Orientation and Membrane Partition Free Energy of PeT-Based Voltage-Sensitive Dyes from Molecular Simulations

Voltage measurement via small-molecule fluorescent indicators is a valuable approach in deciphering complex dynamics in electrically excitable cells. However, our understanding of various physicochemical properties governing the performance of fluorescent voltage sensors based on the photoinduced electron transfer (PeT) mechanism remains incomplete. Here, through extensive molecular dynamics and free energy calculations, we systematically examine the orientation and membrane partition of three PeT-based voltage-sensing VoltageFluor (VF) dyes in different lipid environment. We show that the symmetry of the molecular scaffold and the net charge of the hydrophilic headgroup of a given VF dye dominate its orientation and membrane partition, respectively. Our work provides a mechanistic understanding of the physical properties contributing to the voltage sensitivity, signal-to-noise ratio, as well as membrane distribution of VF dyes and sheds light onto rational design principles of PeT-based fluorescent probes in general.

(free).In the limit of low concentration, the chemical potential of bound and free VF dyes are : 27,53 where µ i and C i are the standard chemical potential and the concentration of the VF dyes in the bound state (i = b) and the free state (i = f ), respectively, while C is the standard concentration with the same unit as C b and C f .At equilibrium, the chemical potential in the two states must be equal, i.e., µ b = µ f .The membrane partition free energy of the VF dye is therefore given by: where the subscript eq indicates equilibrium state, while V b and V f denote the volume of the bound domain and the free solution, respectively.As in ref, 23 the homogeneity of bulk solution is invoked to recast the denominator in the last line.Following a previously developed simulation strategy 23,24,31,33 that employs a series of restrained intermediate states, we further compute G tot according to: The above set of equations insert a series of intermediate states into Eq.S2 to compute G tot : a positional (u p ), conformational (u c ) and orientation (u o ) restraining potential is imposed sequentially onto a VF dye in the bound state, which is then transferred reversibly from the lipid membrane to the free solution, where the imposed restraints are removed one by one.Eq.S3a to Eq. S3f correspond to the six components of G tot given by Eq. 3 in the Methods section.With G bound p and G z described therein, below we provide details for the remaining four components as well as derivation of the equation used to compute G z (Eq.6).
G bound c from conformational restraint in the bound state The conformational restraint u c imposed on a bound VF dye in the presence of u p results in a free energy cost given by e The conformational restraint used in this work is identical to the term u c employed in earlier protein-ligand 23 or protein-protein 31 binding free energy calculations.Here, the geometrically optimized structure of the VF dyes, prepared by our lab in a previous study, 16 was used as the reference structure for calculating the RMSD ⇠ of atomic positions of the VF dye.The conformational restraint u c has a harmonic form: where k c is the force constant of the restraint.Evaluation of the above equation is achieved through determining W (⇠), the PMF along ⇠ in the presence of u p , via the eABF method (Fig. S6).Parameters used in this and other eABF calculations are provided in the last section of this Supporting Information.
(S5) Evaluation of the above equation is similar to that of Eq.S4 via the eABF method.
G z as the membrane partition free energy of a geometrically restrained VF dye To obtain Eq. 6 in the Methods section, we first define a function as in ref: where in cylindrical coordinates r 1 = (⇢, , z).Far away from the membrane, the function   S3) contributes significantly to G bound o .For both POPC and POPC:CHL bilayers, initial structures of the W (✓) calculation were obtained from the aforementioned W (⇠) eABF runs.Next, to prepare for the eABF calculation of W (z), a 50-ns steered MD (sMD) simulation was performed to pull (force constant: 100 kcal/(mol/ Å2 )) the conformationally and orientationally restrained VF dye from z = 5 Å to z = 55 Å. Subsequent eABF calculations of W (z) were then performed in up to 27 windows spanning the range 0-5 Å  z  49-57 Å with initial structures obtained from the above sMD simulations.
The range of z depends on the preferred depth of di↵erent VF dyes within a membrane.
Again, due to the exponential term involving u p , only the part of W (z) near the center of u p (Table S3) makes significant contribution to G z .Finally, G free c is obtained by computing W (⇠) in the free solution using initial structures obtained from the W (z) eABF runs.Similar as W (⇠) calculation in the bound state, two windows jointly spanning 0.5 Å  ⇠  2.5 Å were employed.In all eABF calculations, the parameter extendedTimeConstant was set to 200 fs.Instantaneous forces were collected in bins of width 0.05 Å, 1 , and 0.1 Å for W (⇠), W (✓), and W (z), respectively, with the parameter extendedFluctuation equal to the bin width.
Force constants of positional (k p ), conformational (k c ), and orientational (k o ) restraints were set to 100 kcal/(mol Å2 ), 10 kcal/(mol Å2 ), and 0.1 kcal/(mol degree 2 ), respectively, while the center of each restraint is given in Table S3.The total simulation time for each of the above PMF calculations is given in Table S4.Convergence of the eABF calculations was analyzed by computing G tot using an increasing percentage of the total eABF simulations, i.e., at a given sampling percentage s, where s = 10%, 20%, .., 100%, all components of G tot were calculated using only the first s percentage of the corresponding eABF runs,

S7
with the exception of G bound p and G free o , which, as described earlier, were obtained from equilibrium MD simulations and numerical integration, respectively.
in the bound state Following the computation of G bound c , subsequent eABF runs of a positionally and conformationally restrained VF dye in the membrane yield the PMF along ✓, W (✓), the minimum of which is used as reference to set ✓ 0 in the orientational restraint u o = 1 2 k o (✓ ✓ 0 ) 2 , where k o is the spring constant of the harmonic restraint.Compared with the orientational restraint in proteinligand association 23 which involved three Euler angles, the u o term here is much simpler due to the lateral homogeneity of the membrane.The free energy cost G bound o of introducing this orientational restraint to a positionally and conformationally restrained VF dye in the bound state is given by: z z ⇤ ) is the lateral area of the membrane, and W (z) is the potential of mean force of the VF dye as a function of z in the presence of the conformational restraint u c and orientational restraint u o : in the free state Computation of G free o is known to be straightforward thanks to the homogeneity and isotropy of bulk solution. 23This contribution from the orientational restraint u o applied on a conformationally restrained VF dye in the free state is given by: yields G bound c , which is followed by G bound o calculation with W (✓) (Fig S7) computed via eABF using either a single window spanning 0 < ✓  35 (in POPC:CHL) or up to three windows jointly spanning 0 < ✓  50-70 (in POPC).The range of ✓ varies in the POPC system due to di↵erent tilting tendencies of the three VF dyes in this bilayer.Note that the exponential term involving u o in Eq.S5 dictates that only the part of W (✓) (Fig.S7) near the center of u o (Table

Figure S1 :
Figure S1: Probability density distribution of the tilt angle ⇢(✓) of msVF (black), dsVF (red) and isoVF (cyan) computed from principle component analysis (solid), the vector connecting the aniline nitrogen and the fluorescein C1 atom (dotted), or the vector connecting the center-of-mass locations of the sulfofluorescein and the rest of the dye molecule (dashed).

Figure S2 :
Figure S2: 2D radial pair distribution function g(r) of msVF (black), dsVF (red) and isoVF (cyan) from equilibrium MD simulations in POPC (top) and POPC:CHL (middle and bottom) bilayers, respectively.The g(r) calculation was performed between atom C1 of VF dye fluorescein and the phosphorus (P) atom of POPC or the oxygen atom (O) of CHL (see Methods).

Figure S3 :
Figure S3: Convergence of the PMF W (z). At a given sampling percentage s, where s shown in the figure ranges from 40% to 100%, W (z) was computed using the first s percentage of the eABF runs, where a positionally, conformationally and orientationally restrained VF dye was transferred reversibly from the lipid membrane to the free solution.

Figure S4 :
Figure S4: Convergence of G tot for msVF (black), dsVF (red) and isoVF (cyan) in POPC (solid) and POPC:CHL (dashed) bilayers.At a given sampling percentage s, all components of G tot , except for G bound p and G free o , were computed using the first s percentage of the corresponding eABF runs, which were then combined to yield G tot via Eq. 4.

Table S1 :
Mean value of the membrane thickness, measured as the average distance between phosphorus atoms in the two leaflets, z coordinate of CoM position of VF dye relative to membrane center z MemCen , and z coordinate of CoM position of VF dye relative to the average position of upper-layer phosphorus atoms z upperP .

Table S3 :
Parameter values of z p-L , z p-U and ✓ 0 used in membrane partition free energy calculations.