mDia1 senses both force and torque during F-actin filament polymerization

Formins, an important family of force-bearing actin-polymerizing factors, function as homodimers that bind with the barbed end of actin filaments through a ring-like structure assembled from dimerized FH2 domains. It has been hypothesized that force applied to formin may facilitate transition of the FH2 ring from an inhibitory closed conformation to a permissive open conformation, speeding up actin polymerization. We confirm this hypothesis for mDia1 dependent actin polymerization by stretching a single-actin filament in the absence of profilin using magnetic tweezers, and observe that increasing force from 0.5 to 10 pN can drastically speed up the actin polymerization rate. Further, we find that this force-promoted actin polymerization requires torsionally unconstrained actin filament, suggesting that mDia1 also senses torque. As actin filaments are subject to complex mechanical constraints in living cells, these results provide important insights into how formin senses these mechanical constraints and regulates actin organization accordingly.

Supplementary figure 3. mDia1DN3-mediated actin polymerization rate of a single filament at several forces. Data show that the force-dependent polymerization rate is insensitive to the force changing order.
Supplementary figure 4. Force-dependent polymerization rate of Bni1(FH1-FH2)p mediated actin polymerization. Data show that the force-dependence of Bni1(FH1-FH2)p mediated actin polymerization also has a force-sensitive species (solid squares) and a force-insensitive species (hollow squares), similar to that observed for mDia1-mediated polymerization. Vertical error bars represent standard errors of mean obtained from multiple data points obtained at the force. Horizontal error bars represent the 20% uncertainty in force calibration. The value labelled on each data point indicates the number of independent experiments carried out at the corresponding force. All of the data were collected in the presence of 500 nM G-actin. in the main text), which contributes to a force-dependent conformational entropic free energy of This energy equals −F ∆/2 when ∆(f ) is a constant. The forcedependent probability of the • state becomes: where β = (k B T ) −1 , k B is the Boltzmann constant and T is the temperature. denotes the energy cost of the close-to-open transition of the FH2 ring.
By denoting k • a (F ) and k • d (F ) as the force dependent association and dissociation rates from the barbed end when FH2 is in the • state, the force-dependent association flux and dissociation . Their ratio is: where δ ∼ 2.7 nm is the filament extension increase by adding a new actin monomer to the barbed end, which is half of the size of one actin monomer ( 5.4 nm). The factor of e βF δ is the result of the net extension increase due to recruitment of a new actin monomer that reduces the potential energy by an amount of −F δ after one reaction cycle in the kinetics diagram shown in Fig. 5.
is the association rate to the barbed end with a constitutively open FH2 ring. Force changes the energy barrier of adding an actin monomer by an amount of − Applying Arrhenius' law, The polymerization speed is therefore: In the last line, we have assumed that the dissociation rate k is the critical concentration of mDia1 associated barbed end of actin filament at zero force when the FH2 ring is in the open conformation.
As revealed in the above equation, v(F, c) depends on the elasticity of the FH2 ring described by φ FH2 (F ). Eq. (1) in the main text is recovered in the simplest case where ∆(f ) is a constant.
Stretching angle calibration -The force range used in studies of actin polymerization is from 0.5 pN to 10 pN. At the corresponding magnet-bead separation range, we tune the height of the magnet relative to the coverslip such that the height of a free bead increases 5-8 µm after drifting along the force direction over a distance of 50 µm, which corresponds to a stretching angle range of roughly 6 − 10 degrees.

Supplementary Note 3
Contribution of the 20% uncertainty in force calibration to the variation of force-dependent poly- 6

Supplementary Methods
Preparation of coverslip, seed actin filaments, and superparamagnetic beads -Four different tethering methods were used in our experiments (Fig. 1A), which required different preparations of coverslip, seed actin filaments, and superparamagnetic beads as described below.
In experiments using a protein A-antiGST-GST-mDia1∆N3-actin-superparamagnetic bead tether, the coverslip was functionalized with protein A. To functionalize the coverslip, the coverslip was sonicated with 50 % detergent (Decon 90) for 30 minutes and then with acetone for 20 minutes, before being dried in an oven and plasma cleaned for 10 minutes. The coverslip was then incubated with 1% APTES in methanol for 1 hour at room temperature, washed with distilled water and dried in an oven. Next, the coverslip was made to be part of a channel, then incubated with 0.3 % glutaraldehyde in 2× PBS for 6 hours at room temperature, then rinsed with 1×PBS. Following glutaraldehyde treatment, the coverslip was incubated overnight with 50 µg/mL protein A (Sigma In experiments using a NEM-HMM-actin-biotin-mDia1∆N3-superparamagnetic beads tether, NEM-HMM functionalized polystyrene beads and superparamagnetic beads as described above were used. The seeding actin filaments were polymerized by 750 nM biotin-mDia1∆N3, 2 µM G-actin in KMEI buffer and stabilized with 2 µM Phalloidin.
In experiments using a NEM-HMM-actin-biotin-mDia1∆N3-streptavidin-biotin-DNA-DIG-antiDIG-superparamagnetic beads tether, NEM-HMM functionalized polystyrene beads and the 8 seeding actin filaments polymerized with biotin-mDia1∆N3 as described above were used. The seeding filaments were incubated with streptavidin so that biotin-mDia1∆N3 were attached to streptavidin molecules. The anti-DIG coated superparamagnetic beads were prepared as follows: 1 µm-diameter carboxyl superparamagnetic beads (MyOne, Invitrogen) were treated with EDC and NHS in MES buffer (pH 6.0) for 30 mins at room temperature, then rinsed with 2× PBS, incubated overnight with 50 µg/mL anti-DIG in 1× PBS at room temperature, and blocked in 5 % BSA in 1× PBS. The anti-DIG superparamagnetic beads were then incubated with 445 bp DNA labelled with a DIG on one strand at one end and a biotin on the complimentary strand at the other end for 20 minutes at room temperature. Later, these beads were flowed into channels to search for the streptavidin attached biotin-mDia1∆N3 on the actin filaments.