Synthetic molecular machines for active self-assembly : prototype algorithms, designs, and experimental study

Computer science and electrical engineering have been the great success story of the twentieth century. The neat modularity and mapping of a language onto circuits has led to robots on Mars, desktop computers and smartphones. But these devices are not yet able to do some of the things that life takes for granted: repair a scratch, reproduce, regenerate, or grow exponentially fast–all while remaining functional.

This thesis explores and develops algorithms, molecular implementations, and theoretical proofs in the context of “active self-assembly” of molecular systems. The long-term vision of active self-assembly is the theoretical and physical implementation of materials that are composed of reconfigurable units with the programmability and adaptability of biology’s numerous molecular machines. En route to this goal, we must first find a way to overcome the memory limitations of molecular systems, and to discover the limits of complexity that can be achieved with individual molecules.

One of the main thrusts in molecular programming is to use computer science as a tool for figuring out what can be achieved. While molecular systems that are Turing-complete have been demonstrated [Winfree, 1996], these systems still cannot achieve some of the feats biology has achieved.

One might think that because a system is Turing-complete, capable of computing “anything,” that it can do any arbitrary task. But while it can simulate any digital computational problem, there are many behaviors that are not “computations” in a classical sense, and cannot be directly implemented. Examples include exponential growth and molecular motion relative to a surface.

Passive self-assembly systems cannot implement these behaviors because (a) molecular motion relative to a surface requires a source of fuel that is external to the system, and (b) passive systems are too slow to assemble exponentially-fast-growing structures. We call these behaviors “energetically incomplete” programmable behaviors. This class of behaviors includes any behavior where a passive physical system simply does not have enough physical energy to perform the specified tasks in the requisite amount of time.

As we will demonstrate and prove, a sufficiently expressive implementation of an “active” molecular self-assembly approach can achieve these behaviors. Using an external source of fuel solves part of the the problem, so the system is not “energetically incomplete.” But the programmable system also needs to have sufficient expressive power to achieve the specified behaviors. Perhaps surprisingly, some of these systems do not even require Turing completeness to be sufficiently expressive.

Building on a large variety of work by other scientists in the fields of DNA nanotechnology, chemistry and reconfigurable robotics, this thesis introduces several research contributions in the context of active self-assembly.

We show that simple primitives such as insertion and deletion are able to generate complex and interesting results such as the growth of a linear polymer in logarithmic time and the ability of a linear polymer to treadmill. To this end we developed a formal model for active-self assembly that is directly implementable with DNA molecules. We show that this model is computationally equivalent to a machine capable of producing strings that are stronger than regular languages and, at most, as strong as context-free grammars. This is a great advance in the theory of active self- assembly as prior models were either entirely theoretical or only implementable in the context of macro-scale robotics.

We developed a chain reaction method for the autonomous exponential growth of a linear DNA polymer. Our method is based on the insertion of molecules into the assembly, which generates two new insertion sites for every initial one employed. The building of a line in logarithmic time is a first step toward building a shape in logarithmic time. We demonstrate the first construction of a synthetic linear polymer that grows exponentially fast via insertion. We show that monomer molecules are converted into the polymer in logarithmic time via spectrofluorimetry and gel electrophoresis experiments. We also demonstrate the division of these polymers via the addition of a single DNA complex that competes with the insertion mechanism. This shows the growth of a population of polymers in logarithmic time. We characterize the DNA insertion mechanism that we utilize in Chapter 4. We experimentally demonstrate that we can control the kinetics of this re- action over at least seven orders of magnitude, by programming the sequences of DNA that initiate the reaction.

In addition, we review co-authored work on programming molecular robots using prescriptive landscapes of DNA origami; this was the first microscopic demonstration of programming a molec- ular robot to walk on a 2-dimensional surface. We developed a snapshot method for imaging these random walking molecular robots and a CAPTCHA-like analysis method for difficult-to-interpret imaging data.

An experimental study of the mobility of edge dislocations in pure copper single crystals

The velocity of selectively-introduced edge dislocations in 99.999 percent pure copper crystals has been measured as a function of stress at temperatures from 66°K to 373°K by means of a torsion technique. The range of resolved shear stress was 0 to 15 megadynes/ cm^2 for seven temperatures (66°K, 74°K, 83°K, 123°K, 173°K, 296°K, 296°K, 373°K.

Dislocation mobility is characterized by two distinct features; (a) relatively high velocity at low stress (maximum velocities of about 9000 em/sec were realized at low temperatures), and (b) increasing velocity with decreasing temperature at constant stress.

The relation between dislocation velocity and resolved shear stress is:

v = v_o(τ_r/τ_o)^n

where v is the dislocation velocity at resolved shear stress τ_r, v_o is a constant velocity chosen equal to 2000 cm/ sec, τ_o is the resolved shear stress required to maintain velocity v_o, and n is the mobility coefficient. The experimental results indicate that τ_o decreases from 16.3 x 10^6 to 3.3 x 10^6 dynes/cm^2 and n increases from about 0.9 to 1.1 as the temperature is lowered from 296°K to 66°K.

The experimental dislocation behavior is consistent with an interpretation on the basis of phonon drag. However, the complete temperature dependence of dislocation mobility could not be closely approximated by the predictions of one or a combination of mechanisms.

Experimental study of the upper hybrid echo in plasmas

The two-pulse stimulated radiation of dense (10^9/cm^3 < ne ≤ 10^(11) /cm^3) nonuniform neon and argon afterglow plasma columns longitudinally immersed in a magnetic field is studied. The magnetic field is very homogeneous over the plasma volume (∆B/B~.01%). If the S-band microwave pulses' center frequency is such that they resonantly excite a narrow band of plasma upper hybrid oscillations close to the maximum upper hybrid frequency of the column, strong two pulse echoes are observed. This new echo process is called the upper hybrid echo. The echo spectrum, echo power and echo width were studied as a function of the pulse peak power P, pulse separation τ, relative density (ω_(po)/ω)^2, and relative cyclotron frequency (ω_c/ω). The complex but systematic variations of the echo properties as a function of the above-mentioned parameters arc found to be in qualitative agreement with those predicted by a theory of Gould and Blum based upon a simple nonuniform unidimensional cold plasma slab model. The possible effects of electron neutral and electron ion collisions not retained in the theoretical model are discussed.

The existence of a new type of cyclotron echo, different from that of Hill and Kaplan and not predicted by the Blum and Gould model is documented. It is believed to be also of a collective effect nature and can probably be described in terms of a theory retaining some hot plasma effects.

Experimental study on inertial effects in liquid-solid flows

This thesis presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Reynolds (defined by the shear rate and particle diameter) and Stokes numbers, ranging from 3 ≤ Re ≤ 1.6 × 10³ and 0.4 ≤ St ≤ 195. The experiments use a specifically designed Couette cylindrical rheometer that allows for probing the transition from transporting a pure liquid to transporting a dense suspension of particles. Measurements of the shear stress are presented for a wide range of particle concentration (10 to 60% in volume) and for particle to fluid density ratio between 1 and 1.05. The effective relative viscosity exhibits a strong dependence on the solid fraction for all density ratios tested. For density ratio of 1 the effective viscosity increases with Stokes number (St) for volume fractions (φ) lower than 40% and becomes constant for higher φ. When the particles are denser than the liquid, the effective viscosity shows a stronger dependance on St. An analysis of the particle resuspension for the case with a density ratio of 1.05 is presented and used to predict the local volume fraction where the shear stress measurements take place. When the local volume fraction is considered, the effective viscosity for settling and no settling particles is consistent, indicating that the effective viscosity is independent of differences in density between the solid and liquid phase. Shear stress measurements of pure fluids (no particles) were performed using the same rheometer, and a deviation from laminar behavior is observed for gap Reynolds numbers above 4× 10³, indicating the presence of hydrodynamic instabilities associated with the rotation of the outer cylinder. The increase on the effective viscosity with Stokes numbers observed for mixtures with φ ≤ 30% appears to be affected by such hydrodynamic instabilities. The effective viscosity for the current experiments is considerably higher than the one reported in non-inertial suspensions.

Mass transfer from a cylinder to an air stream in axisymmetrical flow (an experimental study)

Mass transfer from wetted surfaces on one-inch cylinders with unwetted approach sections was studied experimentally by means of the evaporation of n-octane and n-heptane into an air stream in axisymmetrical flow, for Reynolds numbers from 5,000 to 310,000. A transition from the laminar to the turbulent boundary layer was observed to occur at Reynolds numbers from 10,000 to 15,000. The results were expressed in terms of the Sherwood number as a function of the Reynolds number, the Schmidt number, and the ratio of the unwetted approach length to the total length. Empirical formulas were obtained for both laminar and turbulent regimes. The rates of mass transfer obtained were higher than theoretical and experimental results obtained by previous investigators for mass and heat transfer from flat plates.

An experimental study of a stellar neutron source: ^(13)C(α, n)^(16)O

Described in this thesis are measurements made of the thick-target neutron yield from the reaction ¹³C(α, n)¹⁶O. The yield was determined for laboratory bombarding energies between 0.475 and 0.700 MeV, using a stilbene crystal neutron detector and pulse-shape discrimination to eliminate gamma rays. Stellar temperatures between 2.5 and 4.5 x 10^{8 o}K are involved in this energy region. From the neutron yield was extracted the astrophysical cross-section factor S(E), which was found to fit a linear function: S(E) = [(5.48 ± 1.77) + (12.05 ± 3.91)E] x 10⁵ MeV-barns, center-of-mass system. The stellar rate of the ¹³C(α, n)¹⁶O reaction if calculated, and discussed with reference to helium burning and neutron production in the core of a giant star.

Results are also presented of measurements carried out on the reaction ⁹Be(α, n)¹²C, taken with a thin Be target. The bombarding energy-range covered was from 0.340 to 0.680 MeV, with excitation curves for the ground- and first excited-state neutrons being reported. Some angular distributions were also measured. Resonances were found at bombarding energies of E_LAB = 0.520 MeV (E_CM = 0.360 MeV, Γ ~ 55 keV CM, ωγ = 3.79 eV CM) and E_LAB = 0.600 MeV (E_CM = 0.415 MeV, Γ ˂ 4 keV CM, ωγ = 0.88 eV CM). The astrophysical rate of the ⁹Be(α, n)¹²C reaction due to these resonances is calculated.

Experimental study study of antiproton-proton annihilation into a pair of charged Pi-Mesons or K-Mesons for incident antiproton mementa in the range from 0.72 GeV/c to 2.62 GeV/c

The cross sections for the two antiproton-proton annihilation-in-flight modes,

ˉp + p → π⁺ + π^-

ˉp + p → k⁺ + k^-

were measured for fifteen laboratory antiproton beam momenta ranging from 0.72 to 2.62 GeV/c. No magnets were used to determine the charges in the final state. As a result, the angular distributions were obtained in the form [dσ/dΩ (Θ_C.M.) + dσ/dΩ (π – Θ_C.M.)] for 45 ≲ Θ_C.M. ≲ 135°.

A hodoscope-counter system was used to discriminate against events with final states having more than two particles and antiproton-proton elastic scattering events. One spark chamber was used to record the track of each of the two charged final particles. A total of about 40,000 pictures were taken. The events were analyzed by measuring the laboratory angle of the track in each chamber. The value of the square of the mass of the final particles was calculated for each event assuming the reaction

ˉp + p → a pair of particles with equal masses.

About 20,000 events were found to be either annihilation into π ^±-pair or k ^±-pair events. The two different charged meson pair modes were also distinctly separated.

The average differential cross section of ˉp + p → π⁺ + π^- varied from ~ 25 µb/sr at antiproton beam momentum 0.72 GeV/c (total energy in center-of-mass system, √s = 2.0 GeV) to ~ 2 µb/sr at beam momentum 2.62 GeV/c (√s = 2.64 GeV). The most striking feature in the angular distribution was a peak at Θ_C.M. = 90° (cos Θ_C.M. = 0) which increased with √s and reached a maximum at √s ~ 2.1 GeV (beam momentum ~ 1.1 GeV/c). Then it diminished and seemed to disappear completely at √s ~ 2.5 GeV (beam momentum ~ 2.13 GeV/c). A valley in the angular distribution occurred at cos Θ_C.M. ≈ 0.4. The differential cross section then increased as cos Θ_C.M. approached 1.

The average differential cross section for ˉp + p → k⁺ + k^- was about one third of that of the π^±-pair mode throughout the energy range of this experiment. At the lower energies, the angular distribution, unlike that of the π^±-pair mode, was quite isotropic. However, a peak at Θ_C.M. = 90° seemed to develop at √s ~ 2.37 GeV (antiproton beam momentum ~ 1.82 GeV/c). No observable change was seen at that energy in the π^±-pair cross section.

The possible connection of these features with the observed meson resonances at 2.2 GeV and 2.38 GeV, and its implications, were discussed.