Photosynthetic electronic energy transport

Another paper to report on (open-access link available here). This work examines electronic energy transport in LH2, a supramolecular photosynthetic complex which is found in the cell membranes of purple bacteria. Lots of people have gotten interested in LH2 ever since Graham Fleming’s group published a paper in 2007 reporting on fancy 2d spectroscopy which observed coherent quantum “beating” between initially prepared electronic states. Beating patterns of this sort are certainly of fundamental interest, and the experiments used to observe it were very nice; however, the consensus which seems to be emerging is that the “beating” is in fact not so important for explaining the efficiency at which photosynthetic systems transport electronic energy across their membranes.

So why did I decide to get involved in LH2? Well, a few reasons. First, my colleague Dr. Tom Oliver has had a longstanding interest in this system. And second, I’ve been extremely confused by the LH2 modelling literature. When we think about excited state and non-adiabatic dynamics in small and medium sized molecules, we think about topological features like conical intersections, avoided crossings, near degeneracies, non-adiabatic coupling vectors, etc. For small molecules, we know that fluctuations in vibrational degrees of freedom are often responsible for bringing electronic states into near-degeneracy, and transferring amplitude between states.

Despite the fact that all of these concepts are extremely mature owing to developments over the years within the small molecule excited state dynamics community, they are nowhere to be found when one reads the LH2 literature. Instead, we read about master equation treatments where every single vibration is anonymised, and folded into a linearly coupled “spectral density function”. Conical intersections? Avoided crossings? Near degeneracies? Non-adiabatic coupling vectors? Entirely absent. It’s almost like LH2 is linked to an entirely different discipline with an entirely different vocabulary.

So my aim with the LH2 work was full representation of vibrations! No more nameless vibrations folded into some anonymous spectral density function. Full representation of each and every vibration, capturing the fullness of its unique dynamical anharmonic identity. It’s the kind of sentiment that seems particularly well aligned with the current populist zeitgeist sweeping the globe.

But LH2 is big, and it has has lots of excited states, so a full representation of all of its vibrations in atomistic detail is a non-trivial challenge. To do it, we built a multi-tiered parallel computational framework (using TDDFT parallelized across GPUs within nodes, and MPI to scale across nodes) for calculating atomic cartesian gradients on each and every excited state. We also introduced some approximations for how to treat cartesian gradients of the excited state dipole moments and the transition dipole moments. This builds on some work we published a couple years ago. Once all that was stabilised, we were then able to run surface-hopping simulations to treat the explicit dynamics of both the atoms and also the electronic degrees of freedom. The picture that emerges is shown in the movie. The key thing which this movie highlights (compared to previous simulations) is the fact that the atomic motion is explicitly being accounted for, along with the electronic motion (which is shown as diffuse blue clouds). In fact, you need to manually speed up the frame-rate to see the atoms moving, because your eyes are more attuned to the flashing blue electronic amplitude than to the subtleties of the atomic motion. But it’s definitely all in there!

The dynamical picture of electronic energy transport which emerges from this work is one of excited states which fluctuate rapidly as a result of the underlying vibrational dynamics of the atoms which make up the constituent LH2 chromophores. The excited states are delocalized over multiple chromophores and undergo frequent crossing on a femtosecond timescale, as depicted in Fig 4A of the paper. Every crossing offers an opportunity to transfer amplitude from one excited state to another. The result is a sort of highly connected excited state network: the frequent crossings combine to create scenario where the states are in a sort of constant “communication” with one another, allowing excitation localized in any one state to travel far and fast. The take-home message? It’s all about the vibrations!

dynamics at diamond surfaces

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We’ve just published a paper (open-access link here) looking at non-equilibrium reaction dynamics at the surface of diamond. As shown in the video, our simulations enabled us to look at the dynamics of a slab of hydrogen capped diamond. We constructed the diamond slab so as to contain a single “dangling” surface methyl group. Diamond is a notoriously good heat conductor: from a microscopic perspective, this means that it dissipates vibrational energy extremely efficiently. So we were surprised to observe that placing some initial heat into the dangling CH3 group (by “plucking” its bonds) led to a statistically significant number of dissociation events. Not an enormous number of events, but enough to matter.

The conventional knowledge is that such events essentially have a probability of zero – owing to the fact that diamond is so efficient at heat dissipation. So we set out to understand why we observed any dissipation. To do so, we formulated an energy-grained master equation model, an area where I’ve been active for while. To some extent, this approach followed on from work we carried out back in 2009, which was aimed at understanding the competition between reaction and relaxation dynamics in organic solvents. Our 2009 study was the first to apply the energy grained master equation to reactions in condensed phases; and to the best of my knowledge, the diamond work represents the first attempt to apply the energy grained master equation to reactions at surfaces.

The big problem with a master equation representation of diamond arises from the fact that it’s not straightforward to separate the “system” degrees of freedom from the “bath” degrees of freedom. For reactions in liquids, the separation is somewhat more straightforward: it is effectively the solute/solvent distinction. For diamond, we simply tried a sensible definition: let the “system” be defined as those atoms and corresponding vibrations which were less than 3 covalent bonds away from the constituent methyl group; and let the “bath” be defined as everything else. This allowed us to calculate energy resolved rate coefficients [k(E)s] for CH3 dissociation from the “system” component of the diamond surface. The next issue a master equation approach faces is this: how do we represent the energy transfer rate from the diamond “system” to the “bath”? Our approach was to run a single long trajectory of the diamond slab (as shown in the video), and then use linear response theory to analyze the characteristic timescale for energy fluctuations within the diamond “system” to dissipate into the “bath”. Then we parameterised an energy transfer function to fit the energy decay curve. With these two ingredients – k(E)s, and an energy transfer function – we could run master equation simulations of the surface reaction dynamics. The results showed the energy dissipation from the system to the bath is definitely fast (with a timescale of ~100 fs) but that there is indeed a non-trivial probability that “prompt” CH3 dissociation events occur – i.e., prior to dissipation of all the energy.

Similar to the 2009 results, we actually found that the master equation did a pretty decent job compared to full MD simulations of CH3 dissociation! But for a computational cost which is 1/100,000 the cost of running the full set of dissociative MD simulations – big savings! As the first of its kind, this work is preliminary in many important respects, but it definitely offers a viable option for relatively cheap modelling of non-equilibrium reaction dynamics at surfaces. Note that all of the input files required to run the model are being made available in MESMER, our cross-platform, open-source master equation solver.

playing with proteins: tying knots & binding ligands

A little bit more progress in our molecular VR research work… Building on the framework which we demoed in Salt Lake City at Supercomputing 2016, we’ve started looking at applications to biomolecular systems with interesting conformational dynamics which are difficult to observe using standard molecular simulation workflows. The two videos that I’ve posted here were made by PhD students Mike O’Connor and Helen Deeks. The videos show Mike & Helen’s view within the real-time Nano Simbox virtual reality environment as they utilize a wireless set of “atomic tweezers” to steer a real-time molecular dynamics simulation (i.e., a real-time GPU accelerated implementation of the AMBER force field).

The first video shows the steps which Helen took to tie a knot in a 10-alanine peptide. Knotting is an interesting application for the VR Simbox, because the manipulations required to tie a knot in a molecular structure are actually pretty complex. For example, if I was going to write some code to tie a molecular knot, it would end up being a rather complicated little piece of software. However, tying knots is the sort of thing that’s actually rather straightforward and intuitive for a human, because we all tie knots all the time (and the sailors and knitters amongst us are even more expert)… There’s a lot of fundamental interest in understanding the kinetic mechanism of knotting, given that 1 – 2% of all known proteins are knotted…

The second video shows the steps which Mike took to interactively dock a single benzylpenicillin drug molecule (initially floating in free solvent) into the active sight of the β-lactamase enzyme. β-Lactamases are amongst the most common molecular tool used by bacteria to break down important classes of β-lactam antibiotics like benzylpenicillin, causing them to lose their antibiotic effect. Understanding the mechanism of β-Lactamases is therefore essential to make progress addressing the growing problem of anti-microbial resistance.

In both of these videos, Mike & Helen were able to generate dynamics pathways which would simply never be observed using conventional simulation methodologies. We’re now working on methods for analysing the user-generated pathways – i.e., enabling us to map conformational states, and also to calculate free energies. The idea is that this will provide insight into conformational kinetics and mechanisms. Stay tuned!

Multi-person molecular virtual reality

We’ve been busy at work over the past few months developing various aspects of our virtual reality environment for real-time interactive molecular dynamics. The thing that I’m totally psyched about right now is the fact that we’ve extended the framework that so we can put multiple people in the same virtual reality!!! Multiple people, stood around the same molecule can all play with it as if it were a tangible object. The very rough cut video I’ve linked to here (a combined effort by myself, Becca Rose, Alice Philips, and Phil Tew) is a quick attempt to try & illustrate what it’s like to inhabit VR with other people, and also to give you some sort of ideas of what you might do with this setup… playing catch with a bucky ball for example!

We’ve had it working for a month now, and we’ve been having all sorts of fun with molecular manipulations – skipping rope with peptides, and even smashing molecules together to get them to undergo chemical reactions. The video shows two people inhabiting VR, both of whom can see each other. For example, you can go to 2:17 in the video to see them bowing to each other. At our VR lab in Bristol, we’ve put as many as six people into the same molecular VR – and we think we can go up to eight. [For those of you who are interested in the full details, the video was actually constructed by letting three people inhabit the same VR; you don’t see the third person because most of the video is in fact “shot” from the third person’s viewpoint, meaning that the video shows something very similar to what the third person number is seeing!]

I’m really excited about this: it moves our virtual reality framework beyond something which is useful for an individual to a social tool that can be used collaboration and communication. Instead of wondering what molecular madness the weirdo with the headset is up to, you can don a headset, jump in their with him/her, and simply see for yourself. There’s lots of exciting applications that I can imagine: it lets researchers share a visualization environment with their colleagues, and it also lets a teacher undertake lessons along with their students…

Barbican Lab: multi-person VR & molecular aesthetics

From 9 – 13 Jan 2017, myself a group of collaborators came together at London’s Barbican to participate in their ‘Open Lab’ programme. The idea of the Open Lab is to provide an experimental arts space where collaborators can investigate directions for future work. With support from EPSRC, Arts Council England, the University of Bristol, and interactive Scientific (iSci), we came to the Barbican with two primary aims. First, we wanted to develop our interactive molecular virtual reality platform into a multi-person experience – i.e., allowing multiple people to simultaneously inhabit and share the same virtual reality. This is an area that I think is really important for VR moving forward, otherwise it risks becoming yet another sophisticated technology for alienating people. Second, we wanted to investigate the potential for this multi-person VR framework to support new approaches toward molecular aesthetics that might operate in an artistic and performative contexts…

We had a talented group of collaborators come together to support this research – some old faces (from the original danceroom Spectroscopy team), and also some new. The team was comprised of three of my Bristol-University based Phd students: Mike O’Connor, Rob Arbon, and Lisa May Thomas. Also involved were digital artist Phill Tew (iSci); electronic musician Prof. Joseph Hyde (Bath Spa University); sonic interaction expert Dr. Tom Mitchell (University of the West of England); contemporary dancer Isabelle Cressy; visual artist Dr. Gemma Anderson (Exeter University), and finally Benjamin de Kosnik, a San-Francisco based digital artist and activist.

It was a great experience! We all lived together for a week in a massive house in Shoreditch, which allowed us to interact as a group after our days spent at the Barbican. It also led to a few nights without much sleep as various team members worked late into the night hacking together various bits and pieces. As a team, we all interacted with one another over the entire period, but our efforts were loosely subdivided into three groups:

  1. Myself, Mike, and Phil were responsible for stabilising the multi-person technology framework that enabled multiple people to simultaneously inhabit the same interactive molecular virtual reality (there’s a video link here that gives you an idea of how the framework we built at the Barbican works);
  2. Tom and Joe were focussed on developing an 8-channel audio system which was integrated into the VR system, so as to allow the virtual reality users to have audio feedback which was spatially localized, depending on their position in space.
  3. Lisa, Izzie, and Gemma were focussed on developing:
    • a choreographic movement vocabulary with the potential to describe the range of ways in which a dancer embedded in VR might user his/her body to interact with a real-time biomolecular dynamics simulations, for potential scientific and also performative applications
    • a series of sketches which could articulate the biomolecular choreographic vocabulary
  4. Rob &Benjamin worked with Gemma to design neural network (NN) algorithms aimed at analyzing the style contained in her analogue drawings of biomolecular dynamics. The question here was: can we use the stylistic flesh of analogue drawings to explore aesthetic possibilities in the digital space – i.e., enabling us to find alternative algorithmic strategies for digitally rendering biomolecular structures. For example, the images below show NN analysis they carried out on one of her drawings.

After five amazing days together, I am glad to report that we made lots of exciting progress in tackling the strands outlined above! We built a framework that allows multiple people to inhabit the same virtual reality. At the moment, we know that it can handle up to four people, and we think that it can go up to eight without many problems… We also made great progress in developing what we have started to call a ‘bio-inspired’ choreography – i.e., a set of human movement principles gleaned from analysing the intricate and beautiful dynamics of biomolecular structures. We also made progress in developing some NN frameworks that allow us to begin exploring alternative digital rendering algorithms for biomolecular structures. The video link above gives a little taster of our journey during the week, but this is just the beginning – and I’m very excited! Stay tuned…

Adaptive BXD in multi-dimensional CV space

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We’ve recently published a paper describing some nice extensions to the “boxed molecular dynamics” (BXD) rare event method (open-access draft available here). BXD is a method that I’ve been working on for the last few years for accelerating rare events in chemical simulations (there’s a 1-d implementation available in the CHARMM package).

The underlying BXD idea is straightforward: assuming I have a chemical transformation that I want to study, and some sense of the collective variables (CVs) that are important along the transformation pathway, I can splice the CV space into a set of ‘boxes’. A “box” is defined as a region of configuration space that lies between two boundaries; within any given box, a trajectory runs on a potential energy surface which is unmodified. If the trajectory crosses a particular box boundary, a velocity inversion operation is performed to keep it within the specified box. BXD simulations are run by locking the system within a set of adjacent ‘boxes’, and then performing statistical analysis of the time spent in the each box, and the relative number of hits at the boundaries which define the box. These quantities define box-to-box rate coefficients, which can then be used to calculate a potential of mean force, which is independent of the boundary locations. Choosing BXD boundaries is analogous to the process of specifying umbrellas (in umbrella sampling). A key difference is the fact that umbrella sampling requires two parameters per umbrella (location and force constant); whereas BXD requires only one parameter (location). With the appropriate set of boxes, it is possible to sample spaces that otherwise have a low probability of being populated.

In our recent paper, we made two useful developments to BXD. We showed that BXD can be: (1) utilized to explore multi-dimensional CV spaces, and (2) formulated in a fashion that enables adaptive exploration of minimum free energy pathways. The video shows BXD adaptively sampling reactive pathways for deuterium transfer between a Fluorine radical and deuterated acetonitrile solvent molecules.  Specifically, we told BXD to adaptively sample the free energy pathway in a 2d CV space (the D–F distance and the C–D distance).

Unlike umbrella sampling or metadynamics, BXD does not bias the underlying potential energy surface of a given system. As a result, it can be shown within certain limits that the BXD dynamics correspond to the “real” system dynamics. The philosophy that guides the adaptive BXD algorithm is therefore very simple: by ‘listening’ to the system dynamics, we get an idea of where the system is trying to go, and are therefore able to adaptively locate box boundaries which nudge the system along so that it does not become trapped. The video in fact shows the box boundaries which BXD places as it ‘listens’ to the system dynamics.

Philip Leverhulme Prize

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I recently found out that I won a Philip Leverhulme Prize! These prizes have been awarded annually since 2001, with the aim to “recognise the achievement of outstanding researchers whose work has already attracted international recognition and whose future career is exceptionally promising.” They’re named after Philip Leverhulme, who died in 2000, and was the grandson of Lord William Leverhulme.

The Leverhulme Trust makes awards and grant schemes that cover a wide range of disciplines – including the natural sciences, the social sciences, the humanities, and the arts. For example, there were thirty Philip Leverhulme awards made in 2016, with 5 prizes in six different subjects: Archaeology, Chemistry, Economics, Engineering, Geography, and Languages/Literatures. The full list of 2016 prize winners in all of the subject areas is available here.

The history of the Leverhulme trust is closely intertwined with the UK chemical industry – namely the FTSE 100 company Unilever. William Hesketh Lever (aka Lord William Leverhulme) was a Victorian businessman and entrepreneur who made his fortune selling soap globally. The Leverhulme Trust was born when Leverhulme died in 1925. He left a portion of his Lever Brothers company in trust for the purpose of supporting two aims: trade charities, and also “scholarships for the purposes of research and education”. In 1929, Lever Brothers subsequently merged with the Dutch Van den Bergh margarine company to form Unilever plc, which remains one of the oldest transnational companies in existence.