Chiral twisting in cytoskeletal polymers regulates filament size and orientation

While cytoskeletal proteins in the actin family are structurally similar, as filaments they act as critical components of diverse cellular processes across all kingdoms of life. In many rod-shaped bacteria, the actin homolog MreB directs cell-wall insertion and maintains cell shape, but it remains unclear how structural changes to MreB affect its physiological function. To bridge this gap, we performed molecular dynamics simulations for Caulobacter crescentus MreB and then utilized a coarse-grained biophysical model to successfully predict MreB filament properties in vivo. We discovered that MreB double protofilaments exhibit left-handed twisting that is dependent on the bound nucleotide and membrane binding; the degree of twisting determines the limit length and orientation of MreB filaments in vivo. Membrane binding of MreB also induces a stable membrane curvature that is physiologically relevant. Together, our data empower the prediction of cytoskeletal filament size from molecular dynamics simulations, providing a paradigm for connecting protein filament structure and mechanics to cellular functions.

action is still obscure. In our simulations, A22 did not affect the MreB monomer opening 125 angle, and only slightly increased the dihedral angle (Fig. 2c). Thus, our results suggest 126 that A22 does not directly affect MreB monomer conformation and is unlikely to alter the 127 ATP-binding pocket, consistent with other studies proposing that A22 blocks phosphate 128 release rather than inhibiting ATP hydrolysis 5,23 .
We next sought to study the conformational changes in single protofilaments with two 159 CcMreB subunits ("2x1 protofilaments") by analyzing the relative movements of the (+) 160 and (-) subunits in the dimer (Fig. 2a,d). We simulated CcMreB 2x1 protofilaments with 161 both subunits bound to ATP or ADP, and quantified their relative orientation changes by 162 calculating the Euler angles that characterize the three orthogonal modes of rotation 163 around the x, y, and z axes (Fig. 2d(i)): θ1 and θ2 characterize bending into the 164 membrane surface and inter-protofilament surface, respectively ( Fig. 2d(ii, iii)), and θ3 165 characterizes twisting along the protofilament (Fig. 2d(iv)). We defined all three Euler 166 angles to be zero in the crystal structure ( Fig. 2d(i)). A stable membrane-binding 167 double-protofilament conformation requires θ1 to be negative and θ2 to be approximately 168 zero to avoid steric clashes ( Fig. 2d(ii,iii)). We found that the largest changes in our 169 simulations occurred in the bending angles (Fig. 2e, Fig. S1j,k), whereas no systematic 170 protofilament twisting was observed (Fig. S1l). The bending angles were also 171 nucleotide-dependent, with ATP-bound protofilaments exhibiting larger bending angles suggesting that the difference in θ2 bending between ATP-and ADP-bound single 203 protofilaments was resolved into double protofilament twisting. To confirm that our 204 observations on bending and twisting were not artefacts due to limited filament size, we 205 performed a larger simulation with eight ATP-bound MreB doublets in water (an 8x2 206 protofilament). In this 60-ns simulation, changes in bending and twisting angles 207 matched our observations in 4x2 protofilaments ( Fig. S2d-f, Movie S1). To verify that 208 the double-protofilament twist was not unique to CcMreB, we constructed a homology 209 model of E. coli MreB (Methods), and found that EcMreB exhibited quantitatively similar 210 left-handed twisting in simulation (Fig. S2g). Thus, higher-order oligomerization can 211 dramatically alter the biophysical properties of MreB filaments. indicated that membrane binding introduced strain into the MreB filaments that may 241 affect membrane conformation. In our simulations, the membrane started flat, but after 242 60 ns, the membrane bent toward the MreB protofilaments (Fig. 3g). In rod-shaped 243 bacterial cells, the membrane also bends toward MreB filaments, forming a curvature 244 dictated by the cell width (Fig. 4h). We computed the curvature at the center of the 245 membrane patch along the protofilament direction and found that the membrane 246 curvatures for all 4x2 protofilament membrane simulations were ~5 µm -1 (Fig. 3i), on the 247 same scale as the membrane curvature of a rod-shaped bacterial cell that is ~0.8 µm in 248 width (~2.5 µm -1 ). 249 13 To validate that the observed membrane curvature changes were related to the twisted 251 nature of 4x2 protofilaments, we performed simulations of 2x1 protofilaments in the 252 presence of a membrane patch as a control. The membrane patches bound to 2x1 253 protofilaments were more variable and did not exhibit a characteristic curvature 254 throughout the simulation (Fig. S2j) 260 We hypothesized that since many MreB mutations alter cell shape, they potentially also 261 induce altered intrinsic twist and membrane interactions as a double protofilament. We 262 identified four MreB mutants that were reported to cause a range of alterations to E. coli We first performed all-atom MD simulations for each of the corresponding CcMreB 269 mutants bound to ATP in a 4x2 protofilament configuration in water. All mutants 270 exhibited similar bending (Fig. S3a,b), but differed widely in twisting angles compared to 271 wild-type CcMreB: E275D (E276D in EcMreB) and R121C (R124C in EcMreB) twisted 272 less than wildtype, whereas V53A (V55A in EcMreB) and I138V (I141V in EcMreB) 273 exhibited more twist (Fig. 4b, Fig. S3c).
274 275 We then asked whether these mutants also exhibit differential twisting when membrane-276 bound by simulating 4x2 protofilaments of R121C and V53A in proximity to a membrane 277 patch. These two mutants were selected because they exhibited the smallest and the The coarse-grained model predicts that the limit length of MreB filaments should 346 decrease with increasing intrinsic twisting (Fig. 4f). Similarly, the local pitch angle θ (Fig.   347 4d) balances between filament bending and twisting: with a pitch angle of 90°, the 348 filament fully untwists but largely preserves bending; when the pitch angle deviates from 349 90°, the filament reduces bending while remaining somewhat twisted. Therefore, from 350 an energetic point of view, our coarse-grained model predicts that the intrinsic twisting 351 in an MreB filament (which we define to be 90% of the limit length) causes its orientation 352 to deviate from the perfect circumferential direction (pitch angle θ = 90°) (Fig. 4f). We 353 further performed sensitivity analyses by altering the parameters that affect filament 354 conformation 28 . For instance, by varying the intrinsic bending k, we find that the limit-355 length predictions are largely unaffected, whereas larger values of k lead to pitch angles 356 closer to 90° (Fig. 4f). Similarly, altering the ratio of bending and twisting moduli (C/K) 357 changes the pitch angle but not limit length (Fig. S3j), while decreasing membrane 358 binding potential decreases the limit length without affecting the pitch angle (Fig. S3k). 359 Notably, despite variation in the predicted values across parameters, our model 360 generally predicts that larger intrinsic twist leads to short filaments with larger pitch 361 angles. 362 18 To verify the results of our coarse-grained model, we experimentally constructed E. coli 364 strains expressing the MreB mutants (Fig. 4a) with a sandwich fusion of monomeric 365 super-folder green fluorescent protein (msfGFP) 31 as the sole copy of MreB. To quantify 366 the shape and size of the MreB filaments, we imaged each strain using super-resolution 367 structured illumination microscopy (Methods). In wild-type cells, MreB formed short 368 filaments with a limit length of ~200-300 nm (Fig. 4g), approximately consistent with the 369 prediction of our coarse-grained model (Fig. 4f). The E276D and R124C mutants clearly 370 contained much longer filaments that spanned roughly half the cell periphery, whereas 371 V55A and I141V had very short MreB filaments (Fig. 4g). We quantified the distribution 372 of MreB patch areas in each mutant as a proxy for filament length, and indeed E276D 373 and R124C had larger MreB patches than wildtype, and V55A and I141V had smaller 374 patches (Fig. 4h). We used the 99 th percentile of patch size as an approximation for 375 filament limit length in each mutant, and found that it was highly negatively correlated 376 with the twisting angles we observed in all-atom MD simulations (Fig. 4h,

386
Here, we used MD simulations to reveal a new twisted double-protofilament 387 conformation of CcMreB (Fig. 3c) and EcMreB (Fig. S2g). We determined that twisting 388 is regulated by various factors including the binding nucleotide (Fig. 3c), the membrane 389 (Fig. 3c), genetic perturbations (Fig. 4b), and regulatory proteins (Fig. 4c). While    f) The coarse-grained model predicts that filaments with larger intrinsic twisting 566 have shorter limit length. Similarly, the coarse-grained model predicts that the 567 orientation of a short filament (90% of the corresponding limit length) deviates 568 more from 90° as the intrinsic twist increases. Increasing the intrinsic bending k 569 did not affect the limit length, but reduced the pitch angle to be closer to 90°. these two opening angles (Fig. 2b, left). The dihedral angle was defined as the angle 634 between the vector normal to a plane defined by subdomains IA, IB, and IIA and the 635 vector normal to a plane defined by subdomains IIB, IIA, and IA (Fig. 2b, right). (or each subunit pair) was defined using three unit vectors (d1, d2, d3) 50 . For single 640 protofilaments, d3 approximately aligns to the center of mass between the two subunits, 641 d2 is defined to be perpendicular to the membrane plane, and d1 = d3 × d2 (Fig. 2d) Table   686 S2.
36 688 The total energy per unit length was minimized for an infinite-length filament bound to 689 an infinitely long cylinder by searching for solutions that are periodic over an arc 690 distance l. The boundary conditions were set to be 691 (0) = 0, ( ) = 2 .

692
The Hamiltonian was then minimized with respect to θ, ψ, and l, yielding both the 693 equilibrium period l and the equilibrium filament shape described by θ and ψ. . 710 Results were assessed to have converged after ~10 7 Monte Carlo steps, as defined by 711 energy fluctuations lower than 1% of the minimized energy across the last 10 4 steps. 712 The corresponding period l leading to the minimized energy was identified using a 713 Golden-section search. Twenty independent replicate simulations were carried out for 714 each parameter set to ensure that a global minimum was reached.