Catalysis of Protein Folding by Chaperones Accelerates Evolutionary Dynamics in Adapting Cell Populations

Although molecular chaperones are essential components of protein homeostatic machinery, their mechanism of action and impact on adaptation and evolutionary dynamics remain controversial. Here we developed a physics-based ab initio multi-scale model of a living cell for population dynamics simulations to elucidate the effect of chaperones on adaptive evolution. The 6-loci genomes of model cells encode model proteins, whose folding and interactions in cellular milieu can be evaluated exactly from their genome sequences. A genotype-phenotype relationship that is based on a simple yet non-trivially postulated protein-protein interaction (PPI) network determines the cell division rate. Model proteins can exist in native and molten globule states and participate in functional and all possible promiscuous non-functional PPIs. We find that an active chaperone mechanism, whereby chaperones directly catalyze protein folding, has a significant impact on the cellular fitness and the rate of evolutionary dynamics, while passive chaperones, which just maintain misfolded proteins in soluble complexes have a negligible effect on the fitness. We find that by partially releasing the constraint on protein stability, active chaperones promote a deeper exploration of sequence space to strengthen functional PPIs, and diminish the non-functional PPIs. A key experimentally testable prediction emerging from our analysis is that down-regulation of chaperones that catalyze protein folding significantly slows down the adaptation dynamics

Manifold algorithmic errors in quantum computers with static internal imperfections

The inevitable existence of static internal imperfections and residual interactions in some quantum computer architectures result in internal decoherence, dissipation, and destructive unitary shifts of active algorithms. By exact numerical simulations we determine the relative importance and origin of these errors for a Josephson charge qubit quantum computer. In particular we determine that the dynamics of a CNOT gate interacting with its idle neighboring qubits via native residual coupling behaves much like a perturbed kicked top in the exponential decay regime, where fidelity decay is only weakly dependent on perturbation strength. This means that retroactive removal of gate errors (whether unitary or non-unitary) may not be possible, and that effective error correction schemes must operate concurrently with the implementation of subcomponents of the gate

Kraus decomposition for chaotic environments

We consider a system interacting with a chaotic thermodynamic bath. We derive an explicit and exact Kraus operator sum representation (OSR) for the open system reduced density. The OSR preserves the Hermiticity, complete positivity and norm. We show that it is useful as a numerical tool by testing it against exact results for a qubit interacting with an isolated flawed quantum computer. We also discuss some interesting qualitative aspects of the OSR

Quantum pathology of static internal imperfections in flawed quantum computers

Even in the absence of external influences the operability of a quantum computer (QC) is not guaranteed because of the effects of residual one- and two-body imperfections. Here we investigate how these internal flaws affect the performance of a quantum controlled-NOT (CNOT) gate in an isolated flawed QC. First we find that the performance of the CNOT gate is considerably better when the two-body imperfections are strong. Secondly, we find that the largest source of error is due to a coherent shift rather than decoherence or dissipation. Our results suggest that the problem of internal imperfections should be given much more attention in designing scalable QC architectures

Probing internal bath dynamics by a Rabi oscillator-based detector

By exact numerical and master equation approaches, we show that a central spin-1/2 can be configured to probe internal bath dynamics. System-bath interactions cause Rabi oscillations in the detector and periodic behavior of fidelity. This period is highly sensitive to the strength of the bath self-interactions, and can be used to calculate the intra-bath coupling

Exact norm-conserving stochastic time-dependent Hartree-Fock

We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise-interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method we calculate the low energy spectrum of Helium. An extension of the method to bosons is outlined.Comment: 21 pages, 3 figures, LaTeX fil

Kraus decomposition for chaotic environments including time-dependent subsystem Hamiltonians

We derive an exact and explicit Kraus decomposition for the reduced density of a quantum system simultaneously interacting with time-dependent external fields and a chaotic environment of thermodynamic dimension. We test the accuracy of the Kraus decomposition against exact numerical results for a CNOT gate performed on two qubits of an $(N+2)$-qubit statically flawed isolated quantum computer. Here the $N$ idle qubits comprise the finite environment. We obtain very good agreement even for small $N$

The time evolution of mean sequence entropy is plotted in the absence and presence of chaperones, i.e. for (blue lines) and (red lines), respectively, at temperature <i>T</i> = 0.85.

<p>The time evolution of mean sequence entropy is given in (A) for the monomer , in (B) for the heterodimer , and in (C) for date triangle proteins .</p

The time evolution of the fitness ratios (i.e. the ratio of birth rates with chaperones and without chaperones) are presented for the active in (A) and passive model in (B) for three different temperatures.

<p>The fitness ratios and evolutionary time are in log scale to convey the events clearly across all time scales. All data here and in the subsequent figures are ensemble averages over 100 independent stochastic trajectories.</p

Pictorial depictions of molecular interactions, chaperone interaction surface, and free energy-reaction coordinates diagram.

<p>(A) A schematic representation of molecular interactions in the model cell. The folded (red cubes) and MG state (blue cubes) proteins in the cytosol of model cell are allowed to interact with each other to form functional (red solid lines) and non-functional (black dashed lines) interactions, which include homodimeric self-interactions (black dashed loops). Black solid lines represent the PPI network of chaperone (green square). (B) Chaperone interaction surface. A single face of cube, consisting of nine amino acid residues is used to model the interaction between chaperone and unfolded proteins. (C) Reaction (rxn) coordinate vs. free energy diagram for protein folding with and without chaperones, highlighting the catalytic activity of chaperones.</p