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A publication of the Foresight Institute
Molecular mechanics software can be used to model molecular machines, and a suitable product is now available for the Macintosh computer. The following gives a brief sketch of molecular mechanics and its applicability, then reviews the program Chem3D Plus from Cambridge Scientific Computing. If you have the right computer for the job, an interest in molecular machinery, and don't already have access to modeling software, you may want to buy it.
Visit the CambridgeSoft Web site for current information about Chem 3D.
As chemists know, molecular mechanics models describe atoms as
soft, elastic spheres subject to mutual attraction and repulsion.
Bonded pairs of atoms overlap, and stretching of the bond is
described by a spring constant. Bonded triplets of atoms define
an interbond angle, and the angular degree of freedom has an
associated spring constant. A series of four bonded atoms defines
a dihedral angle, which is associated with a set of sinusoidal
potentials. Further energy terms can be added (and are, in the
more accurate models), resulting in a potential energy function
of considerable flexibility. This function relates energy to
molecular shape, thereby defining forces, accelerations,
stiffnesses, and so forth. If the potential function is good, it
describes real molecules with reasonable accuracy.
For the design of future molecular machinery, the best potential energy function in general use today is MM2, developed by Norman Allinger and colleagues (MM2 was discussed in Update No. 10 in connection with Ted Kaehler's project to develop a library of nanoscale bracket designs). It describes the structure and energy of a wide range of organic molecules with enough accuracy to be useful to chemists; since chemical equilibria are sensitive to energy differences that are negligible in many nanomechanical engineering contexts, this indicates that it gives a sufficiently accurate picture of reality for many purposes--if the user knows enough chemistry to know when MM2 is lying. Among the lies are these: bonds (described with both quadratic and cubic terms) break too easily unless a quartic bond-stretching term is added (but with it, they don't break at all). Amine nitrogen atoms cannot undergo inversion, because the pseudo-atom representing the electron lone pair stays on one side; this and other situations can trap a molecular model in an unrealistic energy minimum. MM2 does not model chemical reactions, and hence cannot describe mechanochemical processes or structural damage to devices. Bonds bend somewhat too easily,underestimating the stiffness of structures. The list goes on, but an alert user with some knowledge of chemistry will usually be able to tell what is reasonable and what is not, and the set of adequately-modeled structures is astronomical. It contains many workable devices yet to be discovered.
Cambridge Scientific Computing has implemented a graphical
molecular modeling system with an interface that enables rapid
and easy construction of three-dimensional molecular structures,
enabling control of rotation and viewing: this is Chem3D. More
recently, Cambridge Scientific has implemented an extension which
includes a version of the MM2 potential, enabling the user to
turn on simulated molecular forces and watch the molecule settle
into a minimum-energy configuration: this is Chem3D Plus.
Alternatively, the user can set a target temperature, turn on
molecular forces and dynamics, and observe the molecules in
motion. For large structures (hundreds of atoms) each step takes
many seconds, but the results can be reviewed after letting the
computer crunch by itself for as long as necessary (all speeds
here are on a Mac IIci, which includes a math coprocessor).
Chem3D Plus is powerful enough to enable the design of small
nanomechanisms, and with the caveats above, its mathematical
model is accurate enough to provide trustworthy answers to many
questions. For this purpose, it appears far superior to other
programs now available on the Macintosh.
|Figure 1. End view of a van der Waals contact bearing; note the six-fold symmetry of the inner structure (shaft) and the eleven-fold symmetry of the supporting ring. This combination results in low static friction (energy barriers less than 0.001 kT at room temperature, in the MM2/Chem 3D Plus model). ©1991 K. Eric Drexler. All rights reserved.|
Chem3D Plus 3.0 will be an impressive package even if no
improvements are made from the late beta-test version now in
hand. It adheres closely to the standard features of the
Macintosh user interface, making it easy to learn and use.
Operations including dragging and atom-type-changing can be
performed on large sets of atoms using selection rectangles and
shift-clicking. Display modes include wireframe (fast), ball and
stick (moderately fast, easy to work with), and space-filling
(slow, but offering a better representation of the final
Parts can be rotated around bonds or rotated as a whole by several convenient methods. Selected molecules can be rotated in precise 0.5 degree increments around coordinate axes or axes defined by pairs of selected atoms, and pairs and triples of atoms can be aligned with Cartesian axes or planes by menu commands. These capabilities make it possible to align components and rotate them with respect to one another--for example, to study the smoothness of the rotational potential energy function of a bearing like that in Figures 1 and 2.
|With Chem 3D Plus we can design small nanomechanisms|
Structures can be built by clicking, dragging, copying, and
pasting with a variety of options for automatic clean-up of the
resulting object. Energy minimization can be performed with a
quick and dirty potential or with MM2 itself. Selection can be
used to restrict energy minimization or dynamics to a chosen
subset of atoms; this enables the user to calculate the elastic
properties of components by moving a set of anchored atoms to
several different positions and comparing the energies of the
resulting deformed structures. The potential energy function can
be customized or extended: when needed parameters are missing
from MM2, Chem3D Plus prompts the user; it will open to the
appropriate locations in the parameter file while highlighting
the offending parts of the structure.
In addition to reporting the total energy (and its division into several MM2-defined components), the interface makes it easy to analyze the geometry of the structure. Pointing, or pointing and clicking, pops up a small window giving relevant atom types, bond types, distances, angles, and the like. A preferences window (which can generate a saved preferences file) keeps track of a huge number of options for the geometry reports, display options, and much else.
On the input and output side, files can be read from or written to many different standard formats, permitting interchange with other programs, including quantum-mechanical modeling systems such as MOPAC. Molecules can be saved or copied to the clipboard in Encapsulated Postscript form, and print as crisp ball-and-stick or intersecting-spheres images (with options for controlling atom sizes, colors, depth cuing, and so forth).
|Figure 2. Exploded view of the bearing in Figure 1. The grey ridge within the ring fits into the groove on the shaft, providing substantial stiffness against all displacements and rotations save that about the axis of the shaft. Further details will appear in a book now in preparation. ©1991 K. Eric Drexler. All rights reserved.|
In its user interface, modeling capabilities, flexibility, and
overall quality, Chem3D Plus bears comparison to packages costing
tens of thousands of dollars. Indeed, is so surprisingly good
(and has improved so much since version 2) that I am willing to
believe that its remaining warts will be removed. At the moment,
these include some bugs in support of foreign file formats, and
serious performance problems in drawing and manipulating what are
(unfortunately) precisely the sorts of structures of most
interest in a nanomechanical context: large, polycyclic molecules
with a family resemblance to bits of diamond. The program gives
special attention to ring structures at inappropriate times
(e.g., when cutting and pasting structures, and even when
selecting atoms), and that special attention can consume minutes
to hours of CPU time with no visible result beyond what a
conventional drawing program would accomplish in a fraction of a
second. It is wise to have reading material on hand. On the
positive side, Chem 3D Plus generally succeeds in performing the
specified operations, even though it was not designed and tuned
for this class of structures; these performance problems cam
clearly be fixed in future releases. Perhaps if they had more
users building these structures... (Note: This paragraph
became obsolete within 12 hours of being faxed to Cambridge
Scientific: selection operations that had taken hours are now
almost instantaneous, and the other problems are receiving
Chem3D Plus can handle several hundred to a thousand or so atoms in 3 megabytes of RAM: enough to design a variety of struts, gears, bearings, and shafts, and to calculate their mechanical properties. To do so in a reasonable time, however, will require either great patience or a Macintosh with a floating-point chip, although any machine able to support System 6.0.4 or later can run the program (warning: upgrade to 6.0.5 or later: Chem3D Plus does not presently tolerate the bugs in System 6.0.4). On a IIci, it is a rewarding tool for nanomechanical design and analysis. On machines that are slower or have less RAM it should still be, at the very least, an excellent almost-hands-on introduction to the mechanical properties of molecules as objects.
Several years ago, Roger Gregory predicted that molecular modeling on personal computers would enable widespread participation in nanomechanical design on a serious-hobby basis, years before advances in positional synthesis enable the designs to be built (Foresight Update No. 2). This design-ahead process can speed understanding of the potential of nanotechnology, and can substitute concrete detail for earlier abstract arguments. The software and hardware are available today.
Chem3D Plus is available from Cambridge Scientific Computing, 875 Massachusetts Avenue, Suite 41, Cambridge, MA 02139, 617-491-6862. The single-copy price is $895 for corporations and $595 for academic institutions. Cambridge Scientific is interested in the possibility that a new, non-institutional market may exist among Foresight members interested in molecular nanotechnology; please call the Foresight office (415-324-2490) for current information on pricing policy for Foresight members.
Visit the CambridgeSoft Web site for current information about Chem 3D.
K. Eric Drexler does exploratory molecular engineering. He is a Visiting Scholar at Stanford University's Dept. of Computer Science and serves as president of the Foresight Institute.
|Foresight Update 11 - Table of Contents|
The molecular-scale devices that evolution has made available to us form an impressive list. They include:
Here we see analogs of most basic devices upon which
industrial technology is based. A more detailed list would
include familiar items such as hinges, propellers, lids, plugs,
tubes, ratchets, etc.
It is anyone's guess whether the easiest approach to developing nanotechnology will be to design and build entirely new molecular devices, or to modify existing devices in a series of small steps by means of genetic and protein engineering. But it is certainly possible to imagine constructing molecular workshops by combining and modifying the molecular devices we have discovered but did not design. Let us keep this in mind as we look at some recent studies of several such devices.
Several kinds of motors have been found in living cells.
Dynein and kinesin are motor molecules that transport objects
within cells by hauling them along guiding fibers called
"microtubules," using adenosine triphosphate (ATP) as
an source of chemical energy. The motor molecule responsible for
muscle contraction -- myosin -- works in a similar manner by
pulling on actin fibers.
Although dynein and kinesin motors are too small to see by light microscopy, the objects they transport can be seen and photographed. In a recent study [Steven M. Block, et al., Nature 348:348-352,22Nov90--MEDLINE Abstract], researchers attached kinesin motors to silica beads, then used optical tweezers (a trap generated by a laser beam) to place the beads against a microtubule. Often the motors would attach and begin moving their load along this track. Beads having few motors moved only a short distance before coming loose, suggesting that individual motors go through cycles of attachment, movement, and detachment. During in vivo operation each load is presumably bound to the track by several motors, reducing the chance of derailment.
In another study [A. Ashkin, et al., Nature 348:346-348,22Nov90--MEDLINE Abstract], mitochondria were observed being transported by (presumed) dynein motors along microtubules inside the giant amoeba Reticulomyxa. Optical tweezers were used to halt and hold these loads momentarily; when laser power was reduced, the motors would overcome the trapping force and escape. The force generated by a single motor was determined to be 2.6x10-7 dynes.
Perhaps the most significant aspect of this work is the use of optical tweezers to manipulate single molecules by means of the larger objects to which they are attached. A similar technique might be of use in constructing a complex molecular machine. Components would be temporarily fastened to "handles" much larger than themselves; an operator using optical tweezers could then move each such unit to an assembly area where the unit would be allowed to bump its way randomly into a binding site; the handle could be removed chemically. Or perhaps optical tweezers could be used to transfer components from various storage depots to molecular motors running along tracks leading to an assembly area; the motors would haul the components into place. Such schemes involve molecular design and construction beyond current abilities, but they seem simpler than schemes requiring automation of the entire process -- parts acquisition, transport, and assembly.
A flagellar motor is considerably more complex than kinesin, dynein, or actin motors. Found in many species of bacteria, including E. coli, this motor is embedded in the cell membrane; it drives a helical filament (or "flagellum") that projects into the surrounding medium, and can be switched between clockwise and counterclockwise rotation. An excellent review article by David F. Blair [Seminars in Cell Biology, 1:75-85,1990--MEDLINE Abstract] surveys what is known about the structure, genetics and dynamics of the bacterial flagellar motor. He puts forward a low resolution model of the motor's structure and a plausible explanation of torque generation.
According to the model, the motor and its supporting structure have eight-fold symmetry and consist of somewhat more than a hundred protein molecules of about a dozen different types. The helical flagellum connects to a rod via a flexible segment at its base. The rod passes through a bushing in the outer bacterial membrane and flares out to become a rotor element embedded in the inner membrane. The outer rim of the rotor holds approximately 1000 proton acceptors -- possibly carboxyl groups. The stator, located just inside the inner membrane, consists of eight proton channels spanning the inner membrane and an eight-pointed star-shaped structure bearing a cluster of negative charges at each tip. The rotor's rim passes within half a nanometer of the charge clusters.
The energy source for the flagellar motor is a pH difference between the inside and outside of the cell. The proton (H+) density is high outside the cell and low inside. When a proton channel in the stator conducts a proton across the cell membrane, that proton is deposited in a negatively charged proton acceptor on the rotor rim, thus neutralizing the charge. The neutralized site can now move freely past the charge cluster on the stator, whereupon the proton passenger immediately jumps out into the low-H+ interior of the cell leaving the acceptor negatively charged again. The rotor has thus moved one notch ahead. The direction of movement is determined by the geometry -- if protons are deposited into sites on the clockwise side of the charge clusters then rotor will rotate counterclockwise. If the geometry changes so that the proton channel terminates on the counterclockwise side then the motor will run in reverse. Apparently there is a mechanism to accomplish this -- bacteria do reverse their motors, apparently.
Some 35 genes are required for the assembly of a normal flagellar structure; many of the them have been cloned and some have been sequenced. About half of the genes code for proteins identifiable in the motor and flagellum; the other half may be involved in assembling, installing, and controlling the structure. Some of the assembly steps have already been deduced. The tools of site-specific mutagenesis are now being brought to bear to reveal the correspondence between structure and function.
The bacterial flagellar motor has considerable appeal as a starting point for the engineering of complex molecular devices:
When chemists recreate biological polypeptides outside the
cells of origin -- either with protein synthesizers or by cloning
and expressing genes in different organisms -- they often find
that the resulting molecules don't fold properly. The reason in
many cases is that protein folding in the original organism was
being assisted by molecular "chaperones."
Chaperones are found in all living cells and in organelles such as mitochondria and plastids. They fall into several unrelated families. By definition, they are proteins that mediate the correct assembly of other polypeptides but are not components of the assembled structures. Some chaperones bind temporarily to specific regions of unfolded polypeptide chains, thereby preventing them from binding incorrectly to other parts of the chain until the latter are folded and out of reach. Others bind to already folded protein monomers, covering charges that might otherwise cause them to dimerize incorrectly. Chaperones are also involved in protein transport, DNA replication, masking of hormone receptors, and refolding of proteins damaged by heat. Some of the chaperones have been sequenced; their structure and mechanisms of action are currently being studied. A review by R. John Ellis [Science, 250:954-959,16Nov90] discusses the history and current status of chaperone research. Ellis suggests that the problem of obtaining properly folded proteins from transgenic plants might be solved by including chaperone genetic sequences along with the genes of interest.
Molecular chaperones may offer shortcuts to nanotechnology. Their role, in essence, is to enable functional proteins to be made from amino acid sequences that otherwise would fold incorrectly. This translates into far greater freedom for protein designers who, in the future, will probably design several chaperones along with a target protein.
Recent work on T4 lysozyme (an enzyme that dissolves bacterial
membranes) has shown that this molecule contains a hinge [Nature,
Abstract]. It is thought that the molecule has two
domains joined by this hinge -- like a pair of jaws. When the
jaws are open, substrates can reach the enzyme's active site; the
jaws then close, creating conditions that favor reaction of the
Work by Richard Aldrich et al. at Stanford has revealed that certain ion channels in nerve cells are opened and closed by a structure resembling a ball and chain [Science, 250:506-507, 26Oct90--MEDLINE Abstract and MEDLINE Abstract]. These ion channels, made up of protein molecules arranged around a central cavity, serve as pores connecting the inside and outside of nerve cells. By studying the consequences of altering amino acids in these proteins, Aldrich deduced that closure of the channel must be carried out by a ball formed from 19 amino acids, connected by an amino acid chain to the ion channel protein at the channel's cytoplasmic end. It remains to be seen how voltage changes cause this molecular plug to be inserted or removed.
"Inclusion compounds" consist of a molecule with a
large cavity and a small molecule confined within this cavity. A
great variety of such compounds are possible. One group with
interesting electronic properties is easily made by mixing metal
iodides with alpha-cyclodextrin in water and then drying. A
recent survey by E.A. Rietman [Mat. Res. Bull., 25:649-655,1990]
discusses the structure and properties of these compounds.
Alpha-cyclodextrin is a ring-shaped molecule that crystallizes in stacks -- like parallel stacks of donuts. When a metal iodide is present during crystallization, the iodine atoms take up residence in the channels formed by the holes, while the metal atoms occupy the spaces left between cyclodextrins in adjacent stacks. Most of these materials are poor conductors, but several can conduct in one dimension -- probably along the iodine chains. Future developments along these lines may lead to self-assembling conductors and semi-conductors with applications in molecular electronics.
As ordinary human endothelial cells grow old they become
larger and lose the ability to divide. The lifespan of such cells
is limited to about 70 cell divisions. Researchers at the
American Red Cross have now developed a short DNA chain that
appears to suppress this decline in the ability to proliferate.
[Jeanette A.M. Maier, et al., in Science 249:1570-1574,28Sep90--MEDLINE
Earlier work had shown an accumulation in aging cells of a potent inhibitor of cell division, interleukin-1-alpha. If production of this molecule could be impeded, the investigators reasoned that the cells might retain the ability to divide. An "anti-sense" DNA molecule 18 bases long was therefore designed to inhibit the synthesis in vivo of interleukin-1-alpha. When cultures of human endothelial cells were exposed daily to this DNA they retained the ability to divide for about 140 doublings, and their appearance resembled that of young cells.
Anti-sense DNA works by binding to specific sequences in messenger RNA molecules, thereby preventing these mRNAs from being translated into protein. Since all cells employ mRNA to convey information from genes to the devices that make proteins, anti-sense DNA holds promise as a molecular tool for controlling a broad range of diseases and other cellular processes. Anti-sense DNA can also bind to, and inactivate, the genes themselves; applications based on this ability are under active study in many laboratories.
Dr. Mills directs a small research company in California.
From Foresight Update 11, originally published 15 March 1991.