MULTI-Valued and parallel molecular logic
(Presented by Barbara Fresch, University of Liege, Belgium)
Molecular systems are characterized by several internal states that can be addressed electrically, optically
or chemically. Inter and intra-molecular dynamical processes depend on external perturbations and on the
state of the chemical system. The objective of MULTI is to propose a radical departure from the prevailing
combinatorial and Boolean logic implementations, taking advantage of the atomic and molecular scales.
The basic questions that MULTI aims answering are: “what is a natural and efficient way for a molecular
logic device to physically implement logic operations”, “how do we input different instructions to such a
device” and “how does the inherent time evolution of the device deliver different outputs for different
inputs”. The complexity of molecular systems and their response to external stimuli are investigated in
order to implement
 Multivalued computations up to and including continuous logic
 Devices that physically unify data processing and data storage. Molecular machines endowed
with a built-in memory.
 Parallel processing and parallel output reading
 Reconfigurable/programmable logic machines
These “unconventional” ways to compute are physically grounded in basic properties of the matter at the
molecular scale. MULTI proposes implementations up to the proof of concept on three different kinds of
molecular systems: optically addressed multi-chromophoric complexes1, electrically addressed artificial
atoms in solid state and chemically addressed DNA machines2-6. The dynamics of these systems is followed
in time by state of the art experimental techniques: 2D photon-echo spectroscopy characterizes energy
transfer in chromophoric systems, pulsed gate voltage experiments reveal intramolecular dynamics in solidstate devices and time resolved fluorescence tracks the evolution of DNA assemblies. The unconventional
logic design is thus implemented at the hardware level, based on the physics of the time evolution of these
multi-state chemical systems.
To illustrate our approach, two logic schemes recently developed will be presented. We implemented a
logical decision tree in a dimer molecule interacting with three laser pulses in a 2D photon echo (PE)
experiment and we analysed it in terms of finite state logic machine capable of performing parallel
computation. The dynamics of the dimer system is described by the evolution of its density matrix
(schematically represented in the Figure) and the different Feynman pathways contributing to the
measured signal represent the logic structure. The use of graph-based representation of logical tasks opens
an interesting avenue for the implementation at the molecular scale because it unveils the formal structure
that need to be mapped in the molecular response. As a second example we will report on the use of the
Mg2+-dependent DNAzyme as a functional unit for the construction of the logically reversible Toffoli and
Fredkin gates. These systems follow the fundamental definition of logical reversibility, in which the relation
between the set of inputs and outputs is one to one. However, we emphasize that the systems undergo
thermodynamically irreversible dynamics that physically precludes the reversing of the outputs to the
inputs.
References
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Fresch, B., Hiluf, D., Collini, E., Levine, R. D. & Remacle, F. Molecular decision trees realized by
ultrafast electronic spectroscopy. Proceedings of the National Academy of Sciences,
doi:10.1073/pnas.1314978110 (2013).
Cecconello, A., Lu, C.-H., Elbaz, J. & Willner, I. Au Nanoparticle/DNA Rotaxane Hybrid
Nanostructures Exhibiting Switchable Fluorescence Properties. Nano Letters 13, 6275-6280,
doi:10.1021/nl403884w (2013).
Lu, C.-H., Cecconello, A., Elbaz, J., Credi, A. & Willner, I. A Three-Station DNA Catenane Rotary
Motor with Controlled Directionality. Nano Letters 13, 2303-2308, doi:10.1021/nl401010e (2013).
Orbach, R., Mostinski, L., Wang, F. & Willner, I. Nucleic Acid Driven DNA Machineries Synthesizing
Mg2+-Dependent DNAzymes: An Interplay between DNA Sensing and Logic-Gate Operations.
Chemistry – A European Journal 18, 14689-14694, doi:10.1002/chem.201201995 (2012).
Orbach, R., Remacle, F., Levine, R. D. & Willner, I. Logic reversibility and thermodynamic
irreversibility demonstrated by DNAzyme-based Toffoli and Fredkin logic gates. Proceedings of the
National Academy of Sciences 109, 21228-21233, doi:10.1073/pnas.1219672110 (2012).
Orbach, R., Remacle, F., Levine, R. D. & Willner, I. DNAzyme-based 2:1 and 4:1 multiplexers and 1:2
demultiplexer. Chemical Science 5, 1074-1081, doi:10.1039/C3SC52752B (2014).