solution salts are 
 key players in the regulation of the actin cytoskeleton . a high affinity ( in the nanomolar range )
cation is associated with 
 and stabilizes the conformation of a bound nucleotide , which affects 
 actin monomer structure and filament structure and assembly .
low 
 affinity ( in the millimolar range ) cation interactions induce polymerization 
 and regulate mechanical properties of filaments . structural bioinformatics and site - specific 
 mutagenesis experiments favor a mechanism in which occupancy of two 
 discrete low affinity cation binding sites positioned longitudinally 
 between actin subunits drives actin assembly and modulates filament 
 stiffness .
these sites have been termed 
 the  polymerization  and  stiffness  sites 
 based on the effect of amino acid substitutions on in vitro assembly and filament rigidity .
structural 
 approaches to date , including x - ray crystallography and cryo - electron 
 microscopy , have been unable to resolve filament - associated cations , 
 which has limited understanding of the molecular origins underlying 
 these two observed behaviors .
computer 
 simulations have proven to be a powerful tool to understand 
 the molecular determinants of actin structural dynamics and allostery , 
 as well as how these are influenced by interactions with regulatory 
 proteins and small molecule cofactors ( e.g. , adenine nucleotides , 
 atp and adp , or adp together with the phosphate anion formed by atp 
 hydrolysis ) .
for example , these simulations have verified the dependence 
 of actin monomer conformations on bound nucleotide identity , initially 
 identified by x - ray crystallography , and 
 delineated the mechanism of bound atp chemical cleavage , thereby explaining 
 the large difference between monomer and filament nucleotide hydrolysis 
 rates .
furthermore , simulations reliably 
 capture nucleotide- and regulatory protein - dependent actin filament 
 bending and torsional stiffness , with absolute persistence length 
 values that agree remarkably well ( within a factor of 2 ) with  wet - lab  
 determinations , despite the experiment and simulation sampling greatly 
 different time scales . filaments with 
 bound adp are more compliant in bending and twisting than those with 
 bound atp ; filaments with bound cofilin are even more flexible .
molecular dynamics ( md ) simulations predict that this behavior arises 
 from differential folding of the actin dnase - binding loop ( d - loop ) , consistent with electron microscopy studies 
 implicating this subdomain in regulating filament structure and mechanics . despite the evidence showing that discrete 
 cation binding plays 
 a critical role in regulating filament polymerization and mechanics , 
 no computational study to date
has included coordinating divalent 
 cations in the stiffness and polymerization sites predicted by biochemical 
 experiments .
a computational study can allow for a detailed molecular 
 understanding of the binding modalities and residues involved , which 
 can inform and drive future experimental studies . in this work , we 
 construct simulation models including coordinated magnesium ions between 
 actin subunits .
we have three goals :   evaluate whether structural 
 models of cation binding sites on filaments are plausible ,   examine 
 in molecular detail the structural changes that must occur at the 
 interface between actin subunits to accommodate coordinated cations , 
 and   determine the effects of cation occupancy on filament mechanical 
 properties .
we show that proposed cation sites are indeed reasonable , 
 and that they stiffen actin filaments by adhering the actin d - loop 
 to the adjacent actin s target binding cleft ( tbc ) .
atomistic 
 models of actin filaments are prepared as in previous studies and as described in the supporting information ( si ) . in brief , the configuration of an actin subunit is formed 
 into a filament structure by repeated translation and rotation . in 
 the case of a pure actin filament , this consists of a shift of 27.6 
  and a rotation of 166.6 such that the actin double helix 
 makes one right - handed half - turn every 13 subunits . in this paper , 

( termed namba , 
 throughout ) . for the second , and the main object of our study ,
a new 
 model subunit must be engineered to accommodate two additional cations 
 per subunit , with bridging longitudinal intersubunit interactions 
 ( termed namba - cation .
the third and fourth systems are filaments constructed 
 for reference from the oda model .
the 
 former is built as in previous studies ( oda ) , and 
 the second contains a bound stiffness magnesium ion designed to mimic 
 the coordination produced in the namba filament , as described in the results section ( oda - cation ) .
additionally , we reanalyze 
 d - loop conformations from previous simulations of an oda filament 
 engineered to contain a folded d - loop from the 1j6z structure as in ref ( 21 ) ( oda - f ) , and the simulations in ref ( 16 ) of a cofilin - bound actin 
 filament with 11 subunits ( cofilin ) .
all actin subunits in this study 
 contain a bound adp and coordinating mg ion in the nucleotide - binding 
 cleft .
polymerization ( yellow ) and stiffness ( purple ) cations are added 
 in putative binding sites between actin subunits in the positions 
 shown .
beads labeled 14 show the center of mass positions 
 of the four actin subdomains as defined in table s3 , while bead 5 shows the center of mass of the d - loop ( residues 
 4051 ) .
a subscript indicates the relative subunit position 
 in the filament ( increasing toward the  pointed  end ) . 

also shown is the 2134 dihedral angle , which is 
 used to measure the planarity of an actin monomer .
simulations were performed as in previous studies 
 ( e.g. , ref ( 24 ) ) using 
 the charmm27+cmap 
 force field with explicit tip3p water 
 molecules using namd .
the system was ionized with monovalent ions to a concentration 
 of 0.180 m kcl using vmd .
simulations 
 employed electrostatics treated with particle mesh ewald method with a 12  cutoff .
simulations were performed 
 at 310 k and 1 atm with temperature maintained using a langevin thermostat with a coefficient of 5 ps and pressure maintained by a langevin piston with a period of 2 ps and a time constant of 1 ps . to facilitate analysis 
 of our atomistic data , we map our simulation data to a coarse - grained 
 representation using the 12-site mapping defined in saunders and voth 
 ( table s3 ) . in this mapping ,
the traditional definitions for the four subdomains 
 ( sd ) of actin are preserved , while several important components such 
 as the sd2 d - loop , are broken out into separate beads such that their 
 fluctuations can be resolved .
the position of each coarse - grained 
 bead is defined as the center of mass of the residues specified in table s3 . for nomenclature , when computing intersubunit 
 quantities , we refer to a bead on one actin simply by its number , 
 and to a position on the second actin by its number and a subscript 
 indicating its relative subunit index , increasing toward the pointed 
 end of the filament ( see figure 1 ) . to quantify 
 the amount of 
 symmetry found in the coordinating oxygen atoms around the mg ions
, we compute the q4 variant of the steinhardt - nelson 
 bond - orientational order parameter . using 
 this formula
, we calculate that a perfect octahedral geometry formed 
 by six coordinating oxygen atoms will have a q4 value of 
 0.764 , and distorted structures will have smaller values .
see si for further details . to identify the 
 effects of specific cation binding on the conformations of the d - loop 
 without imposing any presupposed interpretations
, we use statistical 
 techniques to automatically classify the d - loop states observed in 
 simulation .
we employ two different methods to help to ensure our 
 conclusions are independent of our method of analysis .
the first technique 
 is dihedral principal component analysis ( dpca ) . in this method
, we perform standard principal component 
 analysis on cosines and sines of the  ,  , and  
 backbone dihedral angles internal to the 12 residues in the d - loop . 

singular value decomposition is performed on this matrix to extract 
 linear combinations of the cosines and sines of the dihedral angles 
 that contain the most information about the variance found in the 
 data set .
the values of the top few principal components can often 
 be used to identify clusters in a set of data , which in a molecular 
 context can help identify discrete conformational states of a protein 
 of interest .
the second technique employed 
 is the diffusion map ( dm ) approach . here , we compute 
 the pairwise rmsds of all d - loop configurations , superposing each 
 configuration using the theobald qcp algorithm as implemented in the mdtraj library .
a matrix of squared distances is constructed , exponentiated , 
 and diagonalized . the eigenvectors with the largest eigenvalues
can 
 be used , in a manner similar to principal components , to separate 
 structures that have distinct conformations .
the persistence length 
 of filaments is computed by fitting the decay of bending fluctuations 
 along the filament to an exponential function . in order to do this ,
the center - of - mass ( com ) of the subunit 
 positions in the two ( a and b ) strands of the actin helix are mapped 
 to a central  strand  running up the center of the filament . 

this procedure is performed as in ref ( 23 ) on a series of 10 ns windows , and the average 
 and standard deviation among different time windows is computed . to 
 extract the torsional rigidity ,
we compute the variance of twist angles 
 in the filaments as in ref ( 40 ) , where here the twist angle is defined ( with the long axis 
 of the filament aligned along the z - axis ) as the 
 angle  between adjacent interstrand vectors pointing from the 
 com of one actin monomer to another ( e.g. , r12 and r34 ) projected in the xy plane .
we can then compute the torsional rigidity as c = kbtd/ , where d is the average distance between the com 
 of subunits in the same strand , and  is the standard deviation 
 in the twist angles ,  , in a single filament snapshot obtained 
 from the simulations .
in order to generate cation binding 
 geometries for the stiffness and polymerization sites , we first had 
 to insert magnesium ions into a structural model for an actin filament 
 near candidate binding pocket sites .
several actin filament models 
 exist , e.g. , refs ( 25 , 26 , 41 , and 42 ) , and all of these share many general features while having some 
 small differences ( e.g. , older models contained a structured n - terminus 
 in each subunit , and the namba model favors longitudinal contacts 
 over lateral contacts by a small subunit ; see refs ( 24 and 42 ) ) . in this work
, we chose to initially 
 construct our cation binding sites from the namba filament model for two reasons .
first , as the filaments used 
 to generate the original namba model were selected to make  f - actin 
 as straight as possible  , we suspect that geometry represents 
 a more rigid subpopulation of actin geometries as has been suggested 
 before .
hence , the namba model may be more representative 
 of actin filament structures found under high divalent - cation conditions . 

second , the stiffness site amino acid side chains and backbone atoms 
 in the namba model are nearly positioned in an ideal binding geometry 
 for a magnesium ion and , hence , require minimal perturbation to make 
 these cation insertions .
in particular , glu167 ( the single 
 tick referring to a position a subunits two away in the pointed - end 
 direction ) , is strongly indicated as being involved in this interaction , 
 is far more proximal to the center of the predicted binding pocket 
 in the current namba geometry ( table s1 ) .
mg binding geometries of structures in the 
 pdb generally contain six coordinating 
 oxygen atoms in an octahedral geometry , with two of the oxygen atoms 
 coming from contacts with water molecules . to construct
a namba filament 
 with bound stiffness and polymerization ions , pentamers of the namba 
 model were built with mg ions inserted in the three actin 
we then performed a series of minimization and 
 molecular dynamics simulations with additional harmonic biases added 
 to the simulation force field , which moved oxygen atoms from selected 
 side chains to be consistent with hexa - coordination ( see si and table s2 ) , with water molecules to be 
 inserted later in the remaining two spots .
further restraints were 
 applied to bring the d - loop ( residues 4051 ) in further contact 
 with residues in the proximal actin subdomain 3 , which proved necessary 
 to prevent the d - loop from collapsing in a manner not observed in 
 known structures of actin .
the particular choice of residues to include 
 in stiffness and polymerization ion coordination was based first on 
 experimental constraints and bioinformatics data in refs ( 2 and 11 ) with a preference for residues 
 having high sequence conservation among actin structures .
the distances to be restrained were iterated 
 many times until reaching a geometry ensuring the mg cations 
 remain in the binding pocket over many nanoseconds .
we note that the 
 resulting d - loop configuration is similar to that observed in a recent 
 structure of actin complexed with tropomyosin .
finally , we constructed a periodic 13-subunit filament 
 based on the configuration of the central actin subunit , and confirmed 
 that mg remain bound in the two actin binding pockets 
 for hundreds of nanoseconds .
this 13-subunit filament was used for 
 all subsequent analysis . to further confirm the effect of stiffness 
 ion occupancy on filament 
 rigidity
, we built a 13-subunit oda filament with bound stiffness 
 ion employing the same distance constraints and minimization protocol 
 as one used to build the namba - cation model .
the resulting starting 
 configuration also held stiffness ions in place for > 150 ns .
however , 
 the side chain geometry around the magnesium ion in the oda - cation 
 model is not as stable as in the namba - cation model .
moreover , the 
 construction protocol destabilized other contacts in the oda system , 
 such that drifts in coarse - grained observables , could be observed 
 over long simulations .
hence , since this structure would require additional 
 manipulation to produce a fully stable initial geometry , we do not 
 examine this simulation in detail any further , but only include calculations 
 of persistence length and torsional rigidity for the early period 
 of the simulation where coordination and filament properties appear 
 stable .
the details of the minimization protocols employed here , 
 including 
 considerations when choosing the distances to constrain , and the force 
 constants used to enforce the constraints , are detailed in the si .
additionally , the si contains a pdb file of an equilibrated 13-subunit filament namba - cation and oda - cation filaments with ions produced by these procedures .
the constructed  polymerization  
 and  stiffness  cation binding sites of our namba - cation 
 model relax in the first few nanoseconds of simulation .
typical snapshots 
 of the ion binding sites from the namba and nation - cation systems 
 are compared in figure 2 , and are discussed in detail below .
considering oxygen  magnesium 
 distances within 3  as interactions , both magnesium ions remain 
 stably bound in an octahedral geometry with six coordinating oxygen 
 atoms for more than 200 ns of subsequent dynamics .
the binding geometry 
 in the stiffness ( s ) site stays more symmetric and more similar to 
 ideal octahedral binding than does the polymerization ( p ) site ( figure 3a ) , as assessed by 
 measuring the steinhardt - nelson order parameter , q4 ( see methods section and the si for further details ) .
most of the amino 
 acid residues hypothesized to be involved in cation coordination proved 
 reasonable ( figure 2 ) .
however , some significant differences did emerge from the simulations , 
 as discussed below .
typical snapshots from simulations of the namba model 
 with ( a , c ) 
 and without ( b , d ) additional coordinated mg ions .
panels 
 a and b show an overview , and c and d show a closer view .
( a , c ) polymerization 
 cations shown in yellow , and stiffness cations are shown in purple . 

protein residues and water molecules within 5  of the central 
 cations are atomically resolved , as are residues d292 and 
 k61 , which form a salt bridge when the stiffness ion is added .
( b , d ) 
 residue positions that will form the core of the polymerization site 
 ( e205 , d286 , d286 , and i287 ) and form the 
 stiffness site ( q49 , k50 , d51 , e57 , e167 ) are shown in detail , 
 as well as water within 5  of d286 , d288 and 
 e167. the side chain of k61 is oriented such that it forms 
 a salt bridge with e167. ( a ) cation binding geometry is six coordinate and has high symmetry . 

vertical dashed line shows the value of q4 for an ideal 
 octahedron . the polymerization site ( p ) , while still symmetric , is 
 more distorted than the binding in the stiffness site ( s ) .
( b ) distance 
 between charged atoms in residues suspected to form a salt bridge 
 in actin .
alternative salt bridge is 
 persistent in the cation - coordinated system , and breaks when the stiffness 
 ions are removed .
we compute cation coordination in the 
 namba - cation system every 50 ps after waiting 75 ns for the binding 
 pockets to find their preferred conformations .
, 
 k50 , e57 , and e167 and two water molecules for 70% of the 
 simulation time . among these snapshots of the stiffness ion coordination , 

15% have k50 replaced by an interaction with the neutral side chain 
 oxygen of e167. in one of the 13 stiffness sites in the periodic 
 filament , the q49 side chain was replaced by a water oxygen in the 
 first 50 ns ; subsequently , the k50 interaction was lost in the next 
 25 ns and replaced by a water molecule .
hence , for the final 150 ns 
 of simulation , 1/13 of the magnesium sites is coordinated only by 
 e57 and e167. in no case was a simulation snapshot observed 
 lacking a bound e167 oxygen , consistent with this residue 
 playing a critical role in cation coordination .
every polymerization 
 site magnesium 
 ion was initially coordinated by four side chain oxygen atoms and 
 two water oxygen atoms in the equilibrated namba - cation filament model . 
 for simulation times following the 75 ns of binding equilibration , 
  72% of the magnesium ions
sixty - five percent of the configurations 
 are found with double coordination ( associated with both the charged 
 and uncharged side chain oxygen ) by d286 and e205 
 with a single coordinating d288 , while , in the remaining cases , 
 the magnesium is doubly bound by d288 and singly bound to 
 d286. the remaining 28% of coordination sites cases are split 
 18% with two bonds to e205 and one each to d286 and 
 d288 , and 10% doubly bound to d286 , and singly 
 bound to d288 and e205. although it was biased 
 to be included in the initial binding , t202 did not directly coordinate 
 the polymerization site ion . in the namba filament without magnesium 
 ions , the side chain of t202 formed h - bonds with d286 occasionally , 
 and virtually never with any other binding partner , while in our namba - cation 
 model hydrogen bonding
was observed with subunit i+2 residue d286 
 and also with side chains of subunits i+1 residues s271 ( as previously 
 observed , e.g. , in ref ( 42 ) ) and d179 and the backbone of e270 ( as seen , e.g. , in ref ( 26 ) ) .
our namba - cation model 
 simulations suggest that these effects could potentially arise by 
 indirectly compromising magnesium coordination at the polymerization 
 site .
kang et al . have noted that the existence of the e167-magnesium 
 interaction precludes the k61-e167 salt bridge present in 
 other actin filament models , including our namba and oda filaments lacking coordinated mg in the stiffness sites ( figure 2b ) . to ensure that we have not excluded this 
 important salt - bridge interaction through our choice of molecular 
 mechanics force field
, we performed one simulation where we removed 
 the 13 stiffness site mg ions after simulation for 200 
 ns ( 26 random cl ions more than 10  from 
 the filament were also removed to maintain neutrality ; this does not 
 substantially change the monovalent salt concentration ) .
the distance 
 between the k61 and e167 side is stable in the magnesium - bound 
 simulation , but relaxes in just a few nanoseconds to the salt - bridge 
 distance observed in the oda model after the magnesium ions are removed 
 ( figure 3b ) . in the 
 cation - bound system , an alternative salt bridge between k61 and d292 
 is formed ( figure 2a ) . to determine the extent 
 to which our addition of coordinated magnesium ions influences the 
 actin subunit and filament conformation , it is most insightful to 
 look at distributions of coarse - grained observables .
two of the most 
 relevant ones are the distribution of the twist angle ( the rotation 
 between adjacent subunits ) and the subunit separation in the longitudinal 
 direction (  rise  ) observed in the filament .
we observe 
 that adding coordinated mg ions to the namba filament 
 narrows the distribution of actin twist angles ( figure 4a ) .
it also results in a slightly more broad 
 distribution of rise distances , with more density in small intersubunit 
 distance range ( figure 4b ) .
this is likely a simple consequence of stronger longitudinal 
 interaction strength . another major consideration is whether adding 
 these coordinated ions modifies the individual subunit flatness , which 
 can be measured by the 2134 dihedral angle between 
 the four coarse - grained sites representing actin subdomains 14 
 ( see figure 1 ) .
there 
 is little difference in our two namba filament models ( figure 4c ) , indicating that the addition 
 of these ions does not have a large effect on subunit conformation , 
 especially when compared to the more substantial perturbation of binding 
 cofilin ( short dashed line ) . coarse - grained distribution functions .
( d ) angle formed between subdomains 2 and 4 in an actin filament , 
 and subdomain 3 in the actin two subunits away .
( e ) distance between 
 the actin d - loop and the coordinated subdomain 3 .
( f ) distance within 
 a subunit between subdomain 3 and the center - of - mass of the d - loop . to ascertain the effect of the 
 polymerization ion on subunit conformation
, 
 we have examined all of the distributions of coarse - grained distances 
 and angles containing coarse - grained domains 2 , 4 , and 32 , between which it is situated ( see figure 1 ) .
we find little difference in the quantities , 
 in particular the direct distance between domains 2 and 4 ( not shown ) , 
 and the angle formed between these three domains hardly changes on 
 inclusion of the polymerization site ion ( figure 4d ) , and conclude that this addition largely 
 imposes a local backbone rearrangement to accommodate a different 
 packing of side chains .
the stiffness cation has a very large 
 effect on the longitudinal 
 interaction between subunits .
it substantially reduces the distance 
 between the d - loop and sd3 ( figure 4e ) , and results in a much tighter distribution , indicating 
 a much stronger interaction between these two components .
the decreased 
 flexibility of the d - loop can also be corroborated by looking at the 
 distribution of intra - actin distances between the d - loop and the center 
 of mass of sd2 , which is also substantially reduced in width ( figure 4f ) . to accommodate the additional 
 coordination of the stiffness cation between the actin d - loop and 
 sd3 , the d - loop loses great deal of its flexibility and is much more 
 strongly coordinated to the i+2 target binding cleft 
 as discussed in the previous section . to quantify this effect , we 
 used vmd to compute the solvent - accessible 
 surface area ( sasa ) of the d - loop in actin i that 
 is buried by actin i+2 by computing the difference 
 in sasa between the d - loop alone and the sasa of the d - loop in the 
 presence of the rest of the actin ( table 1 and table 2 ) .
we find that our mg - bound namba filaments 
 have substantially less accessible surface area compared to our namba 
 system without mg .
moreover , access is restricted to 
 important conserved residues in the d - loop , which presumably accounts 
 for inhibition of cofilin binding and 
 may regulate interaction with other regulatory proteins .
for example , 
 met44 ( and met47 ) oxidation by mical can promote filament disassembly .
our results suggest strongly that the susceptibility 
 of these residues to mical oxidation would be strongly reduced under 
 high divalent cation concentrations ( see also ref ( 45 ) ) . in the cofilin bound cases ,
some 
 of the surface area is instead in contact with cofilin ; it is not 
 totally solvent exposed . in the cofilin 
 bound cases , some 
 of the surface area is instead in contact with cofilin ; it is not 
 totally solvent exposed . to investigate how mg modulates the conformations 
 accessed by the d - loop , we study the conformations using dpca and 
 dm ( figure 5 ) . we include 
 additional simulations of filaments with folded d - loops to expand 
 the types of structures that can be identified .
the dpca analysis 
 shows that the d - loop can adopt several distinct conformational in 
 filaments .
the d - loop conformations explored in our namba - mg simulations are predominately similar to unfolded d - loop conformations 
 observed in the standard namba and oda simulations .
our dpca and dm 
 data do show that our standard namba simulations explore some cofilin - like 
 and folded - like structures ( although none are classified as having 
 helical content by the stride algorithm ) .
( a ) first two principal components from dpca 
 analysis reveal three states , folded , unfolded and cofilin - like .
results for filament 
 with coordinated mg are restricted to a subset of unfolded 
 structures .
( c ) typical snapshots taken from the different states 
 identified in ( a ) .
all are oriented from n - term to c - term going from 
 left to right .
unfolded conformations have pc1 > 1 and 
 pc2 
 < 2 , folded conformations have pc > 2.5 , and cofilin - like structures 
 have pc1 < 1 .
( d , e ) interface between segments with and 
 without coordinated stiffness ion .
twenty snapshots for d - loop and 
 adjacent residues ( 4062 ) are shown every 2.5 ps from a representative 
 molecular dynamics trajectory .
the d - loop conformations in the ion - bound 
 system are more tightly bound to the adjacent subdomain 3 ( figure 4 ) .
the dm indicates that the addition of mg ions restricts 
 the conformations accessed to one  corner  of available 
 state space .
hence , mg occupancy restricts the entropy 
 of the d - loop conformational ensemble , as compared to the standard 
 namba filament .
the thermodynamically linked dissociation of magnesium 
 ions and subsequent d - loop disorder presumably 
 contribute to the positive entropy associated with cofilin binding .
cations increase 
 the filament bending 
 persistence length and torsional rigidity relative to the namba filaments 
 from which they have been constructed ( table 3 ) .
the namba - cation model shows a persistence 
 length increase comparable to that observed in  wet - lab  
 experiments varying divalent cation concentration .
we note that the values from ref ( 11 ) in table 3 correspond to low monovalent salt concentrations , 
 while our simulations correspond to a physiological monovalent salt 
 concentration where the filament starts out in a more rigid state , 
 and hence we would not expect as large of a fractional increase in 
 persistence length . our results do suggest that the increase in stiffness 
 from coordinating magnesium ions can occur at higher concentrations 
 of kcl than were studied in that work .
persistence 
 length and torsional 
 rigidity were computed on 10 ns sliding windows ( with a 5 ns shift ) 
 covering simulation times from 10 to 60 ns .
the values reported are 
 the average and standard deviation from the different time windows . 
 measured values from kang et al .
represent 
 the lowest persistence length observed and an extrapolation to saturating 
 divalent cation conditions in that work .
for both the namba and oda case , we predict an increase 
 in torsional 
 rigidity in addition to the increase in persistence length .
we note 
 that for the data in table 3 we compute overall filament properties in the first part 
 of our simulation to ensure that the results refer to the precise 
 state of the system that we constructed .
the increase in stiffness 
 due to addition of magnesium ions persists for the duration of the 
 simulations run ( table s4 ) .
in this work , we have built an all - atom structural model of actin 
 filaments consistent with experimental observations that suggest the 
 existence of specific cation binding modalities in filamentous actin . 
 using molecular dynamics simulations ,
we have been able to refine 
 hypotheses on which residues are likely to play an important role 
 in the specific ion binding .
the model generated in this manner is 
 stable for hundreds of nanoseconds , although it likely represents 
 only one of some number of states that the actin filament can interconvert 
 between on longer ( ms to s ) time scales .
our simulations exhibit an increase in torsional rigidity and persistence 
 length of the filament , reaching values similar to what is seen in 
 experiment and certainly reproducing the observed experimental trends .
all magnesium ions in the stiffness site remained bound stably 
 for over 200 ns of simulation , but we did observe a deviation from 
 an ideal octahedral side - chain coordination by four actin oxygen atoms . 
 while this is not altogether unusual , we can also speculate that our 
 namba filament ( as well as the original model ) has been constructed with bound adp , while the stiffness ion is 
 coordinated during initial polymerization of atp - bound monomers . having 
 a bound cation in a slightly destabilized binding geometry after atp 
 hydrolysis could be another mechanism by which actin filaments promote 
 depolymerization .
our results suggest that only a particular 
 subpopulation of d - loop 
 conformations will be accessed when filaments contain coordinated 
 divalent cations in the predicted stiffness site .
the change in the 
 conformational ensemble accessible when ion - coordinated versus when 
 bound by cofilin may partially contribute to the positive entropic 
 contributions associated with cofilin binding .
we also see restricted access to conserved d - loop residues , 
 which presumably slows cofilin binding kinetics .
we predict that at high divalent cation concentrations 
 the accessibility of the d - loop to enzymes that modify residues on 
 it ( e.g. , mical ) decreases . the existence of discrete d - loop 
 states and the fact that each 
 d - loop and polymerization site can exist in a discrete bound or unbound 
 state could be incorporated into coarse - grained models for actin filaments , 
 e.g. , through the recently developed ultracoarse - graining methodology . due to the intrinsically spatially heterogeneous way in which ion 
 binding might affect filament stiffness ,
such behavior is likely to 
 have important and interesting consequences for designing large multiscale , 
 coarse - grained simulations of actin networks .
it seems that 
 cytoskeletal networks have adopted a simple modality 
 by which adjusting ion concentration can change material properties 
 on very long ( up to micrometer ) length scales , as well as yet another 
 way to modify rates in a complex regulatory network controlling their 
 assembly and disassembly .
we also believe this structural motif to 
 be a useful guide for those who might hope to design adaptive materials 
 inspired by biological paradigms .
 ions 
 regulate the assembly and mechanical properties of actin filaments . 
 
 recent work using structural bioinformatics and site - specific mutagenesis 
 favors the existence of two discrete and specific divalent cation 
 binding sites on actin filaments , positioned in the long axis between 
 actin subunits . 
 cation binding at one site drives polymerization , 
 while the other modulates filament stiffness and plays a role in filament 
 severing by the regulatory protein , cofilin . 
 existing structural methods 
 have not been able to resolve filament - associated cations , and so 
 in this work we turn to molecular dynamics simulations to suggest 
 a candidate binding pocket geometry for each site and to elucidate 
 the mechanism by which occupancy of the  stiffness site  
 affects filament mechanical properties . incorporating a magnesium 
 ion in the  polymerization site  
 does not seem to require 
 any large - scale change to an actin subunit s conformation . 
 
 binding of a magnesium ion in the  stiffness site  adheres 
 the actin dnase - binding loop ( d - loop ) to its long - axis neighbor , which 
 increases the filament torsional stiffness and bending persistence 
 length . 
 our analysis shows that bound d - loops occupy a smaller region 
 of accessible conformational space . 
 cation occupancy buries key conserved 
 residues of the d - loop , restricting accessibility to regulatory proteins 
 and enzymes that target these amino acids . 
Introduction
Methods
Results and Discussion
Conclusions