryotic cell shape usual load forces for these proteins was applied todetermination but not cell envelope synthesis. the non-fixed end: 100 pico-Newtons, and 100Research on Bacillus subtilis showed that the large micro-Newtons. This led to interesting resultsspirals encircling the cytoplasm under the cell wherein displacement along inside edge of bothmembrane suggests that mreB forms filamentous proteins could be determined and outputted as astructures in bacteria similar to the eukaryotic actin graph.cytoskeleton. In vitro, purified mreB formspolymers consisting of protofilaments of 51 Resultsangstroms which is close to the spacing between thesubunits of filamentous actin which is 55angstroms. The three-dimensional structure of actinand mreB is also very similar. The strikingdifference between mreB and actin is that the F-actin twists around each other whereas mreBprotofilaments are straight.Research Design and MethodsWe used COMSOL to model the actin and MreB Figure 1a: COMSOL Diagram of Actin Protein,based on the values determined through literature Front Viewresearch; this includes density, Youngs Modulus,Poissons ratio, and the dimensions of F-actin, aswell as the dimensions of its subunits. The valueswe have determined are as follows: F-actin totaldiameter 7 nm, length of interest 20 nm, subunitdiameter of 5.4nm, Youngs Modulus of 44e6 Nm-2,and a Poissons ratio of 0.3. The length of interestwas determined to be the length at which it makes
  • 3. Figure 1b: COMSOL Diagram of Actin Protein, Figure 4: COMSOL Diagram of MreB with Front View, Meshed Force Applied, Boundary View Figure 5: COMSOL Diagram of MreB withFigure 2: COMSOL Diagram of MreB Protein, Force Applied, Streamline View Front View Figure 6: COMSOL Diagram of Actin with Figure 3: COMSOL Diagram of Actin with Displacement Edge Outlined in Red Force Applied, Boundary View Figure 7: COMSOL Diagram of Total
  • 4. Displacement Along Actin Edge, Load of 100 Micro-Newtons Figure 11: COMSOL Diagram of Total Displacement Along MreB Edge, Load of 100 Figure 8: COMSOL Diagram of Total Pico-NewtonsDisplacement Along Actin Edge, Load of 100 Pico-Newtons Maximum Protein Displacement Actin 1.8e-8 meters 4.614e-28 MreB meters Figure 12: Maximum Displacements with 100 Pico-Newtons LoadFigure 9: COMSOL Diagram of MreB with Discussion Displacement Edge Outlined in Red Maximum displacement was measured and analyzed for both actin and MreB. The displacement curve of actin (Figures 7 and 8) is exponential, which can be explained by the angle of the subunit on which the force is applied due to the helical conformation of the protein. In contrast, the displacement of MreB (Figures 10 and 11) is linear because the uniaxial force is applied in parallel to the major axis of the MreB filaments. Based on our results, it is apparent that the maximum displacement of MreB (Figure 4) is significantly smaller than that of actin (Figure 3). This can be Figure 10: COMSOL Diagram of Total explained by the rotational twist in the F-actinDisplacement Along MreB Edge, Load of 100 conformation, which makes the protein less rigid. Micro-Newtons Thus, it can be inferred that these homologue proteins, which have similar amino acid sequences and tertiary structures, play different roles in eukaryotic and prokaryotic cells. Since actin must handle multiple functions in a eukaryotic cell, including mechanical support, cell motility, cargo transport, and cytokinesis, flexibility and an ability to change conformations efficiently may be an essential characteristic for the protein. The larger
  • 5. displacement that was observed supports this motif. MreC/D and other actin-like proteins for properHowever, the primary function of MreB in bacteria localization." BMC Cell Biology. PubMed central, 3 Mar.is to provide the organism with a rigid, inter-cellular 2005. Web. 3 Dec. 2009.backbone. Consequently, the smaller displacement <http://www.ncbi.nlm.nih.gov/pmc/articles/PMC555950/observed in MreB upholds the notion that the >.bacterial protein must be relatively inflexible andstiff. The models of actin and MreB that wereconstructed represent the fundamental buildingblocks of the two proteins. Only four subunits of theprotein were modeled, and in the future, a largernumber of subunits can be modeled to verify thatthe proteins behave similarly at the subunit leveland as a complete protein. Moreover, theinteractions between the individual filaments, suchas hydrogen bonding and amino acid interactions,were not considered. In order to account for theseinteractions, the individual amino acids can bemodeled to determine if these interactions affect thedisplacement of the protein as a whole. Once athorough model of actin is established, it would beinteresting to study the elongation of the actinfilament and the biomechanics that underlies thepropagation of the protein through the cytosol of acell.Limitations:  did not take into account interactions between the actin filaments  only modeled 4 subunits of the proteinFuture Studies:  interactions between actin and other proteins  elongation of actinReferences1. Figge, Rainer M., Arun V. Divakaruni, and James W. Gober. "MreB, the cell shape-determining bacterial actin homologue, co-ordinates cell wall morphogenesis in Caulobacter crescentus."Molecular Microbiology 2004: 1321-332. Blackwell Publishing Ltd. Web. <http://www.biochemistry.ucla.edu/biochem/Faculty/Gob er/PDF/1321.pdf>.2. Van den Ent, Fusinita, Linda Amos, and Jan Löwe. "Bacterial Ancestry of Actin and Tubulin."Current Opinion in Microbiology 2001: 634-48. Elsevier Science Ltd. Web. 3 Dec. 2009. <http://www2.mrc- lmb.cam.ac.uk/groups/jyl/PDF/current%20opinion%20mi cro%202001.pdf>.3. Defeu, Joël, and Peter Graumann. "Bacillus subtilis actin- like protein MreB influences the positioning of the replication machinery and requires membrane proteins