molecular machines

COSTBI-1066; NO. OF PAGES 6

Molecular machinesRon Elber1,2 and Serdal Kirmizialtin2

Available online at www.sciencedirect.com

Molecular machines (MM) are essential components of living

cells. They conduct mechanical work, transport materials into

and out of cells, assist in processing enzymatic reactions, and

more. Their operations are frequently combined with significant

conformational transitions. Computational studies of these

conformational transitions and their coupling to molecular

functions are discussed. It is argued that coarse descriptions of

these molecules which are based on mass density and shape

provide useful information on directions of action. It is further

argued that MM are likely to have well focused and narrow

reaction pathways. The proposal for such pathways is

supported by evolutionary analyses of homologous machines.

Finally, these observations are used to build atomically detailed

models of these systems that are making the link from structure

to functions (kinetics and thermodynamics). For that purpose

enhanced sampling techniques are required.

Addresses1 Department of Chemistry and Biochemistry, University of Texas at

Austin, 105 East 24th St., Stop A5300 Austin, TX 78712-0165, USA2 Institute for Computational Engineering and Sciences, University of

Texas at Austin, 201 East 24th St., Austin, TX 78712-1229, USA

Corresponding authors: Elber, Ron ([email protected]) and

Kirmizialtin, Serdal ([email protected])

Current Opinion in Structural Biology 2012, 23:xx–yy

This review comes from a themed issue on Theory and Simulation

Edited by Jeffrey Skolnick and Richard Friesner

0959-440X/$ – see front matter, # 2012 Elsevier Ltd. All rights

reserved.

http://dx.doi.org/10.1016/j.sbi.2012.12.002

IntroductionWe define molecular machines (MM) as molecules that

change their shapes, or have a significant moving part that

is doing work during function. The changes to shape must

be reversible. A complete cycle of the conformational

transition and a return to the initial state is expected. The

motions associated with machine functions can be driven

by an energy source (like ATP) or released upon binding

and processing of a ligand. MM are typically proteins,

though more ‘machine-like’ functions are discovered

periodically for RNA. They participate in catalyzing

essential biochemical reactions, in converting bio-

chemical energy to mechanical work, in transportation

of cargo and small essential molecules, in signaling differ-

ent states of the environment to cells, and in numerous

other functions.

Please cite this article in press as: Elber R, Kirmizialtin S. Molecular machines, Curr Opin Stru

www.sciencedirect.com

The present opinion considers computational modeling

of MM. Computer simulations of biophysical processes

and computational studies in structural bioinformatics

make it possible to investigate in atomic detail the

operation of MM. Before setting up concrete goals to

the present opinion, it is important to emphasize the

challenges, in modeling MM:

� Hierarchy of spatial scales requires multiscale

modeling of initiation events and of large-scale

motions.

� The time scales of machine operations extend to

milliseconds and seconds, far too long for straightfor-

ward molecular dynamics simulations.

� The translation of biochemical energy to mechanical

energy is still poorly understood.

What kind of questions can we effectively address com-

putationally and how can these theoretical predictions be

tested? While there are many approaches to address these

challenges in the present opinion we have chosen to

consider the subset below

(1) We seek a simple picture of the large-scale motions of

MM. Are there a small number of characteristic

modes that capture most of the motions of MM? How

can we subject to experimental tests the predictions

of essential modes?

(2) What do we know, and what remains to be learnt on

the ‘ignition’ of MM?

(3) Can we quantitatively link between the structural

changes and MM function, that is, can we make the

connection between conformational transitions and

the thermodynamics and kinetics of the operation of

the machines?

The pathways and collective modes ofmolecular machinesIn a typical study of MM we are given experimental

structures at the beginning and at the end of the

operation. The two end structures are long-lived and

are therefore accessible to measurement by many

experimental techniques. The transient conformations

between the stable states are short-lived and are more

difficult to capture and quantify experimentally. While

transient conformations can be stabilized by clever use

of biochemical manipulation such as the replacement of

a metal in heme [1], or by rapid techniques [2], the

measurements are, in general, of a lower quality than

measurements conducted on the end points. We have

ct Biol (2013), http://dx.doi.org/10.1016/j.sbi.2012.12.002

Current Opinion in Structural Biology 2013, 23:1–6


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2 Theory and Simulation


chosen the above examples from the classical machine

of hemoglobin. The limited experimental information

on transient structures motivates the use of simulations

and structural bioinformatic analysis.

It is useful to consider a widely different set of models

in exploration of pathways and to seek a consensus

between different approaches to modeling. We differ-

entiate between approaches that retain atomically

detailed description and approaches that use coarse-

grained models. Of course there are also intermediate

approaches that keep most critical atoms in place.

An obvious example is the coarse graining of solvent

by continuum modeling. In a typical coarse graining

model the solvent influences the process only

indirectly, through an effective potential, and a single

or a reduced number of particles represent an amino

acid.

In one of the popular and coarser approaches to inves-

tigate MM the sought-after modes are searched for in the

shapes and mass densities of these macromolecules. An

argument is made that the directions of conformational

changes of MM are imprinted in their experimentally

determined coarse folds. The theory of small displace-

ments in the neighborhood of fixed solid shapes (with a

given mass density and internal resistance to change) is

the theory of elasticity. For example with elasticity

theory we can predict that a rod is more likely to bend

than to stretch. This result remains unchanged if the rod

is made of wood or metal. Similarly, the ‘material’ of

which proteins are made is assumed not important to

establish the direction of soft vibrational modes. If the

argument is valid then the dynamics of MM can be

calculated from continuous protein shapes, regardless

of the sequences of the proteins and their biochemical

properties.

Analysis of objects with complex forms using continuum

mechanics is far from trivial. The use of particle

mechanics is simpler. It is therefore convenient to step

back from the continuum picture and approximate the

mass density by a sample of discrete point masses. The

point masses are spread over the volume of the object,

and connected by springs to represent the internal

elasticity parameters such as Young modulus [3]. This

boils down to elastic network models that gained con-

siderable popularity in the last decade for diverse appli-

cations (see for instance [4,5]). The theory is restricted

to vibrations with length scales larger than the size of

individual amino acids and to small displacements in the

neighborhood of the reference structure. The elastic

network can be analyzed with the tools of normal

modes, identifying the least costly (in terms of elastic

energy) modes of motion. Such analysis suggests that

the T state in hemoglobin is broader than the R

state [6].



A challenge for studying conformational transitions by

elastic networks is that the network provides small-dis-

placement descriptions of the system in the neighbor-

hood of a single stable structure. Transformations of MM

require at a minimum two stable states. Maragakis and

Karplus put forward a clever idea to interpolate between

two stable conformations [7] using the empirical valence

bond theory [8]. Others used the same interpolation

scheme [9]. Tekpinar and Zheng [10�] recently followed

the same general idea of network interpolation with an

alternative scheme to connect the two stable states.

Despite the elegant solution to interpolation between

states there remains the problem of comparison to exper-

imental data. What can be computed from pathways of

MM that are based on elastic network and be compared to

experiment? An interesting suggestion was to examine

the consistency of structures of homologous proteins with

conformations generated by low energy displacements

predicted by elastic network models. The observed cor-

relation is surprisingly good. Hence, structures of hom-

ologous proteins that are ‘displaced’ by evolutionary

forces were found to be similar to computational struc-

tures generated along a pathway connecting two protein

stable states and displaced mechanically along low energy

modes. Elber and Karplus [11] pointed out the connec-

tion between short-time functional dynamics of a single

protein (myoglobin) and evolutionary changes of proteins

that belong to the same family. A similar phenomenon for

pathways of MM is illustrated here using elastic networks

[12]. Particularly interesting is the small number of modes

or coarse variables that capture the evolutionary displace-

ments. We can push this observation further and argue

that the elastic networks are unusually stable with respect

to point mutation by design and by virtue of their

extended length scale. Their large scale adds significantly

to their overall stability in sequence space. An interesting

review on ‘robust normal modes’ was published by Zheng

et al. [13].

Models with a bias to the native foldNevertheless, despite the successes of elastic networks

more work remains to be done to understand the oper-

ations of MM. For example, the impact of point mutations

and the resulting variations in the machine operation are

of significant interest, even if the overall contributing

modes remain the same. At the least these variations are

accessible to experimental verification. Alternative

coarse-grained approaches are available that retain more

information on the biochemical specifics of the machine.

Analysis of frustration and sequence dependence of allo-

steric proteins illustrate that large-scale motions are sup-

ported evolutionary [14�]. Another approach, the Go

model, uses a similar concept to the elastic network model

in which the stable end structures dictated the dynamics

and the reaction coordinate of the MM. However, it is

doing so while retaining atomic and residue specific




Molecular machines Elber and Kirmizialtin 3


Figure 1

Current Opinion in Structural Biology

Structural changes in HIV reverse transcriptase. Note the significant

changes in the (charged) side chain position during the transition while

the overall displacement of the backbone remains small. The snap shots

are taken along a minimum free energy path that was also used for

Milestoning calculations. In black we show the substrate, in multiple

colors and shade levels we show the lysine displacements along the

minimum free energy path illustrating the closing up on the nucleotide.

We show backbone and secondary structure displacements by

modifying sequentially darker blue to light blue. In green and yellow we

plotted the DNA.

features. The assumption is that contacts and inter-

actions in the native folds are, by design, more favorable

than other contacts. Since many interactions in biology

are subtle and are difficult to produce from first prin-

ciples, building in these interactions as part of the model

can overcome the inaccuracies inherent to calculations of

energy and forces based on a general and transferrable set

of interaction parameters. An interesting application of

such a coarse graining approach was discussed in [15�].Consider a classical molecular machine like kinesin.

Kinesin walks on cytoskeletal filaments in a particular

(plus-end) direction, carrying cargo, and is one of the

most fascinating molecular motors in nature. Structural

rearrangements in the highly similar Ncd motors reverse

the direction of the walk. Biman et al. [15�] used a Go

model for this system and were able to account for the

reversal of motion in Ncd motor. They proposed a

mechanism to explain the phenomenon based on re-

arrangement of structural elements of the motor. The

Go model has numerous successes in studies of protein

folding [16] and of protein assembly [17]. Here it

branches to another field of structural biology in which

we assume that flexibility (in addition to shape, which is

the original assumption of the Go model) is imprinted in

the native fold.

Another type of coarse graining approach that was effec-

tively applied to MM in general and to kinesin in

particular is the SOP model of Zhang and Thirumalai

[18�]. The SOP model has a single interaction site per

amino acid and was used in a variety of problems in-

cluding the study of GroEl [19] and ATP-induced

detachment of myosin V from actin [20]. Brownian

dynamics is used to model the conformational changes.

Calibrating the parameters for Brownian dynamics allows

for computations of time scales that are in remarkable

agreement with experiment. ATP binding to kinesin is

modeled by modifying the interaction between the neck-

linker and the motor head and a detailed three-step

mechanism that involves the neck linker and the motor

head is proposed [18�].

The modeling of ATP impact on kinesin brings us to

‘initiation’ of molecular motors. A molecular motor is not

always active, and it needs to be ‘fed’ biological energy

(ATP) or receive a signal to start operating. To further

illustrate the diversity of MM we consider another type of

molecule, an enzyme, in which binding of a substrate

motivates a structural change preparing the ligand for

processing [21]. In this case the machine does not require

an injection of energy but facilitates instead a potentially

spontaneous chemical reaction. The protein HIV reverse

transcriptase (HIV RT) synthesizes DNA according to a

RNA template. It accepts a nucleotide and adds it to a

DNA if it matches. Hence, the role of this MM is not

to provide the extra push for an uphill process but rather

to select the correct substrate. The conformational



transition is significant but is not as large as one finds

in motors (Figure 1). The backbone motions are particu-

larly small. Modeling based on large spatial scales is not

appropriate for this case in which the emphasis is on

fitness of a relatively small substrate. Atomically detailed

simulations are necessary.

Atomically detailed simulationsThe challenge of conducting atomically detailed simu-

lations of MM is of time scales. The time scale of the

conformational transitions of MM (even if spatially

restricted) is in microseconds and milliseconds far longer

than the time scale accessible to straightforward Molecu-

lar Dynamics (MD) simulations in a typical laboratory.

We should keep in mind that for the calculations of

kinetics an ensemble (hundreds) of trajectories or transi-

tional events is needed which is a significant addition to

the calculation cost. Enhanced sampling techniques are

required to study these processes that are able to interp-

olate between the two well-defined end states. This

requirement means (for example) that replica exchange

simulations are not appropriate. High temperature runs of

some of the replicas are likely to distort or unfold the

intermediate structures. It will be hard and computation-

ally expensive to refold transient unfolded conformations.

Metadynamics [22] and TAMD [23] that focus on






Figure 2

i-1 i+1

Reaction coordinate

i


A schematic view of Milestoning along a one-dimensional reaction

coordinate. The reaction coordinate is precomputed, typically by

functional optimization, and the milestones are defined as the interfaces

orthogonal to the reaction coordinate. The three interfaces are at

milestones i, i + 1, and i � 1. In the figure trajectory fragments are

initiated at interface i in the forward (green) and backward direction. An

ensemble of such trajectories provides the transition probability from i to

i + 1. From the probabilities of transitions between the interfaces and

their termination times, a stochastic kinetic model is constructed and

solved [36,37]. The model gives the thermodynamic and kinetic

properties of the system.

Figure 3

0 10 20 30 40Reaction Coordinate

50 60 70 800

5

10

15

20

25

30

Free

Ene

rgy

(kca

l/mol

)


Free energy profiles for binding a substrate to HIV RT. The solid line

follows the binding curve for a corrected nucleotide while the dashed

line shows the binding free energy for an incorrect nucleotide. The

significant free energy change is coupled to the conformational transition

and to the fitness of the protein with the substrate. The reaction

coordinate is parameterized by the structure index along the path.

Profiles were computed in Ref. [30�].

enhanced sampling of a subset of variables are more likely

to provide useful information on the mechanism of the

process. Indeed, investigations by TAMD of confor-

mational transitions of MM have been reported in which

the free energy landscape of several coarse variables is

sampled [24]. Given the concrete and well-focused direc-

tion of machine motions, it is likely that a low dimensional

description of machine operation is valid. Such a focus is

illustrated not only at the elastic network or SOP levels

but also at the atomic level. At the extreme we argue that

the reaction follows a reasonably narrow tube in confor-

mation space that includes a large fraction of the transi-

tional trajectories. If this picture holds it is plausible that

the reaction path approach that defines an optimal tube

for the process will be effective. Reaction path calcu-

lations for complex biomolecular systems have been

around for a while [25] mostly based on global path

and functional optimization. These methods recently

gained in popularity following the development of the

string method [26]. The string method enables the deter-

mination of minimum free energy pathways in the space of

coarse variables. In free energy it is based on a clever

extension to a minimum energy path algorithm [27].

Calculations of minimum energy/free energy pathways

with global pathway methods were conducted for the MM

myosin II [28], myosin VI [29�], and more recently in the

study of selectivity of HIV reverse transcriptase (HIV

RT) [30�]. Other approaches determine approximate

trajectories and were applied to interesting systems, for

example, accelerated MD (aMD) [31,32] and targeted

MD [33–35].

The calculation of minimum energy or free energy paths

as a set of coordinate vectors along the reaction coordinate

provides valuable information on mechanisms and order

of events. However, they do not make quantitative links

to measurements of functions, for example, the determi-

nation of the rate of DNA production by HIV RT and the

thermodynamic bias toward the products. A compu-

tational approach that provides both the kinetics and

thermodynamics along a predetermined pathway or a

reduced reaction space is Milestoning [36,37]. While

the use of other approaches to estimate the free energy

profile such as umbrella sampling [38] is possible, Mile-

stoning and related technologies such as PPTIS [39] and

forward flux [40] are unique by allowing direct calcu-

lations of kinetics and thermodynamics. It is based on

partitioning the phase space using interfaces or mile-

stones and computing the fluxes through the interfaces

separating cells (Figure 2). It is particularly efficient in

calculations along a one-dimensional reaction coordinate.

Indeed in the studies of MM (Scapharca hemoglobin,

Myosin II, and HIV RT) Speed up of the simulations by

factors of thousands to millions was observed compared to

straightforward MD [28,30�,41]. Milestoning uses high

dimensional interfaces (milestones) to capture local

kinetics. The interfaces are spread and orthonormal to

Please cite this article in press as: Elber R, Kirmizialtin S. Molecular machines, Curr Opin Struct Biol (2013), http://dx.doi.org/10.1016/j.sbi.2012.12.002

Current Opinion in Structural Biology 2013, 23:1–6 www.sciencedirect.com


https://www.researchgate.net/publication/51058602_Revisiting_and_Computing_Reaction_Coordinates_with_Directional_Milestoning?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx


https://www.researchgate.net/publication/221772831_The_Conformational_Transition_Pathways_of_ATP-Binding_Cassette_Transporter_BtuCD_Revealed_by_Targeted_Molecular_Dynamics_Simulation?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx

https://www.researchgate.net/publication/51454439_Forward_Flux_Sampling_for_rare_event_simulations?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx

https://www.researchgate.net/publication/222612701_Free-energy_of_spheres_with_dipoles-Monte-Carlo_with_multistage_sampling?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx

https://www.researchgate.net/publication/8440150_Rate_Constants_for_Diffusive_Processes_by_Partial_Path_Sampling?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx

https://www.researchgate.net/publication/51636703_The_active-inactive_transition_of_human_thymidylate_synthase_Targeted_molecular_dynamics_simulations?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx

https://www.researchgate.net/publication/41426564_The_Mechanism_of_the_Translocation_Step_in_DNA_Replication_by_DNA_Polymerase_I_A_Computer_Simulation_Analysis?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx

https://www.researchgate.net/publication/8441702_Computing_Time_Scales_from_Reaction_Coordinates_by_Milestoning?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx


https://www.researchgate.net/publication/224918035_Multi-Timescale_Conformational_Dynamics_of_the_SH3_Domain_of_CD2-Associated_Protein_using_NMR_Spectroscopy_and_Accelerated_Molecular_Dynamics?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx

Molecular machines Elber and Kirmizialtin 5


a reaction coordinate and information about local kinetics

is accumulated to obtain the overall rate and free energy

landscape. This algorithm is profoundly more efficient

than straightforward MD without giving up atomically

detailed picture. Typical speed-ups are in factors of

millions and more, primarily due to enhanced probability

of observing activated events [42].

In Figure 3 we show free energy profiles for a confor-

mational transition in HIV RT. The solid curve describes

the free energy for the binding of the correct nucleotide

and the dashed curve is for the incorrect substrate. It is an

interesting illustration for a conformational transition of a

‘machine’ which is ‘fitted’ to select the correct substrate

[30�].

ConclusionsBiological MM operate at unprecedented precision and

efficiency. The design by evolution of these molecules

seems to select structural and dynamical features. Per-

haps not surprisingly from efficiency consideration, evol-

ution selected a small subspace of coarse variables to span

the reaction space of the MM. A broad range of tech-

niques can study these coarse modes. The simplest

approach is the elastic network model. It provides an

exact solution to a simple linear model of the system

elasticity. Less coarse approaches provide more detailed

biochemical pictures. For example a Go model and the

principle of minimal frustration enable the study of motor

directionality and specific large-scale modes. The use of

the coarse-grained SOP energy allows the investigation of

relevant time scales and the overall effect of ATP bind-

ing. To connect the reduced subspace with function,

atomically detailed simulations proved useful. The com-

bination of minimum free energy path calculations with

Milestoning allows the determination of relative stability

of reactant and products and of kinetics. It is illustrated

that conformational change is made to match the correct

substrate and an ‘induced-fit’ mechanism has an import-

ant contribution to machine specificity.

Finally we comment about a future direction. We specu-

late that modeling MM will include merging of different

technologies. A single multiscale scheme that uses coarse

grained modeling to search for plausible reaction path-

ways will be combined with atomically detailed simu-

lations to estimate functional parameters.

References and recommended readingPapers of particular interest, published within the period of review,have been highlighted as:

� of special interest

�� of outstanding interest

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Li WF, Wolynes PG, Takada S: Frustration, specific sequencedependence, and nonlinearity in large-amplitude fluctuationsof allosteric proteins. Proc Natl Acad Sci USA 2011,108:3504-3509.

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Zhang ZC, Thirumalai D: Dissecting the kinematics of thekinesin step. Structure 2012, 20:628-640.



http://dx.doi.org/10.1002/prot.24180

http://dx.doi.org/10.1002/prot.24180


https://www.researchgate.net/publication/237053095_Extending_molecular_dynamics_timescales_with_milestoning_Example_of_complex_kinetics_in_a_solvated_peptide?el=1_x_8&enrichId=rgreq-a5a6887ad7994f1e5b60f81303e156a6-XXX&enrichSource=Y292ZXJQYWdlOzIzNDEwMzk5MDtBUzo5ODkzNzkxNDUyNzc1OEAxNDAwNjAwMDQ1NzAx



A coarse grained (SOP) investigation of kinesin in which the ‘walking’mechanism is simulated, the ATP effect is modeled by variation inbonding energy, and the correct kinetic is obtained.

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Ovchinnikov V, Karplus M, Vanden-Eijnden E: Free energy ofconformational transition paths in biomolecules: the stringmethod and its application to myosin VI. J Chem Phys 2011:134.

An impressive application of the string approach to compute free energypathways for the motor Myosin VI. Atomically detailed simulations areused.

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An application of the string method to compute free energy pathway andof the milestoning approach to compute kinetics to investigate theselection mechanism of the correct nucleotide in HIV RT. It is shownthat the conformational transition plays a crucial role in the selectionprocess of the correct nucleotide.

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