There are two main ways to assemble parts. In self assembly, the parts move randomly under the influence of 
thermal noise and explore the space of possible mutual orientations. If some particular arrangement is more stable, then it will be preferred. Given sufficient time, this preferred arrangement will be adopted. For example, two complementary strands of DNA in solution will eventually find each other and stick together in a double-helical configuration.
In positional assembly, some restoring force keeps the part positioned at or near a particular location, and two parts are assembled when they are deliberately moved into close proximity and linked together. While common at the scale of humans (we commonly hold, position and assemble parts with our hands) this ability is still quite novel at the molecular scale. Thermal noise still plays a significant role, as "holding" a molecular part does not provide absolute certainty about its position but instead imposes a bias on the range of positions it can adopt. Using a linear approximation, an object might be subjected to a restoring force F which is proportional to its distance from the desired location, i.e., F = ks x, where x is the distance between the part and its desired location, and ks is the restoring force.
Restoring forces on the order of 10 N/m (Newtons/meter) or better can be achieved with scanning probe microscopes, which can position an object quite accurately. The fundamental equation relating positional uncertainty, temperature and stiffness is4:
s2 = kbT/ks
Where s is the mean error in position, kb is Boltzmann's constant, T is the temperature in Kelvins, and ks is the "spring constant" of the restoring force. If ks is 10 N/m, the positional uncertainty s at room temperature is ~0.02 nm (nanometers). This is accurate enough to permit alignment of molecular parts to within a fraction of an atomic diameter. It is important to remember, however, that the actual error could be many times s. The probability that the actual error is xerr is exp[-ks xerr2/(2s2)] / (s sqrt(2p)). Errors of a few times s are common, but errors of 20 times s would be extremely unlikely.
The distinction between self assembly and positional assembly is not binary, but moves continuously along a scale depending on the positional uncertainty (which is a function of the restoring force and the temperature). When the positional uncertainty s is large, we are near the self assembly end of the spectrum. When s is small, we are at the positional assembly end of the spectrum. Intermediate points along this spectrum are occupied by, for example, a molecule "tethered" to an SPM tip by a polymer; or an object held by optical tweezers (a restoring force of 10-4 N/m implies a positional uncertainty s at room temperature of ~6 nm).
While the SPM provides programmable positional control (you can adjust x, y and z to essentially any values), a simple form of positional assembly can also be seen in enzymes which bind two substrate molecules. The two bound molecules are positioned with respect to each other, thus facilitating their assembly. A limited form of positional assembly is also used in the ribosome, which can position the end of a growing protein adjacent to the next amino acid to be incorporated into that protein5.
This combination of positional assembly and self assembly can also be seen at the macroscopic scale. The vibratory bowl feeder6 is commonly used in manufacturing to position parts with sizes on the order of a centimeter. The bowl is shaken by a motor, causing parts in the bowl to bounce onto and along a spiral track leading out of the bowl. By careful design of the track, parts in the right orientation continue to move along it, out of the bowl and into further assembly steps. Parts in the wrong orientation are bounced back into the bowl, where they can try again to move up the spiral path leading out of the bowl.
While the power of self assembly has been amply demonstrated by the wide range of complex molecular structures it has made (including a remarkable range of biological structures), we have barely begun to explore the power of positional assembly at the molecular scale. Despite this, it seems clear that this new capability will play a major role in our future ability to synthesize molecular structures. The power of positional assembly has been amply demonstrated at the macroscopic scale in today's factories and by our own ability to make things with our hands. While its application at the molecular scale will differ in many details, it will provide a new and remarkably powerful tool for extending the range of structures that we can make.
thermal noise and explore the space of possible mutual orientations. If some particular arrangement is more stable, then it will be preferred. Given sufficient time, this preferred arrangement will be adopted. For example, two complementary strands of DNA in solution will eventually find each other and stick together in a double-helical configuration.In positional assembly, some restoring force keeps the part positioned at or near a particular location, and two parts are assembled when they are deliberately moved into close proximity and linked together. While common at the scale of humans (we commonly hold, position and assemble parts with our hands) this ability is still quite novel at the molecular scale. Thermal noise still plays a significant role, as "holding" a molecular part does not provide absolute certainty about its position but instead imposes a bias on the range of positions it can adopt. Using a linear approximation, an object might be subjected to a restoring force F which is proportional to its distance from the desired location, i.e., F = ks x, where x is the distance between the part and its desired location, and ks is the restoring force.
Restoring forces on the order of 10 N/m (Newtons/meter) or better can be achieved with scanning probe microscopes, which can position an object quite accurately. The fundamental equation relating positional uncertainty, temperature and stiffness is4:
s2 = kbT/ks
Where s is the mean error in position, kb is Boltzmann's constant, T is the temperature in Kelvins, and ks is the "spring constant" of the restoring force. If ks is 10 N/m, the positional uncertainty s at room temperature is ~0.02 nm (nanometers). This is accurate enough to permit alignment of molecular parts to within a fraction of an atomic diameter. It is important to remember, however, that the actual error could be many times s. The probability that the actual error is xerr is exp[-ks xerr2/(2s2)] / (s sqrt(2p)). Errors of a few times s are common, but errors of 20 times s would be extremely unlikely.
The distinction between self assembly and positional assembly is not binary, but moves continuously along a scale depending on the positional uncertainty (which is a function of the restoring force and the temperature). When the positional uncertainty s is large, we are near the self assembly end of the spectrum. When s is small, we are at the positional assembly end of the spectrum. Intermediate points along this spectrum are occupied by, for example, a molecule "tethered" to an SPM tip by a polymer; or an object held by optical tweezers (a restoring force of 10-4 N/m implies a positional uncertainty s at room temperature of ~6 nm).
While the SPM provides programmable positional control (you can adjust x, y and z to essentially any values), a simple form of positional assembly can also be seen in enzymes which bind two substrate molecules. The two bound molecules are positioned with respect to each other, thus facilitating their assembly. A limited form of positional assembly is also used in the ribosome, which can position the end of a growing protein adjacent to the next amino acid to be incorporated into that protein5.
This combination of positional assembly and self assembly can also be seen at the macroscopic scale. The vibratory bowl feeder6 is commonly used in manufacturing to position parts with sizes on the order of a centimeter. The bowl is shaken by a motor, causing parts in the bowl to bounce onto and along a spiral track leading out of the bowl. By careful design of the track, parts in the right orientation continue to move along it, out of the bowl and into further assembly steps. Parts in the wrong orientation are bounced back into the bowl, where they can try again to move up the spiral path leading out of the bowl.
While the power of self assembly has been amply demonstrated by the wide range of complex molecular structures it has made (including a remarkable range of biological structures), we have barely begun to explore the power of positional assembly at the molecular scale. Despite this, it seems clear that this new capability will play a major role in our future ability to synthesize molecular structures. The power of positional assembly has been amply demonstrated at the macroscopic scale in today's factories and by our own ability to make things with our hands. While its application at the molecular scale will differ in many details, it will provide a new and remarkably powerful tool for extending the range of structures that we can make.