Edit: Jan 2024 – applications for these positions are now closed
We are looking for new members to join our Wellcome-funded team of cardiac electrophysiology modellers, to develop mathematical models of ion channel currents and cardiac cells for assessing the safety of new pharmaceutical drugs.
Two posts are available, and these are one year fixed-term research positions available from 1st Feb 2024 until 31st Jan 2025. You’ll be joining a research team including me, 4 postdocs, 3 PhD students and a Research Software Engineer, so you’ll gain great experience of teamwork in what I call “unusually-applied” maths.
A Senior role is available for experienced postdoctoral researchers, which is appointed on the same pay grade as a Lecturer/Assistant Professor; whilst the other will be suitable for you if you have just finished/are finishing a PhD or have a few years of postdoc experience.
We are looking for experience in EITHER:
Mathematical modelling of a biological system involving numerical simulations. We’ll probably focus on ODE models but experience of e.g. ODE, PDE or stochastic/agent-based modelling is fine. Some experience of electrophysiology modelling would be a plus but is not essential and can be learned ‘on the job’.
Statistics/data science – fitting mechanistic models to real experimental data and performing uncertainty quantification/inference in a frequentist or Bayesian framework. Experimental design and/or considering model discrepancy are desirable but not essential.
Your particular focus (depending on the strengths and interests of the successful candidates) could include:
How best to use the dynamic-clamp (real time simulation/experiment interaction) technique in model building.
Cell-specific / drug-specific electrophysiology model construction.
Working on methods for experimental design, to optimise parameter identifiability, but also to perform model selection, minimise the influence of experimental artefacts, and assess/forecast the difference between the model and reality.
Building on the Cardiac Electrophysiology Web Lab (https://scrambler.cs.ox.ac.uk/) to record and reproduce the process of fitting a model to data and testing it.
I think that our main problems in terms of “making quantitative predictions” in the cardiac modelling field are related to deriving biophysically-based mechanistic models from experimental data (replacing what are often subjective modelling choices with automated algorithms to make this reliable and reproducible). Plus making future predictions with appropriately quantified uncertainty due to all the factors about which we’re uncertain (not just parameter uncertainty… but all the sources of uncertainty and variability that I bang on about in talks).
You’ll find a lot of our open questions discussed in various past posts here on this blog and in our recent publications.
We’ll be working closely with: pharmaceutical industry labs; pharmaceutical regulators (including the FDA) who we have worked with to develop ways to assess trustworthiness of cardiac simulations and uncertainty quantification for regulatory use; and academic labs (in particular Teun de Boer’s lab in UMC Utrecht in the Netherlands and Adam Hill & Jamie Vandenberg‘s labs in Victor Chang Cardiac Research Institute, Sydney, Australia) with whom we are looking at the dynamic clamp technique and ways to gain more information on drug binding to ion channels. So candidates must enjoy teamwork, collaborative inter-disciplinary projects, and be prepared to get into the lab for a few weeks to really get to grips with the experiments we are trying to use.
Here are the links to the full role profiles and application forms, the deadline for applications is 15th January:
The chapter is about computational modelling of drug-induced pro-arrhythmic risk. So what does that mean?
Below are a couple of real electrocardiograms (ECGs). An ECG records the difference in electrical potential between two points on the outside of your body through time, and since the heart is the main source of electrical activity it dominates the signal (although you can also pick up signals from other muscles if you don’t stay still!). The top one is mine from a smartphone device and app measuring the electrical potential between my index fingers. When you think about it, there being any difference between electrical potential on opposite hands reflects the fact there’s asymmetry in heart chamber shapes and sizes (one side pumps to just lungs, other bigger one to all the rest of body), and/or heart orientation in the chest, and/or how waves of activity move through the heart.
(Incidentally, by putting 10 different electrodes in certain places on arms/legs/chest you – or at least an expert cardiologist – can read a surprising amount into what is going on in the full 3D electrical activity of the heart through time. Somewhat confusingly this is called a “12 lead ECG”. That’s because looking at 12 differences between combinations of the 10 electrodes is usually considered comprehensive enough to figure out what’s going on without causing cardiologists’ brains to explode. There’s research work with patients wearing jackets with hundreds of electrodes, and computers figuring out what’s going on, called “ECG imaging“.)
In the healthy top trace the 7 big spikes relate to the ventricles – the big main pumping chambers at the bottom of the heart – activating or depolarising. That is, going from low to high voltage and starting the chain of events that leads to contraction of the muscle. A large difference in electrical potential occurs across space as the activation wave travels up the ventricles, and so the time of maximum difference in potential between your left and right hands gives the peak of the big spike, and there’s one spike per heart beat, so we’re looking at 7 heartbeats here. When the ventricles are completely depolarised there’s no potential difference across the body, and the signal goes relatively flat again, before the lower and wider big bump relating to ventricles repolarising (going back from high to low voltage ready for the next beat and starting the relaxation of the muscle). Then there are longer flat bits where nothing happens until my next heartbeat. (Aside, the little bump before the big spike corresponds to the atria activating – the little chambers at the top of the heart that pump blood into the ventricles)
In the middle of the second ECG from wikipedia we see a kind of rhythm disturbance (arrhythmia) called Torsade de Pointes (TdP). Here there are no ‘flat bits’ at all, suggesting waves moving constantly around the heart, and the oscillatory nature with the spikes getting higher and lower over about 10 spikes suggests some sort of shifting axis of rotation or drifting spiral activity (“torsade” = French for “twist”) as symmetry is broken in different ways with different wave directions.
Looking at the timescale (the medium sized squares in the background are the same scale on both plots – 0.2 seconds wide each) we see how the TdP spikes occur at a rate of pretty much one every 0.2 seconds, this 0.2 seconds is not really long enough for each cell to recover from being activated, suggesting activation chasing repolarisation constantly, round and round the heart. So at all times throughout the TdP episode somewhere in the ventricles is recovered whilst other bits are activated. This is bad news, because the heart doesn’t pump efficiently, or at all, when waves of activity are going all over the place like this, as opposed to nicely coordinating muscle contraction and relaxation with the whole of the ventricles being activated at once. Blood pumping will almost stop completely when the ECG looks like this, giving you just a few minutes to survive unless you can snap out of this arrhythmia spontaneously, which does happen sometimes. Here a shock is applied, sending the voltage off the axis at the end which basically forces the whole heart to depolarise at once and gives the heart a chance to break the TdP cycle and get back into a healthy rhythm (this is what all defibrillators try and do).
We are particularly interested in TdP from a drug safety point of view, as quite a number of drugs introduced in the 1990s and early 2000s increased the risk of TdP happening. Even in the ‘riskier’ drugs TdP was very very rare (typically 1 TdP event in 10,000 patient-years of dosing or something like that) but when millions of people take a drug regularly, those TdP events do occur in a significant number of people. So for things like a hayfever drug it was not worth the risk* and they were pulled off the market. A lot of effort has gone into making sure this doesn’t happen with new drugs today, without being overcautious and ruling out potentially good drugs, which is what the textbook chapter discusses from a computational modelling standpoint.
So I hope the chapter provides a relatively accessible introduction to computational cardiac electrophysiology modelling for assessing pro-arrhythmic risk of new compounds, for both modellers and experimental safety pharmacologists.
For computational modellers, there are a couple of bits in the chapter that I hope you read in particular:
Firstly, it’s the first time I’ve put down in a publication the argument here from an earlier blog, about the usefulness of ever-increasing realism in simulations being limited by rarity of TdP that I mentioned above. In a nutshell, with enough realism the simulations will show TdP too rarely to be useful, so we need simplified models, and it’s not obvious what degree of simplification is best!
Secondly, and somewhat in tension with the previous point, it would still be very nice to understand more about tissue-level arrhythmia mechanisms. What is actually going on in the heart to start and sustain an episode of TdP? It would be nice to model the TdP ECG arising, see how the waves move around the heart, then have a look at what is going on at a cell and even ion channel level.
We could then think about (or just simulate with brute force!) what drug properties make starting and sustaining TdP more or less likely, particularly looking at what drug properties are important for tissue-level relative to those that determine simpler cell-level properties like action potential duration or ‘qNet’ from the CiPA papers that we already know work quite well.
Those simulations are done on a 25×25 grid of 625 cells, and appear to capture a surprising amount of what might be going on in terms of wandering rotors that give rise to this characteristic oscillatory waveform in Torsade de Pointes.
Below is an example I pulled out of a much more recent paper on simulating TdP risk with whole ventricles models, with millions of nodes in the mesh that each have an action potential model attached. So here is a computational mesh and a simulated ECG underneath
A
We seem to have lost the ‘continual’ spiking activity in the ECG – lots of flat bits appear here which is a bit un-TdP like to me and suggesting 50% of the time there are no waves anywhere. So perhaps this is not quite such a good mechanistic representation of what’s going on in TdP?
In another example in this simulation below, the rapid spikes in the pseudo-ECG don’t appear to have the long slow ‘twisting’, and they turn out to relate to the red-arrow membrane voltage, at -30 to +30mV oscillations (not repolarizing down to the usual -80mV at all) which is an interesting prediction, but not what other simulations do as far as I know (or optical mapping of TdP-like arrhythmias suggests as far as I know – comments pointing to examples of cellular action potential recordings/optical mapping during TdP episodes are very welcome!).
I’m not trying to pick on these papers in particular, most of the whole-organ sims I’ve seen show these kinds of differences you might not want. So, alongside a few other slightly provocative comments (that I hope spice it up and make it worth a read) you’ll find this sentence in my textbook chapter:
“Strikingly, the ECG-like waveforms in [Abildskov & Lux] appear to be more realistic representations of Torsade-de-Pointes than those in some of the recent publications using whole ventricle three-dimensional simulations in realistic geometries that use millions of action potential models, suggesting that it is worth revisiting and examining the basic mechanisms that we need to observe Torsade-like electrocardiograms.”
There is a notable exception to this that I know about, very happy to learn about more in the comments, which is some work done by Jeremy Rice at IBM with their cardioid simulator which I first saw in 2013. The video below is hosted on that cardioid link:
So the good news is that quite realistic TdP ECGs are possible to simulate. The bad news is that sadly Jeremy is no longer with us, and I haven’t been able to find anyone with the code to run this simulation, and although Cardioid was introduced here, I don’t think the simulation above ever appeared in a publication or showed what the membrane voltages looked like underneath. I remember Jeremy mentioning in person using “M cell islands” when he showed this, which are controversial let’s say. But whatever the setup was, it evidently resulted in an arrhythmia in this video that captures a lot of what is going on in TdP.
Another honourable mention is “R-From-T as a Common Mechanism of Arrhythmia Initiation in Long QT Syndromes” by Michael Liu and co. who have one or two TdP-like ECGs, they also included a Purkinje system. Below is a screenshot from one of their supplementary movies in one of their most TdP like sims, where we see that voltage does seem to go back down to circa -80mV. Seems a closed source CUDA code was used for this so difficult to play more.
For example in the above we can see the Purkinje system on the right, normally this carries the activation from the atria to ventricles through these specialised conductive fibres. But you can get waves going back into the Purkinje system and popping out again to keep arrhythmic behaviour going – is that important/necessary here?
So consider this a friendly challenge to big-tissue-simulation people. It would be nice to assemble a review of what sort of cell properties/geometries lead to what sort of TdP-like arrhythmias, what do we need to have in the simulations? And once we have established what mechanisms are necessary/sufficient, can we make sure open source codes are all published with the necessary meshes etc. so that people can reload, run and investigate them further…
*people have actually debated that: terfenadine was the first antihistamine that didn’t make you drowsy, so arguably taking it off the market could have led to a significant or even larger number of deaths (e.g.) from people falling asleep at the wheel when they reverted to the previous drugs. Drug safety and risk/benefit analysis is tough. Luckily, within a couple of years, drug developers figured out that a metabolite of terfenadine was also an effective antihistamine, kept its non-drowsy property, but had very low TdP risk, and that drug is still in use today (fexofenadine).
We are looking for new members to join our Wellcome-funded team of cardiac electrophysiology modellers, to develop mathematical models of ion channel currents and cardiac cells for assessing the safety of new pharmaceutical drugs. You’ll be joining a research team including me, postdocs, PhD students and a Research Software Engineer.
Two posts are available, and these are fixed-term research positions available from now until the end of January 2025.
A Senior role is available for experienced postdoctoral researchers, which is appointed on the same pay grade as a Lecturer/Assistant Professor; whilst the other will be suitable for you if you have just finished/are finishing a PhD or have a few years of postdoc experience.
We are looking for experience in ANY ONE OF:
Mathematical modelling of a biological system involving numerical simulations, e.g. ODE, PDE or stochastic/agent-based modelling.
Statistics/data science – fitting mechanistic models to real experimental data and performing uncertainty quantification/inference in a frequentist or Bayesian framework. Experimental design and/or considering model discrepancy are desirable.
Experimental electrophysiology (e.g. manual patch clamp) – for instance, using voltage-clamp protocols to characterise an ion channel current. In this case you will have a desire to combine extended overseas visits to collaborators’ labs to undertake your own experiments with learning to do your own experimental design and computational ion channel modelling here in Nottingham.
Your particular focus (depending on the strengths and interests of the successful candidates) could include:
Use of dynamic-clamp (real time simulation/experiment interaction) in model building.
Cell-specific electrophysiology model construction.
Working on methods for experimental design, to optimise parameter identifiability, but also to perform model selection, minimise the influence of experimental artefacts, and assess/forecast the difference between the model and reality.
Building on the Cardiac Electrophysiology Web Lab (https://scrambler.cs.ox.ac.uk/) to record and reproduce the process of fitting a model to data and testing it.
I think that our main problems in terms of “making quantitative predictions” in the cardiac modelling field are related to deriving biophysically-based mechanistic models from experimental data (replacing what are often subjective modelling choices with automated algorithms to make this reliable and reproducible). Plus making future predictions with appropriately quantified uncertainty due to all the factors about which we’re uncertain (not just parameter uncertainty…).
You’ll find a lot of our open questions discussed in various past posts here on this blog and in our recent publications.
We’ll be working closely with: industry labs; pharmaceutical regulators (including the FDA); and academic labs (in particular Teun de Boer’s lab in UMC Utrecht in the Netherlands and Adam Hill & Jamie Vandenberg‘s labs in Victor Chang Cardiac Research Institute, Sydney, Australia). So candidates must enjoy teamwork, collaborative inter-disciplinary projects, and be prepared to get into the lab for a few weeks to really get to grips with the experiments we are trying to use.
Informal enquiries to gary.mirams@nottingham.ac.uk are welcome, but applications must be via the link above. The closing date is Friday 27th January 2023
One of my UK students is going to visit the USA soon, so I promised this overdue blog.
As a Brit visiting the USA there are certain things that can leave you a bit baffled, that just work differently (I’m a legal alien). There is nothing more embarrassing to us than causing minor inconvenience as a result, so here are some pointers (mostly applicable in Canada too!).
Money
Taxes – it is almost impossible to work out the cost of anything before you buy it in the USA, either on price tags or menus. Various state and federal taxes are added at the till, probably to rub them in your face so that you aren’t tempted to become too socialist. So don’t try to buy something with a $10 price tag if you only have $10 in your pocket. I don’t know whether Americans are all great at mental arithmetic, or whether they are happy just estimating and tend to use credit cards all the time.
Tips – it’s much more expected in USA to give (what seems to us) a generous tip, about 15-20% of the pre-tax bill for normal service. Rather than just tipping table waiting staff, who are pretty much the only people to reliably get tips in the UK, you tip a lot more people. The ones most likely to catch you out are: a dollar for each drink for bar staff (even if you go to the bar yourself or sit at the bar), the hotel porter who grabs your suitcase for you if you go to a hotel that is a bit posh, and taxi drivers (Uber is useful here nowadays to include a sensible amount easily). There’s actually a lower minimum wage for staff who can get tips in most states in the USA, so it’s definitely not cricket to give just UK tips!
The Bill Ritual – in the UK you look at the amount, tap the machine for contactless payment and you are done (or if it is over £100, put your card in the machine and type in PIN). In the USA there is The Ritual for paying for things in cafe/restaurant/bar/hotel which takes some getting used to:
Ask for the “check” and wait for them to bring the bill over. I don’t know what they call cheques.
Put your debit/credit card with the bill and display prominently on the edge of table.
Wait a few minutes for them to take it away and bring it back (note to Americans, don’t ever let your credit card out of your sight in the UK, you must be a lot more honest than we are). Presumably card details or pre-authorisation are taken behind the scenes.
There will be gaps at the bottom of the bill when they bring it back. Write on a Tip and then Full Amount (to save on arithmetic I sometimes just put a bigger round full amount and don’t worry about the tip line, I do not know if this is breaking convention but it seems to satisfy The Ritual).
Sign your name (in the UK before we had chip and pin, staff used to check your signature against the one on the back of your card, but again Americans are more trusting and don’t seem to bother with that step as you’ve already got your card back at this point).
There are two copies of the bill, one for you and one for them, repeat 4 and 5 on the other one.
Stick one copy in your wallet and leave the other one on the table.
You can then leave the venue immediately without talking to anyone if you are confident you have mastered The Ritual. But you can hand it over and ask for confirmation it is all OK if you are feeling British. I recommend the latter until you feel you have mastered The Ritual.
Getting some dollars – Don’t bother getting any dollars from a Bureau de Change in the airport, they give you an awful exchange rate. It is always a better exchange rate with your debit card in cash machines in the airport when you land. A free Monzo account charges 0% currency fees when you pay by card and lets you get a bit of cash out of machines for free each month (£200 worth of cash every 30 days, and 3% after that). For comparison, with HSBC it is 2.75% on all debit card transactions and at least 4.75% on cash machine transactions, and more for credit cards. Even if your bank does charge currency exchange fees, they will still be less than a Bureau de Change, so use the cash machine anyway!
Cash Machines 1 – when you put your debit card in a cash machine in the US it will ask you an unfamiliar question: to ‘choose between Checking/Savings/Credit‘. If you press the wrong button the withdrawal might fail. ‘Checking‘ seems to work, I’ve no idea whether Americans have one card for three accounts or what. You might want to warn your bank you are going abroad so they don’t stop your card when you get there and leave you in a pickle (can usually do this via internet banking, or you don’t need to bother with this for Monzo).
Cash Machines 2 – If a cash/card machine asks whether you want to bill your card in GBP say “No use dollars”. You will always get a worse exchange rate than your bank uses if you say yes.
Eating
What cheese would you like? You could be asked this at cafes/restaurants/bars and in particular in a classic roadside diner or burger joint. In the UK this question would make no sense – we would reply with things like “Wensleydale”, “Stinking Bishop” or “Double Gloucester” or hundreds of other possible cheeses and the proprietor could not possibly stock even the sensible/common replies. In the USA as far as I can work out there are just 3 cheeses: American (the luminous square squishy plastic stuff); Cheddar; and Swiss. Cheddar is the safest option.
How would you like your eggs? In the UK the answers are “boiled”, “fried”, “scrambled” and (if you are somewhere posh) “poached”. That is pretty much the same in the USA, but being the land of customer service, there are extra options to say exactly how you would like fried eggs cooked as well:
“Sunny-side up”: fried, but not flipped, very soft yolk (the normal UK style of fried egg).
“over-easy”, “over-medium”, or “over-hard”: fried then flipped and left long enough that the yolk is still runny, slightly soft, or hard, respectively.
Drinking
Take passport to bars – because drinking age is 21 it seems like the policy is “ask for ID if they haven’t got grey hair” in many bars. So you could well be asked for ID even if that hasn’t happened in the UK for years.
Free refills – definitely an improvement on the UK! Nearly every pub/diner/restaurant will give you free refills on “soda” (that is fizzy/soft drinks) and you just ask for a refill as many times as you like. Generally waiting staff will periodically ask if you’d like a refill, and it is safe to just say yes. There might be some etiquette in terms of a limit that I don’t know, but nobody’s been visibly annoyed about this even when having as much as I could possibly drink.
Electricity
Electric plugs – no most things aren’t earthed, yes it is normal for live terminals to be visible when the plug dangles out of the wall, and for you to see sparks when you plug things in. It’s a wonder everything in the US hasn’t burnt down. If you want to see a well-designed plug, visit the UK! You’ll want to buy a plug adaptor before you go.
Walking
In most/all of the USA it is illegal to “jaywalk” (just cross the road wherever you like), and you have to use a pedestrian crossing. People do actually get told off and fined for this by the police.
Personally I find this an annoying-on-a-daily-basis infringement of my civil liberties. Presumably it is motivated by community safety overriding personal freedom. Strange to a Brit that people can be perfectly happy being denied the right to cross the road and at the same time say they absolutely need the right to carry guns about. It is a strange place of contradictions.
On another note, as a pedestrian, don’t be surprised when cars rush up to you whilst you are using a crossing. It is a bit unnerving but they should always give way if you are walking on a ‘WALK’ symbol! Which brings us to…
Driving
Turning at cross roads – most people know it is legal for drivers to turn right at a red traffic light in the US as long as nothing is coming (exceptions being New York City or when there is a red right arrow). What is not common knowledge is that unlike UK there is no separate “pedestrians cross” in the traffic light sequence, and so pedestrians take their chances when some cars are moving towards them. That means it is NOT SAFE to turn on a green light when there are no cars in the way like it would be in the UK; you might kill a stream of pedestrians who have the green man/WALK symbol for walking across at the same time as you do to drive across their crossing! So unless you are going straight ahead you need to give way to pedestrians, even on a green light. Counter-intuitively, you won’t kill any pedestrians on the right if you do turn right on a red light, because they won’t be walking across then. Confused? You will be. Just be very careful. Luckily roads are wider and drivers tend to be a bit slower and more relaxed (because they drive automatics that don’t accelerate very well is my guess). Canadians are even more relaxed, and there you should give way to any pedestrian anywhere as far as I could work out.
Traffic lights and pedestrians at USA crossroads
Quirky petrol pumps – some US petrol stations, generally older ones out in the sticks, have pumps where you have to lift a handle after taking out the nozzle, like this. There are none of these in the UK! If you don’t know, you will stand there like a lemon for quite a long time wondering why the pump won’t work, before you finally give up and embrace the embarrassment, talk to the attendant, and have them look at you like you’ve never filled up a car before. They also call petrol “gas”. USA also use different octane calculation so their 3 choices (87 Regular, 89 Plus, 91+ Super) and are not as rough as they sound to UK ears (where the options are normal 95 or super 97+): consult inside of petrol cap to see which you should use. Incidentally, USA also has a smaller gallon than the UK (3.785 versus 4.546 litres), so your miles per gallon are not lower just because of inefficient “gas-guzzling” automatic cars!
Immigration
Take a pen on the plane – you have to fill in a form to give to the customs people when you land, and it wants to know where you will be staying, so also make sure you have written that down somewhere before you get on the flight, or in case you run out of phone battery by the time you get there. Also take phone charger and adapter in hand luggage so you can charge it if your luggage gets lost!
ESTA – a few weeks before you go be sure to get your ESTA (electronic visa waiver). Don’t just click the top link after googling: it will be a scam site taking a cut for no good reason, or just stealing your money and details! Look for the one with web address ending ‘.gov’.
Global Entry – If you are going to the US fairly regularly as a UK citizen, consider paying a bit more for Global Entry. You first have to pay for a UK background check (£42), then apply to US system ($100). You also need to be in the USA to activate it: after a discussion with/grilling by a border agent, they register your passport to allow you to use the automated Global Entry gates like the locals, and then you can save yourself an hour or more in immigration queues every time you visit, for the next 5 years.
They don’t mean to be rude
You may arrive in the USA and ask at an information desk “Excuse me, would you mind telling me how to get to…?”, they might say something like “OK, here’s wattcha gonna do!“. Try and resist the urge to say “I will be the judge of that, my good man“, it is just their abrupt way and they aren’t trying to be rude.
Anything else I’ve missed? Let me know in the comments!
We are looking for new members to join our Wellcome-funded team of cardiac electrophysiology modellers, to develop mathematical models of ion channel currents and cardiac cells for assessing the safety of new pharmaceutical drugs. You’ll be joining a research team including me, postdocs, PhD students and a Research Software Engineer.
Two posts are available, and these are fixed-term research positions available from now until the end of January 2025. A Senior role is available for experienced postdoctoral researchers, which is appointed on the same pay grade as a Lecturer/Assistant Professor; whilst the other will be suitable for someone who has just finished a PhD or has a few years of postdoc experience. We are looking for:
Either for people with experience in computational modelling of biological systems.
OR for people with experience in statistics/inference for mechanistic models – in which case no previous experience of biological modelling is required.
I think that our main problems in terms of “making quantitative predictions” in the cardiac modelling field are related to reliably and reproducibly deriving biophysically-based mechanistic models from experimental data, and then making future predictions with appropriately quantified uncertainty.
You’ll find a lot of our open questions discussed in various past posts here on this blog, but here are a few questions that we are tackling in this project. You don’t need to be able to do any/all of this before you start – we are still working on all of it…
Modelling drug-ion channel interactions, and their effects on ion currents. With a focus on figuring out exactly how drugs are binding (especially state-dependence of binding) and the consequences of this in whole cell (action potential) models.
Parameter inference and model selection: Deciding appropriate baseline models for the ion currents (see my talk at Banff research station on this topic), and parameterising these models effectively is a big pre-requisite for our research. There are open challenges on how to do model selection as well as parameterisation, whilst accounting for all models being imperfect. Building appropriate noise/observation models for use in likelihood-based methods is an interesting part of this (just sum of square errors probably doesn’t really do the job here!).
Designing experiments to get more information for the above tasks, which we’ve been working on recently in these papers– sinusoidal protocols, high-throughput model building. In particular in the new roles we’ll be adapting these for models of how drugs bind to ion channels, and making sure that they can run on high-throughput automated machines. There are open challenges in how to design these experiments for (global) parameter optimisation, model selection, model validation, to minimise experimental artefacts, and to assess/capture/model the discrepancies.
Considering all of this in a probabilistic/statistical framework that accounts for uncertainty and variability in a lot of different aspects:
our datasets due to experimental artefacts,
model parameters,
model structures/equations themselves,
discrepancy between models and reality,
our subsequent drug safety predictions.
And working on open source software and web tools that everyone can use for these tasks.
We’ll be working closely with: industry labs (in particular at GlaxoSmithKline and Roche); pharmaceutical regulators (including the FDA); and academic labs (in particular Teun de Boer’s lab in UMC Utrecht in the Netherlands and Adam Hill & Jamie Vandenberg‘s labs in Victor Chang Cardiac Research Institute, Sydney, Australia). So candidates must enjoy teamwork, collaborative inter-disciplinary projects, and be prepared to get into the lab for a few weeks to really get to grips with the experiments we are trying to use.
Regular readers might know I’m one of the developers and users of Chaste – Cancer, Heart and Soft Tissue Environment, a C++ library for computational cell biology and physiology problems including cardiac simulations, lung airway simulations and individual-cell based modelling.
I’m pleased to say that a BBSRC grant led by Alex Fletcher in Sheffield, Dave Gavaghan in Oxford and me in Nottingham was awarded recently to support Chaste development as a resource for biological modelling. It funds a research software engineer (RSE) half-time in each institution – click to find out more about the RSE role if you aren’t familiar with it. Because it’s a cross-institution grant there will be a lot of teamwork involved.
In Nottingham, we have teamed up with the Digital Research Service, which houses a lot of Nottingham’s RSEs to offer a full time post for 30 months, by combining with a role to support researchers in getting their codes ready to take advantage of the UK Midlands (Tier 2) supercomputer called Sulis. (Tier 2 means it is bigger than the Tier 3 supercomputers in individual unis, but smaller than the national Tier 1 supercomputer Archer).
Chaste is a big and mature piece of software in scientific research terms, development began in 2005 and it has lasted so well because rigorous software engineering was applied from the start – including version control, unit testing, memory testing, etc. We describe that all in detail in a 2013 PLoS CB paper if you’d like more of a flavour of how Chaste has been developed, and what Chaste does.
SBML import for cell cycle/signalling pathway models (analagous to the CellML import we already have for cardiac models).
Interfacing with inference software in R, Python, etc.
Lowering barriers to entry with Docker containers, Jupyter notebooks and workshop material.
Supporting researchers in using Chaste for scientific studies.
At Nottingham we’ll focus on SBML import and interfacing with other software, but will get stuck in to all the other tasks as well.
Here’s a link to the full ADVERT AND LINKS TO APPLY, deadline is 14th Feb. I am happy to take informal questions/enquiries on the Chaste side of the role at gary.mirams@nottingham.ac.uk, and Maurice Hendrix (Maurice.Hendrix@nottingham.ac.uk) is another RSE who will be involved in Nottingham who can answer questions on both sides of the role and working in the Digital Research Service.
(Post edited: to reflect that abstract submission is closed and update link to late registration)
On Wednesday 10th November 2021 we will be holding an online workshop dedicated to the in-silico modelling aspects of the Comprehensive in-vitro Pro-arrhythmia Assay (CiPA). As in Toronto 2017, this will be a Satellite Meeting to Cardiac Physiome 2021.
If you aren’t familiar with this effort, CiPA is an attempt to replace the pre-existing electrocardiogram QT interval-based clinical pro-arrhythmic safety assessment of potential new drugs (because this is late in drug development, expensive and not specific – returns many false positives). The new CiPA risk assessment will “not [be] measured exclusively by potency of hERG block and not at all by QT prolongation” and a cornerstone of this is a mathematical model-based assessment of pro-arrhythmic risk based on ion channel screening.
To inform the cardiac modelling community about progress within the CiPA initiative.
For the FDA modelling team to get feedback on their work to date.
To draw attention to other new academic or industrial research in the area.
To discuss the next steps for CiPA’s modelling efforts.
To spark more research and collaborations in this area.
This will be an online meeting for the international community. To make it accessible across time zones, most of the talks will be pre-recorded and available to view in advance – with live questions and discussion on 10th November.
Free registration for the meeting is open now and will continue to be available until 9th November 2021.
Please note you will also be automatically signed up to the main Cardiac Physiome meeting on 11-12th Nov too, but this is also free and hopefully interesting. In particular industry scientists might also wish to attend two other Cardiac Physiome satellite sessions on ‘Cardiac Modelling in Pharma: Quantitative Systems Pharmacology (QSP)/Quantitative Systems Toxicology (QST)‘ and ‘Industry Software/Computational Methodologies‘.
We hope as many people as possible can get involved, please pass on this invitation to anyone who might be interested.
Hope to see lots of you there,
Gary Mirams (University of Nottingham) Zhihua Li (FDA)
It was quite a challenging thing to write, because tons of people have suggested tons of ways of doing this, and you could spend a whole PhD thesis comparing different optimisation and inference algorithms for the tasks involved.
But I think it’s much more important to learn the principles, tips and tricks and then you can apply them to use of any particular optimisation algorithm and dataset. So instead we chose to do it a bit differently, and turn it into a “what we wish we’d known when we started” primer on parameter fitting for ion channel and action potential modelling, which hopefully also refers you on to most of the work you might want to find.
Here I’ve distilled out some of the main themes I think we should think about when fitting models:
Overfitting, training and validation, as I’ve talked about on this blog before.
Identifiability, we have a really nice example of what can go wrong without it in an ion channel model in Figure 3 of the new paper.
Parameter Transforms – make a surprising amount of difference to even simple optimisation problems, as seen in Figure 8 which uses a simple dose-response curve as the example. We included suggested transforms for ion channel rate parameters, as seen in Fig 3 of Michael Clerx’s “Four Ways to Fit An Ion Channel Model” paper, and there is much more on the relative performance of an optimiser with different transforms in the supplement of that paper. We’ve also included some that we found useful when fitting conductances in action potential models.
Priors/Constraints – mainly discussed in the “sinusoidal wave” paper and “4 ways to fit“, it can be very sensible to constrain parameters with either a transform or a prior to only take physical values and this can help an optimisation algorithm. A ‘hard’ constraint might be helpful too as this prevents numerical schemes running into trouble when they hit parameters that give ridiculously fast rates or big/small numbers.
The benefits of fitting to whole trace data – rather than derived summary statistics, and particularly derived summary statistics that include post-processing such as time constants, as shown in Fig 11 of “4 ways to fit…” these can really make the objective surface a nightmare.
And last but certainly not least – Synthetic data studies. I’ll go out on a limb and say it is ALWAYS a good idea to simulate some data that looks like the stuff you want to fit to, and see what happens when you try to recover parameters from that. We always learn something useful whenever we do this, whether it is about identifiability of parameters, robustness of the optimisation algorithm or suitable transforms to use.
Anyway, hope there is some useful stuff in the paper for all cardiac model makers. Comments welcome below!
N.B. Applications for this position are now closed.
We are offering a 3 year position as a research fellow in statistical inference for mechanistic models. This is offered at either Postdoc or Senior postdoc level (equivalent grade to Assistant Professor) here in the Centre for Mathematical Medicine & Biology and Statistics & Probability groups, based in Mathematical Sciences, University of Nottingham.
We have started a Wellcome Trust funded project entitled “Developing cardiac electrophysiology models for drug safety studies”. This is an exciting opportunity to get involved in a substantial research team that will consist of at least two new postdoctoral research associate positions, together with Dominic Whittaker, me and a dedicated research software engineerMaurice Hendrix in collaboration with colleagues in statistics & probability within Nottingham (in particular Simon Preston and Theo Kypraois).
Over the last 10 years I’ve been doing cardiac modelling, I have come to think that our main problems in the field are related to reliably and reproducibly choosing and deriving biophysically-based mechanistic models from experimental data, and accounting for uncertainty whilst doing this. There are quite a few challenges involved, so many challenges that we held a month long residential programme on the challenges called the Fickle Heart at the Newton Institute in Cambridge this past summer (videos from final workshop available here).
You’ll find a lot of our open questions discussed in various past blog posts, but here are a few that we will be tackling in this grant:
Deciding appropriate baseline models for the ion currents (see my talk at Banff research station on this topic), and parameterising these models effectively is a big pre-requisite for our research, which we’ve been working on recently in these papers – sinusoidal protocols, high-throughput model building. Open challenges on how to do model selection as well as parameterisation, whilst accounting for all models being imperfect. Selecting appropriate noise models for use in likelihood-based methods is an interesting part of this.
Designing experiments to get information on drug binding to ion channels, and making sure that they can run on high-throughput automated machines. Open challenges in how to design these for (global) parameter optimisation, model selection, model validation, and to assess/capture/model the discrepancies.
Considering all of this in a probabilistic/statistical framework that accounts for uncertainty and variability in a lot of different aspects:
our datasets and the underlying biological systems,
model parameters,
model structures/equations themselves,
discrepancy between models and reality,
our subsequent drug safety predictions.
We’ll be working closely with: industry labs (in particular at GlaxoSmithKline and Roche); pharmaceutical regulators (including the FDA); and academic labs (in particular Teun de Boer’s lab in UMC Utrecht in the Netherlands and Adam Hill & Jamie Vandenberg‘s labs in Victor Chang Cardiac Research Institute, Sydney, Australia). So candidates must enjoy teamwork, collaborative inter-disciplinary projects, and be prepared to get into the lab for a few weeks to really get to grips with the experiments we are trying to infer things from.
If any of that sounds interesting to you – please do apply! Feel free to contact me with informal enquiries.
Hodgkin & Huxley did some incredible work in the 1930s-50s on ion currents flowing through biological membranes. Despite not knowing what an ion channel was, they managed to work out an incredibly accurate predictive mathematical model for the currents that flow through them, and solved the differential equations numerically on a hand calculator. These models are still fundamental to a lot of electrophysiology work – we are still publishing Hodgkin-Huxley style models of particular currents (we just tried to parameterise them better)!
So there are a few points to raise about good old Hodgkin-Huxley models in this blog post!
There’s a recent set of papers updating the original papers for modern conventions.
I’ve sketched how (in the case of ‘powered’ gates) different equivalent Markov models can be written down for the same Hodgkin-Huxley model.
A widely followed but rarely-expressed convention for the Markov diagrams.
Updated Papers
Recently my colleague Angus M Brown at the University of Nottingham published some updates to the landmark (and Nobel-prize winning) series of papers published in the Journal of Physiology in the 1940s-1950s by Hodgkin & Huxley:
I think this is great – there have been changes in conventions since the original papers were published (in particular the sign of Voltage/membrane potential, which is also now relative to earth rather than relative to resting potential). The changes are discussed in the editorial accompanying the papers.
So there is an updated set of equations for the squid axon action potential model in the ‘translated’ 1952 paper. I’d strongly recommend pointing students and colleagues towards this translation instead of the original paper, as I think it resolves a lot of confusions that can arise in trying to do all these convention changes (which you might not even be aware of!) in your head.
Equivalent Markov Models for Hodgkin-Huxley Structures
Quite a few people have asked me how the equivalence between Hodgkin-Huxley gating variables and Markov models works. So I thought I’d sketch it out – my effort is in Figure 1.
Figure 1: Two equivalent Markov Model structures for a Hodgkin-Huxley squared gate. Firstly two Hodgkin-Huxley gates multiplied together can be represented as a square Markov diagram, with the second gating process acting identically regardless of whether the first gating process was ‘closed’ or ‘open’. The rest of the diagram shows a simplification that can be made due to symmetry if these gating processes are identical (i.e. a squared gate like m^2) to reduce the Markov diagram to a linear chain which is one state smaller with related rates and states.
The same procedure holds for higher powers, so that an m^3 Markov model has three closed states and rates of 3α, 2α, α on the top and β, 2β, 3β on the bottom.
Now you haven’t really gained anything by re-casting like this (as it adds an equation in the case I’ve showed above). But if you come to modify the model so that something (like a drug) is interacting with just one of the states and breaking all the independence and symmetry in a Hodgkin-Huxley model, then being able to work out the Markov Model is necessary to simulate what happens then.
A convention for Markov diagrams of voltage-gated ion channels
It took me quite a while working in the field of cardiac electrophysiology to realise that an implicit (and, as such, not always followed!) convention in these diagrams is to have voltage arranging the states, as I’ve sketched in Fig 2. So rates which increase as voltage increases go right/up and rates which increase as voltage decreases go left/down, following this convention arranges the states for you in a consistent way.
Figure 2: a convention to lay out these Markov diagrams such that rates which increase with increasing voltage go from left to right and bottom to top. This is useful as one can tell at a glance “if voltage is high, the states towards the top right will be more occupied” and “if voltage is low the states towards the bottom left will be more occupied”.
So if you have a choice* try to present the diagrams such that increasing voltage pushes you right and up!
*sometimes, for reasons of clarity, it is nice to present bits of the diagram as mirror images, in which case I’ll let you off.
Mathematical Matters of the Heart 