Englishman in New York (travel tips for Brits in the USA)

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:

1. Ask for the “check” and wait for them to bring the bill over. I don’t know what they call cheques.
2. Put your debit/credit card with the bill and display prominently on the edge of table.
3. 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.
4. 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).
5. 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).
6. There are two copies of the bill, one for you and one for them, repeat 4 and 5 on the other one.
7. Stick one copy in your wallet and leave the other one on the table.
8. 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.

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

Equally, 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!

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!

Postdoctoral Research Fellow positions available in our team (recruitment now closed)

Edit: applications 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. 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.

Here is the link to the full role profiles and application form: https://www.nottingham.ac.uk/jobs/currentvacancies/ref/SCI2061

Informal enquiries to gary.mirams@nottingham.ac.uk are welcome, but applications must be via the link above. The closing date is Sunday 3rd April.

Research Software Engineer (C++ and HPC) position available (recruitment now closed).

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.

The workplan for the Chaste grant includes:

• New features in the individual-cell based models (3D versions of vertex models, subcellular element and immersed boundary models – so Chaste will be able to do 3D versions of many different modelling approaches).
• Modernising the C++98 codebase to use C++17 and optimisations/improvements that allows.
• Taking advantage of GPGPUs via FLAME GPU.
• Create python bindings for the C++ simulator.
• 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.

2021 CiPA in-silico Modelling Workshop

(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.

Here is a link to a recent review paper on the in-silico modellling approach by the FDA modelling team leaders.

You can also click here to see a summary and PDFs of the talks that were given at the 2017 meeting.

The aims of this meeting are:

• 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.

CLICK HERE TO REGISTER

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)

on behalf of the
CiPA Steering Committee

Our new review on fitting cardiac models

A reasonably short post to let you know about our recently published paper in WIREs Systems Biology and Medicine on parameter fitting in cardiac ion channel and action potential models with David Christini. There is an accessible introductory news article Dom wrote about it on Advanced Science News.

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.
• Numerical convergence – with respect to parameter changes as discussed on the blog before.
• 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!

 

Job Available: Statistical inference for mechanistic models

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 engineer Maurice 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.
• Tailoring mathematical action potential models to particular cell types, to make predictions of what drugs might do in different species and cell types. Again, we think that doing more informative experiments (working with the Christini lab to build on this) will help a lot.
• 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.

You can apply online here: https://www.nottingham.ac.uk/jobs/currentvacancies/ref/SCI362219. The deadline is Tuesday 5th November.

Hodgkin-Huxley models and Markov equivalents

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!

1. There’s a recent set of papers updating the original papers for modern conventions.
2. I’ve sketched how (in the case of ‘powered’ gates) different equivalent Markov models can be written down for the same Hodgkin-Huxley model.
3. 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:

We now have updated classic #electrophysiology papers by Hodgkin, Huxley and Katz, so that the topics are much more understandable for students. Check out all the translations now: https://t.co/VLlNfKclRH pic.twitter.com/qvjyZwzisL

— Journal of Physiology (@JPhysiol) July 15, 2019

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.

Three potassium channel modelling papers

Just a quick note to tell you about our latest batch of papers in the “Heart By Numbers” special issue of Biophysical Journal which arose from a meeting in Berlin last year. They are all about I_Kr, the rapid-delayed rectifying potassium current carried by the hERG potassium ion channel, which is important in drug safety, as pharmaceutical drugs can block it and lead to dangerous disturbances in your heart’s rhythm. The papers are all open access and supported with open code and datasets (see our Github site).

First paper was led by Michael Clerx and is called “Four Ways to Fit an Ion Channel Model” we thought that a recipe or tutorial about how to make a Hodgkin-Huxley model for a voltage-gated ion channel was needed: why the protocols for ‘activation’, ‘deactivation’, ‘inactivation’ etc. are designed the way they are, how you can assemble data from them to fit time-constant and steady state curves, and which numerical schemes are sensible to use for doing this. In a lot of ways this paper is the partner for Kylie’s sinusoidal clamp paper that we published last year, which explains how people have typically done it, and then goes on to weigh up the pros and cons by trying the four different methods on the same dataset. The basic ways are:

• Method 1: Fitting the model’s analytic equations for steady-states and time constants (e.g. m_∞ and τ_m for a gating variable m) directly to experimentally-derived current-voltage (I-V) and time-constant-voltage (τ-V) curves. This is generally a bad idea if you have more than one gate (for IKr at least, their timescales of gating aren’t as independent as this concept really needs them to be – e.g. inactivation mucks up your measurement of activation). You can show the problem quite easily by running a model forwards with some assumed gating properties. You then simulate the experiment and its post-processing to emulate experimental measurement of steady state and time constant gating properties – you get back different ones than the underlying equations suggest! But this method remains widely used in the literature.
• Method 2: one way round the problem above is simulating the experiments and then deriving I-V and τ-V curves by postprocessing simulated currents, and then fitting these to data. So you get a model whose parameters are consistent with the data. BUT the optimisation problem becomes very hard because of the postprocessing steps to derive I-V and τ-V curves introducing more jumps and discontinuities in the objective function. There can be ‘divide by small number’ effects in the postprocessing, or long time constants fitted to flattish data, that lead to a lot of error on certain summary curve data points too.
• Method 3: Simulating the traditional experiments and fitting directly to experimental current traces. This works surprisingly well, we had thought this optimisation would be difficult and need careful consideration of weighting traces and suchlike, but even a simple approach worked well, and better than Methods 1 and 2.
• Method 4: Kylie’s sinusoidal clamp method. Experiments are very short (hence easier than Method 3), fitting is very simple and reliable.

A few highlights to look out for in this one:

• A phase-plane plot method really helps understanding of the traditional protocol design, see Fig 1:

Fig 1. phase-portrait approach to understand traditional voltage clamp protocols for a two gate (activation/deactivation and inactivation/recovery) Hodgkin-Huxley model phase plane. A-F one for each voltage-clamp protocol. See the paper supplement for a slightly more mad 3D one with voltage as the z-axis!

• Some tips and tricks for reliable parameter optimisation (including the role of parameter transforms, sensible bounds for voltage-dependent ion channel rate parameters, and the solver tolerance issue discussed on this blog before).

The second paper is by Chon Lok Lei, he created a new Method 4 discussed above, but instead of using the sinusoidal clamp, made a similar ‘Staircase Protocol‘ out of conventional steps and ramps which was able to run on a high-throughput 384 well Nanion SyncroPatch machine. This has some distinct advantages: Chon Lok got 124 good cell recordings, in one run of the machine, in about half an hour; compare this to manual patch where getting 10 nice stable cell recordings might take a week or more! So we hope this will let people create models of variants of this channel (e.g. mutations) and what happens to it under drug action much more easily than before. Some important points:

• Fitting the same model using the staircase method returned very similar parameter sets to our previous manual-patch sinusoidal study.
• There’s some nice mostly-automated quality control criteria used in addition to the usual series resistance, seal resistance and cell capacitance.
• There’s some work on leak current and drug-subtraction to isolate IKr that will be worth looking at if you want to repeat such escapades.
• We did 8 validation protocols alongside the staircase protocol that we used for fitting, and got some excellent predictions, for instance Fig. 2:
  

  Fig. 2 a zoom in on one of the panels in Figure 4 of Chon’s paper. Here the black trace at the top is the applied voltage clamp (actually made out of a series of linear ramps and clamps rather than a curve due to machine constraints). The blue trace is the recorded data in one of the 384 wells, and the red trace is the model prediction based on a fit to the Staircase Protocol when that was applied in the same well. The green areas show zoom in on the ‘spikes’ at the start of the action potential. Something we captured extremely well in the model which we weren’t necessarily expecting.

• A hierarchical statistical model allowed us to describe the variability that we saw fitting to data across all the wells.
• The paper includes the invention (we think!) of the ‘reversal ramp‘ to estimate error in applied voltage clamp, a special bit of the protocol designed to estimate an artefact in the experiment (a bit like a leak step does). Due to the parallel nature of the experiment and shared solutions/temperature this allows an estimate of this error in each individual well as shown in Fig 10 of the paper (small, but as we’ll see, maybe now the main source of error…).
• Some strong circumstantial evidence that the principal variability in kinetic parameters fitted to different cells is due to this voltage clamp error rather than extrinsic variability between cells (see Fig. 9 of the paper).

The third and final paper, again by Chon Lok, uses the Staircase Protocol method introduced above to examine the temperature dependence of the parameters we get back. In essence we repeat the experiment at five distinct temperatures, so we can plot out how they vary with temperature. We can then compare this with how they should ‘theoretically’ vary with temperature following either:

1. The commonly-used Q10 formulation.
2. The sometimes-used (what we called ‘typical’) Eyring formulation (not actually as per Wikipedia – a voltage-dependent term is added to the Wikipedia definition in previous ion channel modelling! See our paper for the typical definition).
3. The never-used in ion channel modelling (as far as we know!) Generalised Eyring formulation.

The punchline is that there’s strong evidence that Q10s are insufficient as they don’t give you any temperature-dependence on the parameter that governs the voltage dependence of the rate. But a strong dependence certainly appears in our refitted models. The typically-used Eyring formulation does confer some temperature dependence to this parameter, but is actually no better as the temperature-dependence can sometimes be constrained to be in the wrong direction (increasing with temperature instead of decreasing or vice-versa). The more generalised Eyring formulation, previously used in some electrical engineering battery applications, appears to work pretty well. So some significant consequences for any work that is relying on previously-used formulations for temperature dependence of voltage-dependent rate parameters.

If we are right, and the temperature dependence doesn’t follow a Q10, then we expect Q10 estimates to be protocol-dependent, and indeed we can explain some “this paper’s Q10 estimate was higher than this paper’s” (but not all) using our full temperature model with previously used protocols from the literature.

Our punchline is that you probably need to do the experiments at 37°C to be confident you are predicting well there.

In the discussion there are some interesting questions raised about whether the model breaking the first-principles ‘Typical Eyring’ formulation is actually a signpost that the model has some shortcomings/discrepancy, would a better mathematical model follow the first principles trends? Or is the need for a Generalised Eyring relation just a sign that the ‘single energy barrier’ model that the first principles rate equations assume is too simple for a large protein complex which may shift its preferred conformations with temperature. Open question!

Anyway, hope you enjoy the papers: one, two, three; comments welcome below.

Job Available: Research Software Engineer

Edit: please note the deadline for applications has now passed.

Here’s a great opportunity to join our team at the University of Nottingham on a 5 year Research Software Engineering (RSE) position:
https://www.nottingham.ac.uk/jobs/currentvacancies/ref/IS046219
The deadline for applications is 3rd March 2019.

People might not be too familiar with the concept of an ‘RSE’: UK funders and universities have recognised recently, and formally, that there needs to be a career path for people specialising in software engineering for research codes – see the UK RSE homepage for more info. So if you really enjoy the coding aspect of your research it might be the job for you! I am looking for someone with a PhD involving any aspect of computational research who still wants to be involved in doing cutting edge research and publishing, whilst focussing on professional levels of software development to underpin our research and its application to real world problems. You will be working closely with a team of post-doctoral researchers in our group in the Centre for Mathematical Medicine & Biology within Mathematical Sciences for 80% of your time, along with industrial collaborators and experimental academic groups. This is a unique arrangement with your job based in the university’s Digital Research Team so that you can continue to learn software skills there for the remaining 20% of your time. At the end of the 5 years your role will turn into a permanent job within the university’s RSE group.

Some of the software you’ll be involved in developing includes:

• Chaste – our C++ cardiac electrophysiology simulator, the back-end simulation engine for a lot of our work.
• libcellml – the API for the CellML markup language, giving access to hundreds of electrophysiology models in a standardised format.
• The Cardiac Electrophysiology Web Lab – a web-based platform for documenting and reproducing the behaviour of models in different experimental simulations, comparing against experimental data, and documenting the process of deriving a model from data.
• PINTS – probabilistic inference for noisy time series (python). Our main optimisation/inference software that forms the statistical back end for the Web Lab.
• ApPortal – a web portal for safety pharmacology that provides a user-friendly interface to a Chaste-based simulator to run simulations, store and view their results.

Please don’t be put off if you don’t know all those languages and things inside out now, we are looking for someone who can learn them and has enthusiasm for open source software in research. Please get in touch with me if you have any questions about the job.

There are some other jobs being advertised in Nottingham’s Digital Research Team that you might like to have a look at too!

Postdoctoral Research Positions Available

N.B. 16th Jan 2019 – the applications for these positions are now closed.

This post is to let people know about some opportunities for postdoctoral research here in the Centre for Mathematical Medicine & Biology, based in Mathematical Sciences, University of Nottingham.

We are starting a new Wellcome Trust funded project in 2019 entitled “Developing cardiac electrophysiology models for drug safety studies”. As you’ll see from some of the previous blog articles, and associated work on the CiPA project, we’ve been working on ways to understand and predict how certain pharmaceutical drugs are associated with increased pro-arrhythmic risk by using mathematical models of ion channel currents and cardiac cells.

This is an exciting opportunity to get involved in a substantial research team that will consist of at least three postdoctoral research associate positions, together with me and a dedicated research software engineer. 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 and do some of their own experimental work to really get to grips with what we are trying to simulate.

There are quite a few challenges in this area, aspects of which you’ll find discussed in various past blog posts, but here are a few that we will be tackling in this grant:

• Designing experiments to get information on drug binding to ion channels, and making sure that they can run on high-throughput automated patch clamp machines.
  • Deciding appropriate baseline models for the ion currents (see my recent talk in Banff on this topic), and parameterising these models effectively is a big pre-requisite for this, which we’ve been working on recently.
• Simulating drug effects on the whole cell level
  • Tailoring mathematical action potential models to particular cell types, to make predictions of what drugs might do in different species, or stem-cell derived myocytes versus adult human cells. Again, we think that doing more informative experiments (working with the Christini lab to build on this) will help a lot.
• Comparing whole cell simulations with later safety test results: to see whether we quantitatively understand what the drugs are doing, or whether we see unexpected things.
• Considering/building all of this in a probabilistic/statistical framework that accounts for uncertainty and variability in a lot of different aspects:
  • our datasets / biological systems,
  • model parameters,
  • model structures themselves,
  • discrepancy between models and reality,
  • our subsequent decisions / risk predictions.
• And working on open source software tools that everyone can use for these tasks.

If any of that sounds interesting to you – please do apply! Feel free to contact me with informal enquiries.

There is a relevant job advert out now for fixed-term 3 year positions, available to start as soon as possible, details here: Research Associate/Fellow – up to two postdoctoral research positions (closing date for applications is 16th Jan 2019):

• Either for people with experience in computational modelling of biological systems;
  OR
• for people with experience in statistics/inference – in which case no previous experience of biological research is required.

There are also PhD positions available, see: “Optimising experiments for developing ion channel models” which is fully funded for UK and EU students, details here: https://www.nottingham.ac.uk/mathematics/prospective/research/maml.aspx