Mapping behavioral specifications to model parameters in synthetic biology

With recent improvements of protocols for the assembly of transcriptional parts, synthetic biological devices can now more reliably be assembled according to a given design. The standardization of parts open up the way for in silico design tools that improve the construct and optimize devices with respect to given formal design specifications. The simplest such optimization is the selection of kinetic parameters and protein abundances such that the specified design constraints are robustly satisfied. In this work we address the problem of determining parameter values that fulfill specifications expressed in terms of a functional on the trajectories of a dynamical model. We solve this inverse problem by linearizing the forward operator that maps parameter sets to specifications, and then inverting it locally. This approach has two advantages over brute-force random sampling. First, the linearization approach allows us to map back intervals instead of points and second, every obtained value in the parameter region is satisfying the specifications by construction. The method is general and can hence be incorporated in a pipeline for the rational forward design of arbitrary devices in synthetic biology

Hot Giant Fullerenes Eject <i>and</i> Capture C₂ Molecules: QM/MD Simulations with Constant Density

Quantum chemical molecular dynamics (QM/MD) simulations using periodic boundary conditions show that hot giant fullerene (GF) cages can both eject and capture C2 molecules dependent on the concentration of noncage carbons in the simulated system, and that the cage size can therefore both increase and decrease under high temperature conditions. The reaction mechanisms for C2 elimination and incorporation involve sp3 carbon defects and polygonal rings larger than hexagons, and are thus closely related to previously described mechanisms (Murry, R. L.; Strout, D. L.; Odom, G. K.; Scuseria, G. E. Nature 1993, 366, 665). The atoms constituting the cage are gradually replaced by the two processes, suggesting that a fullerene cage during high-temperature synthesis is a dissipative structure in the sense of Ilya Prigogine’s theory of self-organization in nonequilibrium systems. Explicit inclusion of Lennard-Jones-type helium or argon noble gas atoms is found to increase the GF shrinking rate. Large GFs shrink at a greater rate than small GFs. The simulations suggest that in an idealized, closed system the fullerene cage size may grow to a dynamic equilibrium value that depends on initial cage size, temperature, pressure, and overall carbon concentration, whereas in an open system cage shrinking prevails when noncage carbon density decreases as a function of time

Hot Giant Fullerenes Eject <i>and</i> Capture C₂ Molecules: QM/MD Simulations with Constant Density

Quantum chemical molecular dynamics (QM/MD) simulations using periodic boundary conditions show that hot giant fullerene (GF) cages can both eject and capture C2 molecules dependent on the concentration of noncage carbons in the simulated system, and that the cage size can therefore both increase and decrease under high temperature conditions. The reaction mechanisms for C2 elimination and incorporation involve sp3 carbon defects and polygonal rings larger than hexagons, and are thus closely related to previously described mechanisms (Murry, R. L.; Strout, D. L.; Odom, G. K.; Scuseria, G. E. Nature 1993, 366, 665). The atoms constituting the cage are gradually replaced by the two processes, suggesting that a fullerene cage during high-temperature synthesis is a dissipative structure in the sense of Ilya Prigogine’s theory of self-organization in nonequilibrium systems. Explicit inclusion of Lennard-Jones-type helium or argon noble gas atoms is found to increase the GF shrinking rate. Large GFs shrink at a greater rate than small GFs. The simulations suggest that in an idealized, closed system the fullerene cage size may grow to a dynamic equilibrium value that depends on initial cage size, temperature, pressure, and overall carbon concentration, whereas in an open system cage shrinking prevails when noncage carbon density decreases as a function of time

Hot Giant Fullerenes Eject <i>and</i> Capture C₂ Molecules: QM/MD Simulations with Constant Density

Quantum chemical molecular dynamics (QM/MD) simulations using periodic boundary conditions show that hot giant fullerene (GF) cages can both eject and capture C2 molecules dependent on the concentration of noncage carbons in the simulated system, and that the cage size can therefore both increase and decrease under high temperature conditions. The reaction mechanisms for C2 elimination and incorporation involve sp3 carbon defects and polygonal rings larger than hexagons, and are thus closely related to previously described mechanisms (Murry, R. L.; Strout, D. L.; Odom, G. K.; Scuseria, G. E. Nature 1993, 366, 665). The atoms constituting the cage are gradually replaced by the two processes, suggesting that a fullerene cage during high-temperature synthesis is a dissipative structure in the sense of Ilya Prigogine’s theory of self-organization in nonequilibrium systems. Explicit inclusion of Lennard-Jones-type helium or argon noble gas atoms is found to increase the GF shrinking rate. Large GFs shrink at a greater rate than small GFs. The simulations suggest that in an idealized, closed system the fullerene cage size may grow to a dynamic equilibrium value that depends on initial cage size, temperature, pressure, and overall carbon concentration, whereas in an open system cage shrinking prevails when noncage carbon density decreases as a function of time

Hot Giant Fullerenes Eject <i>and</i> Capture C₂ Molecules: QM/MD Simulations with Constant Density

Quantum chemical molecular dynamics (QM/MD) simulations using periodic boundary conditions show that hot giant fullerene (GF) cages can both eject and capture C2 molecules dependent on the concentration of noncage carbons in the simulated system, and that the cage size can therefore both increase and decrease under high temperature conditions. The reaction mechanisms for C2 elimination and incorporation involve sp3 carbon defects and polygonal rings larger than hexagons, and are thus closely related to previously described mechanisms (Murry, R. L.; Strout, D. L.; Odom, G. K.; Scuseria, G. E. Nature 1993, 366, 665). The atoms constituting the cage are gradually replaced by the two processes, suggesting that a fullerene cage during high-temperature synthesis is a dissipative structure in the sense of Ilya Prigogine’s theory of self-organization in nonequilibrium systems. Explicit inclusion of Lennard-Jones-type helium or argon noble gas atoms is found to increase the GF shrinking rate. Large GFs shrink at a greater rate than small GFs. The simulations suggest that in an idealized, closed system the fullerene cage size may grow to a dynamic equilibrium value that depends on initial cage size, temperature, pressure, and overall carbon concentration, whereas in an open system cage shrinking prevails when noncage carbon density decreases as a function of time

Comparison of Geometric, Electronic, and Vibrational Properties for Isomers of Small Fullerenes C₂₀−C₃₆^†

We employ the self-consistent-charge density-functional tight-binding (SCC−DFTB) method for computing geometric, electronic, and vibrational properties for various topological isomers of small fullerenes. We consider all 35 five- and six-member rings containing isomers of small fullerenes, C20, C24, C26, C28, C30, C32, C34, and C36, as first part of a larger effort to catalog CC distance distributions, valence CCC angle distributions, electronic densities of states (DOSs), vibrational densities of states (VDOSs), and infrared (IR) and Raman spectra for fullerenes C20−C180. Common features among the fullerenes are identified and properties characteristic for each specific fullerene isomer are discussed

Self-Consistent Optimization of Excited States within Density-Functional Tight-Binding

We present an implementation of energies and gradients for the ΔDFTB method, an analogue of Δ-self-consistent-field density functional theory (ΔSCF) within density-functional tight-binding, for the lowest singlet excited state of closed-shell molecules. Benchmarks of ΔDFTB excitation energies, optimized geometries, Stokes shifts, and vibrational frequencies reveal that ΔDFTB provides a qualitatively correct description of changes in molecular geometries and vibrational frequencies due to excited-state relaxation. The accuracy of ΔDFTB Stokes shifts is comparable to that of ΔSCF-DFT, and ΔDFTB performs similarly to ΔSCF with the PBE functional for vertical excitation energies of larger chromophores where the need for efficient excited-state methods is most urgent. We provide some justification for the use of an excited-state reference density in the DFTB expansion of the electronic energy and demonstrate that ΔDFTB preserves many of the properties of its parent ΔSCF approach. This implementation fills an important gap in the extended framework of DFTB, where access to excited states has been limited to the time-dependent linear-response approach, and affords access to rapid exploration of a valuable class of excited-state potential energy surfaces

Understanding of the Off–On Response Mechanism in Caged Fluorophores Based on Quantum and Statistical Mechanics

For many years, numerous fluorescent probes have been synthesized and applied to visualize molecules and cells. The development of such probes has accelerated biological and medical investigations. As our interests have been focused on more complicated systems in recent years, the search for probes with sensitive environment off–on response becomes increasingly important. For the design of such sophisticated probes, theoretical analyses of the electronically excited state are inevitable. Especially, understanding of the nonradiative decay process is highly desirable, although this is a challenging task. In this study, we propose an approach to treat the solvent fluctuation based on the reference interaction site model. It was applied to selected bioimaging probes to understand the importance of solvent fluctuation for their off–on response. We revealed that the this switching process involves the nonradiative decay through the charge transfer state, where the solvent relaxation supported the transition between excited and charge transfer states. In addition, energetically favorable solvent relaxation paths were found due to the consideration of multiple solvent configurations. Our approach makes it possible to understand the nonradiative decay facilitated by a detailed analysis and enables the design of novel fluorescent switching probes considering the effect of solvent fluctuation

Polyyne Chain Growth and Ring Collapse Drives Ni-Catalyzed SWNT Growth: A QM/MD Investigation

A mechanism describing Ni38-catalyzed single-walled carbon nanotube (SWNT) growth has been elucidated using quantum mechanical molecular dynamics (QM/MD) methods. This mechanism is dominated by the existence of extended polyyne structures bound to the base of the initial SWNT cap-fragment. Polygonal ring formation, and hence SWNT growth itself, was driven by the continual, simultaneous extension of these polyyne chains and subsequent “ring collapse” (i.e., self-isomerization/interaction of these polyyne chains). The rate of the former exceeded that of the latter, and so this mechanism was self-perpetuating. Consequently, the observed kinetics of Ni38-catalyzed SWNT growth were increased substantially compared to those observed using other transition metal catalysts of comparable size

Polyyne Chain Growth and Ring Collapse Drives Ni-Catalyzed SWNT Growth: A QM/MD Investigation

A mechanism describing Ni38-catalyzed single-walled carbon nanotube (SWNT) growth has been elucidated using quantum mechanical molecular dynamics (QM/MD) methods. This mechanism is dominated by the existence of extended polyyne structures bound to the base of the initial SWNT cap-fragment. Polygonal ring formation, and hence SWNT growth itself, was driven by the continual, simultaneous extension of these polyyne chains and subsequent “ring collapse” (i.e., self-isomerization/interaction of these polyyne chains). The rate of the former exceeded that of the latter, and so this mechanism was self-perpetuating. Consequently, the observed kinetics of Ni38-catalyzed SWNT growth were increased substantially compared to those observed using other transition metal catalysts of comparable size