Dan Gordon

Rooftop solar and batteries, along with other distributed energy resources (DER), add a new demand-side flexibility, which, when harnessed, will enable distribution operators to more efficiently manage their constrained networks. This paper presents network-aware coordination (NAC), an approach for coordinating DER within unbalanced distribution network constraints, which utilises the alternating direction method of multipliers (ADMM) to solve a distributed receding-horizon OPF. As far as we are aware, this paper is the first to report on the practical implementation and performance of an ADMM-based technique solving a significant network problem in live operations. We present real-world trial results of NAC coordinating 31 residential batteries on a constrained feeder within Tasmania’s 11 kV distribution network. The batteries are coordinated to manage the network’s constraints during periods of high feeder demand, decreasing the need for expensive conventional network management, in this case a diesel generator. We achieve a 34% reduction in diesel over 7 peaks with 31 batteries capable of meeting 10% of peak demand. Supplementary simulations indicate the potential for a 74% diesel reduction if battery numbers were increased to 100. We find that compared to uncoordinated battery response, the NAC achieves 13% lower total costs over the trial period.

We present a principled way of extending a classical AI planning formalism with systems of state constraints, which relate - sometimes determine - the values of variables in each state traversed by the plan. This extension occupies an attractive middle ground between expressivity and complexity. It enables modelling a new range of problems, as well as formulating more efficient models of classical planning problems. An example of the former is planning-based control of networked physical systems - power networks, for example - in which a local, discrete control action can have global effects on continuous quantities, such as altering flows across the entire network. At the same time, our extension remains decidable as long as the satisfiability of sets of state constraints is decidable, including in the presence of numeric state variables, and we demonstrate that effective techniques for cost-optimal planning known in the classical setting - in particular, relaxation-based admissible heuristics - can be adapted to the extended formalism. In this paper, we apply our approach to constraints in the form of linear or non-linear equations over numeric state variables, but the approach is independent of the type of state constraints, as long as there exists a procedure that decides their consistency. The planner and the constraint solver interact through a well-defined, narrow interface, in which the solver requires no specialisation to the planning context.

The discovery of new drugs that selectively block or modulate ion channels has great potential to provide new treatments for a host of conditions. One promising avenue revolves around modifying or mimicking certain naturally occurring ion channel modulator toxins. This strategy appears to offer the prospect of designing drugs that are both potent and specific. The use of computational modeling is crucial to this endeavor, as it has the potential to provide lower cost alternatives for exploring the effects of new compounds on ion channels. In addition, computational modeling can provide structural information and theoretical understanding that is not easily derivable from experimental results. In this review, we look at the theory and computational methods that are applicable to the study of ion channel modulators. The first section provides an introduction to various theoretical concepts, including force-fields and the statistical mechanics of binding. We then look at various computational techniques available to the researcher, including molecular dynamics, Brownian dynamics, and molecular docking systems. The latter section of the review explores applications of these techniques, concentrating on pore blocker and gating modifier toxins of potassium and sodium channels. After first discussing the structural features of these channels, and their modes of block, we provide an in-depth review of past computational work that has been carried out. Finally, we discuss prospects for future developments in the field.

We present new Brownian dynamics techniques for studying blockers of ion channels. By treating the channel as a fixed body, simulating the blocker molecules using rigid bodies, and using an implicit water force field with explicit ions, we are able to carry out fast simulations that can be used to investigate the dynamics of block and unblock, deduce binding modes, and calculate binding affinities. We test our program using the NavAb bacterial sodium channel, whose structure was recently solved (Payandeh et al. Nature, 2011, 475, 353–358) in conjunction with the μ-conotoxin PIIIA blocker. We derive an ohmic current–voltage relationship for channel permeation, calculate potentials of mean force for blocker unbinding, and deduce multiple binding modes for the blocker. Our results are shown to be compatible with other computational and experimental results. Finally, we discuss future improvements such as the inclusion of flexible side chains. After these improvements are carried out, we anticipate our program will be an extremely useful new tool that could be used to help develop new drugs to treat a range of ion-channel related diseases.

Using a novel rigid body Brownian dynamics algorithm, we investigate how a spherically asymmetrical polyamine molecule, a branched analogue of spermine, interacts with the external vestibule of the voltage-gated potassium channel, Kv1.2. Simulations reveal that the blocker, with a charge of +4e, inserts one of its charged amine groups into the selectivity filter, while another forms a salt bridge with an aspartate residue located just outside the entrance of the pore. This binding mode mimics features of the binding of polypeptides such as the scorpion venom charybdotoxin to the channel. The potential of mean force constructed with Brownian dynamics is a reasonable match to that obtained from molecular dynamics simulations, with dissociation constants of 4.7 and 22 μM, respectively. The current–voltage relationships obtained with and without a blocker in the external reservoir show that the inward current is severely attenuated by the presence of the blocker, whereas the outward current is only moderately reduced. The computational molecular modeling technique we introduce here can provide detailed insights into ligand–channel interactions and can be used for rapidly screening potential blocker molecules.

We present a new methodology, which combines molecular dynamics and stochastic dynamics, for modeling the permeation of ions across biological ion channels. Using molecular dynamics, a free energy profile is determined for the ion(s) in the channel, and the distribution of random and frictional forces is measured over discrete segments of the ion channel. The parameters thus determined are used in stochastic dynamics simulations based on the nonlinear generalized Langevin equation. We first provide the theoretical basis of this procedure, which we refer to as “distributional molecular dynamics,” and detail the methods for estimating the parameters from molecular dynamics to be used in stochastic dynamics. We test the technique by applying it to study the dynamics of ion permeation across the gramicidin pore. Given the known difficulty in modeling the conduction of ions in gramicidin using classical molecular dynamics, there is a degree of uncertainty regarding the validity of the MD-derived potential of mean force (PMF) for gramicidin. Using our techniques and systematically changing the PMF, we are able to reverse engineer a modified PMF which gives a current-voltage curve closely matching experimental results.

We present a new leapfrog algorithm for the numerical solution of the generalized Langevin equation (GLE) in the case where the friction kernel is exponentially decaying. Like other leapfrog and Verlet algorithms, our algorithm is second order in velocity and third order in position. It is relatively easy to implement compared with other available algorithms, and would therefore make a good candidate for exploring the effects of finite memory time-scales in situations where modelling the precise functional form of the memory kernel was not important. We have tested this algorithm on a one-dimensional barrier crossing model, and found good asymptotic agreement with limits obtained using Brownian dynamics (BD) simulations, as well as with a theoretical asymptotic limit. We have also used the algorithm to perform a more sophisticated simulation of ion conduction through a KcsA channel. The results are a close match to corresponding results obtained using the Langevin equation, thereby helping to justify the use of Brownian dynamics in KcsA and other similar ion channels.