Accurate ionic forces and geometry optimisation in linear scaling density-functional theory with local orbitals

Linear scaling methods for density-functional theory (DFT) simulations are formulated in terms of localised orbitals in real-space, rather than the delocalised eigenstates of conventional approaches. In local-orbital methods, relative to conventional DFT, desirable properties can be lost to some extent, such as the translational invariance of the total energy of a system with respect to small displacements and the smoothness of the potential energy surface. This has repercussions for calculating accurate ionic forces and geometries. In this work we present results from textsc{onetep}, our linear scaling method based on localised orbitals in real-space. The use of psinc functions for the underlying basis set and on-the-fly optimisation of the localised orbitals results in smooth potential energy surfaces that are consistent with ionic forces calculated using the Hellmann-Feynman theorem. This enables accurate geometry optimisation to be performed. Results for surface reconstructions in silicon are presented, along with three example systems demonstrating the performance of a quasi-Newton geometry optimisation algorithm: an organic zwitterion, a point defect in an ionic crystal, and a semiconductor nanostructure.

The cardiac Ca-sensitive regulatory switch, a system in dynamic equilibrium

The Ca-sensitive regulatory switch of cardiac muscle is a paradigmatic example of protein assemblies that communicate ligand binding through allosteric change. The switch is a dimeric complex of troponin C (TnC), an allosteric sensor for Ca, and troponin I (TnI), an allosteric reporter. Time-resolved equilibrium FRET measurements suggest that the switch activates in two steps: a TnI-independent Ca-priming step followed by TnI-dependent opening. To resolve the mechanistic role of TnI in activation we performed stopped-flow FRET measurements of activation following rapid addition of a lacking component (Ca or TnI) and deactivation following rapid chelation of Ca. The time-resolved measurements, stopped-flow measurements, and Ca-titration measurements were globally analyzed in terms of a new quantitative dynamic model of TnC-TnI allostery. The analysis provided a mesoscopic parameterization of distance changes, free energy changes, and transition rates among the accessible coarse-grained states of the system. The results reveal (i) the Ca-induced priming step, which precedes opening, is the rate limiting step in activation, (ii) closing is the rate limiting step in deactivation, (iii) TnI induces opening, (iv) an incompletely deactivated population when regulatory Ca is not bound, which generates an accessory pathway of activation, and (v) incomplete activation by Ca--when regulatory Ca is bound, a 3:2 mixture of dynamically inter-converting open (active) and primed-closed (partially active) conformers is observed (15 C). Temperature-dependent stopped-flow FRET experiments provide a near complete thermo-kinetic parametrization of opening. <Abstract Truncated>

Physical limits on computation by assemblies of allosteric proteins

Assemblies of allosteric proteins, nano-scale Brownian computers, are the principle information processing devices in biology. The troponin C-troponin I (TnC-TnI) complex, the Ca$^{2+}$-sensitive regulatory switch of the heart, is a paradigm for Brownian computation. TnC and TnI specialize in sensing (reading) and reporting (writing) tasks of computation. We have examined this complex using a newly developed phenomenological model of allostery. Nearest-neighbor-limited interactions among members of the assembly place previously unrecognized constrains the topology of the systems free energy landscape and generate degenerate transition probabilities. As a result, signaling fidelity and deactivation kinetics can not be simultaneously optimized. This trade-off places an upper limit on the rate of information processing by assemblies of allosteric proteins that couple to a single ligand chemical bath.

Equality statements for entropy change in open systems

The entropy change of a (non-equilibrium) Markovian ensemble is calculated from (1) the ensemble phase density $p(t)$ evolved as iterative map, $p(t) = mathbb{M}(t) p(t- Delta t)$ under detail balanced transition matrix $mathbb{M}(t)$, and (2) the invariant phase density $pi(t) = mathbb{M}(t)^{infty} pi(t) $. A virtual measurement protocol is employed, where variational entropy is zero, generating exact expressions for irreversible entropy change in terms of the Jeffreys measure, $mathcal{J}(t) = sum_{Gamma} [p(t) - pi(t)] ln bfrac{p(t)}{pi(t)}$, and for reversible entropy change in terms of the Kullbach-Leibler measure, $mathcal{D}_{KL}(t) = sum_{Gamma} pi(0) ln bfrac{pi(0)}{pi(t)}$. Five properties of $mathcal{J}$ are discussed, and Clausius theorem is derived.