By Arturo RobertazziAbout-Science, My-Stories

Multiscale Simulations of DNA: From Quantum Effects To Mesoscopic Processes

When I think of multiscale simulations of DNA… a sweet memory comes. I’m sitting in a university lecture hall, half-listening to a professor drone on about material chemistry when suddenly, the gods of academia shine down upon me and bless me with a revelation. A course on bio-inorganic chemistry. The very idea of it sent my mind spiraling. Chemical concepts used to understand how organisms function? Holy cow. I was hooked.

That course changed the path of my academic career (Thank you Prof. Oliva!). I went full-bio from then on out. From my undergraduate project studying proton transfer in the Guanine-Cytosine pair, to my PhD work on metal-based anticancer agents interacting with DNA – it’s mostly been about proteins and DNA. And to study those, I’ve employed a range of methods – high-level quantum chemistry, DFT, QM/MM, molecular dynamics – all the good stuff.

So, let’s talk about that today: Multiscale simulations of DNA. Get ready, it’s going to be a long journey.

A Chemist’s View of DNA

You know, that funky little thing that makes you, well, you? It’s the 0.1% of your DNA. That bit of information is responsible for your uniqueness, while the other 99.9% is the same as any other person on this planet. So much for feeling special!

DNA, short for deoxyribonucleic acid, is a natural polymer composed of two polynucleotide chains that twist around each other to form a double helix. This evolutionary hero was first identified by Friedrich Meischer in 1869, but it wasn’t until 1953 that Watson and Crick stumbled upon its double helix structure. Of course, we mustn’t forget about Rosalind Franklin and her crucial contribution to that discovery.

Each of the two DNA strands consists of simpler monomeric units called nucleotides, which are composed of a nitrogen-containing nucleobase (cytosine, guanine, adenine, or thymine), a sugar called deoxyribose, and a phosphate group. The nucleotides join together in a chain through covalent bonds and form an alternating sugar-phosphate backbone while hydrogen bonding occurs between the nucleobases.

Remember? Hydrogen bonding is the secret ingredient of life in the universe, and it naturally plays a big role in DNA’s structure. Adenine is paired with thymine via two hydrogen bonds, and cytosine with guanine via three. Easy-peasy.

A second non-covalent force contributes to the DNA structure. It’s one of my favorite topics: pi-stacking. It’s a weaker interaction that “stacks” two nucleobases on top of each other, with a distance of a few angstroms.

You put all this together and here it is, her majesty the DNA:

Beyond a mere DNA fragment, this structure holds the words of a novel. Curious to know how I applied bioinformatics to literature? Discover more in my story: Unveiling Literature’s Genetic Code

Why Multiscale Simulations of DNA?

The study of DNA is like the ultimate melting pot of biology, physics, and chemistry. And theoretical methods have been especially helpful in trying to understand its structure and functions, but let’s face it, this stuff is no joke. It’s like trying to navigate through a maze that ranges from the smallest of small details to the grandest of scale.

Simulating DNA is challenging. Why so, you ask?

Imagine this: If you took all the DNA from a single human cell and stretched it out, it would be a whopping 1,80 meters long! Yet the distance between individual base pairs is in the minuscule angstrom range (10-10 m). Some changes to DNA occur over the course of years (108–1010 s), while others, like chromatin reorganization during the cell cycle, take place within a single day (105 s). Meanwhile, the local movements of nucleobases happen in mere milliseconds (10−3 s), while electronic rearrangements take place in a mind-bending sub-femtosecond time-scale (<10−15 s).

And that’s why simulating DNA is a challenge of epic proportions: because of the wide range of time and spatial scales involved in its processes. For this reason, multiscale simulations of DNA are needed, from quantum chemistry to coarse-graining.

Alright, let’s take a peek at these modeling champions one by one.

Old school animations of the DNA structure. Video Credit: The Royal Institution

Quantum chemistry | Multiscale simulations of DNA

Can you really do quantum chemistry calculations of DNA? Well, the thing is, even with the best software and the fastest supercomputers, in the world of nucleic acids, we’re still a long way off from being able to use quantum chemistry to study the dynamics of long pieces of DNA filaments.

Instead, the great work done so far has aimed to understand the non-covalent interactions between the nucleobases of DNA, such as hydrogen bonding and pi-stacking, and how these building blocks affect the resulting macrostructure.

Now, when you think DNA bases and quantum chemistry, there is one name that stands out: Pavel Hobza – awarded with the Schrödinger medal for his contribution to the understanding of non-covalent interactions and their impact on larger structures of DNA.

For example, the groundbreaking work of Pavel Hobza and his group from back in ’99 still holds up today and covers a wide range of topics on the properties of isolated DNA bases and base pairs. Not only did this monumental effort help create a solid benchmark for classical molecular dynamics (more of that in a second), but damn, it inspired a whole generation of researchers – myself included.

I know, I could ramble on for days about quantum chemistry and DNA bases, but let’s stay on track here – we don’t need to write another book. So, let’s dive into just one more study.

You gotta check out the bold work of Brovarets and Hovorun. Their article, Why the tautomerization of the G·C Watson-Crick base pair does not cause point mutations during DNA replication?, used some serious quantum chemistry to estimate the probability of tautomerization of the G-C Watson-Crick base pair, which may lead to mutations via proton tunneling along two neighboring intermolecular hydrogen bonds.

And guess what? They found that these mutations are way less likely to happen than previously thought. That’s right, after half a century of investigation, it’s time to rethink the whole process of spontaneous point mutations in DNA.

Hybrid quantum/classical Methods | Multiscale simulations of DNA

Full quantum chemistry is still too expensive in terms of computational resources to go beyond a few nucleobases. So, if you really want to capture the complex interplay between nucleobases and resulting DNA structures, you gotta get creative and bring some serious street-smarts to the table.

But fear not, my friends, because we’ve got plenty of clever tricks up our sleeves: let’s talk hybrid quantum/classical methods, aka QM/MM.

Now, applying QM/MM in the study of DNA involves dividing your DNA into smaller, more manageable layers, and then treating those key areas at a quantum level. Meanwhile, the rest is simulated using classical force-fields (I promise, we’re going to see more of this today).

A cool example of this technique is the work conducted by Bacolla & Co, who employed QM/MM (together with all sorts of other computational fancy tools) to figure out how mutations occur. Their work showed that intrinsic features of local DNA structure, such as base-pair flexibility and charge transfer, play a big role in making specific nucleotides more susceptible to base modification and therefore mutations.

With this approach, we may hope to get a better grasp of the mechanisms behind genetic mutations and how they impact disease and cancer development.

Multiscale Simulations of DNA: representative DNA fragments bound to cisplatin - QM/MM
Representative DNA fragments bound to cisplatin, a metal-based anticancer agent. The thinner lines indicate the classical force-field layer, while the thicker lines depict the quantum layer. Adapted from Robertazzi and Platts 2006.

Quantum Molecular Dynamics | Multiscale simulations of DNA

The research we’ve talked about so far is awesome, no doubt. But here’s the deal: it only looks at molecules as if they were frozen (at zero kelvin). But the fact is, molecules are in constant motion, wiggling around and shaking it up. And if we want to truly comprehend the nitty-gritty of biological systems, we have to factor in this dynamic behavior. That’s where things start to get a bit dicey, especially when it comes to quantum chemistry.

Enter Car-Parrinello Molecular Dynamics, or CPMD for short. This clever technique allows us to capture the motions of molecules. The mastermind behind it, Michele Parrinello, is a true giant of the field. His seminal paper is the fifth most cited scientific article in the history of Physical Review Letters – pretty serious stuff.

Unlike classical molecular dynamics (yes, I promised: we will get there!), CPMD is ab initio in that uses first principles, fundamental quantum laws, to simulate the motion of atoms in a system. It does not rely on force fields to describe the interactions between atoms, but rather calculates them from quantum mechanics.

Now, let me tell you about this awesome study by Arcella & Co. This group of researchers, some of whom I used to hang out with during my Trieste days, ran an overall outstanding 100 microseconds of a DNA fragment in the gas phase (I myself played with this concept). Then, on selected snapshots, they performed CPMD simulations. And boy, their findings were downright exciting.

For the first time ever, they fully characterized the dynamic ensemble of DNA in the gas phase. The DNA unfolds upon vaporization, loses memory of its original structure, and shows very rich dynamics in a range of timescales, from picosecond to sub-millisecond.

Besides the actual scientific insight, this study also confirms once again the power of street smarts when it comes to applying quantum chemistry to a complex molecule like DNA.

But, my dear reader, we love to dream big, don’t we? So let’s go bigger, bolder. Yes, you guess right! It’s finally time for some molecular dynamics simulations.

Electron whirlpool. Credit: Christine Daniloff

Classical molecular dynamics | Multiscale simulations of DNA

If you are a quantum chemist at the core, it is hard to let go of electrons. They do some marvelous things. Even kids love them. But we need to let them go if we want to step up our game and capture in one model realistically long DNA fragments, with their flashy surroundings of ions, solvent, and protein companions.

With classical molecular dynamics (aka, MD) you do just that: ignore the electronic degrees of freedom and focus on the interactions between the atoms. These are parametrized in a set of force fields.

Now, I’ve done my fair share of MD simulations in my life, diving deep into the intricacies of myoglobin, haemoglobin, DNA. And… I gotta give some serious props to force fields – those suckers are nothing short of miraculous.

Sure, they rely on a few approximations, but the classical approach has been an absolute paradigm shifter when it comes to understanding the behavior of DNA.

Ready?

These animations reveal the dynamic nature of a DNA origami through molecular dynamics simulations. Video Credit: Yoo and Aksimentiev 2013
Structural transitions of the DNA

Among the enormous number of available studies, the one conducted by Sagui & Co. makes it to the finals.

By coupling MD simulations with state-of-the-art enhanced sampling techniques through non-conventional reaction coordinates, Sagui & Co. tackled the elusive B-to-Z DNA transitions.

Z-DNA may have started out as a mere laboratory curiosity back in ’79, but it’s since proven to be a major player in gene expression, regulation, and recombination. The only problem? For decades, we have been scratching our heads over how the transition from the dominant right-handed form of DNA, B-DNA, to Z-DNA actually happens.

The fact is, the B-Z DNA transition is so complex that even the most advanced experimental and computational studies have resulted in conflicting models. But that did not stop Sagui & Co. No, sir.

The key realization from their work is that there’s not just one path to transition with the same energetic profiles. It’s all about viewing the process as a complex reaction path ensemble. So, let’s get real and embrace the complexity, shall we?

Simulations of epigenetics mechanisms

Epigenetics is a truly fascinating field of study that explores how our behaviors and environment can influence the way our genes work. It’s like a dance between nature and nurture, where our experiences can leave chemical marks on our DNA that impact our health and well-being.

Unlike genetic modifications that alter the actual sequence of our DNA, epigenetic changes are often brought about by the addition or removal of a methyl group on DNA nucleotides. These tiny changes are reversible and simply affect how our body reads that sequence, but they can lead to a range of outcomes, from disease to acquired traits that can even be passed down to future generations.

Carvalho & Co. explored the effects of methylation and hydroxymethylation of cytosine even further, finding that epigenetic modifications change the dynamical landscape of the DNA. This increases its propensity towards essential motions like twist, roll, tilt.

The extent and position of these modifications also has significant effects on the amount of structural variation observed. These conformational differences, dependent on the sequence environment, could potentially provide specificity or affect crucial processes of DNA – like protein binding.

Cool stuff, isn’t it?

DNA structures in unusual environments or mutated nucleobases

Thanks to the incredible flexibility of MD simulations, computational chemists have been able to explore how DNA behaves in all sorts of weird environments. Besides the previously mentioned work of Arcella, who explored what happens when you move a small piece of DNA into a vacuum, there are countless other non-physiological media that computational chemists have investigated when it comes to DNA behavior. We’re talking lipids, different types of dendrimers, silica surfaces, graphene, and even carbon nanotubes.

For example, Case & Co. studied how DNA behaves in crystal lattices. Now, that may sound odd, but it’s actually a really unique setting that can be considered a surrogate for the crowded cellular environment.

Instead of the environment, you could study how the modification of nucleobases would affect the resulting DNA. For example, duplexes that have been damaged by oxidative stress or contain mismatches.

One example of the latter topic is the research by my old friend and former colleague, Giulia Rossetti, who dropped some serious knowledge bombs with her research. Her findings revealed that even though DNA is capable of absorbing the structural impact of mismatches, local structural changes can propagate far from the crime scene via both a through-backbone and a previously unknown through-space mechanism.

Coarse-grained simulations of DNA minicircles. Yoo et al. 2021

coarse graining | Multiscale simulations of DNA

Alright, check this out. Every human cell contains about 1,80 meters of DNA. How does such a long fragment squeeze into a nucleus that’s only about 5-20 μm wide? It’s insane! And yet, somehow, it manages to do it.

The key to this incredible feat is the nucleosome, which is formed when 147 base pairs of DNA wrap around a histone octamer. From there, the nucleosomes are connected by 20-80 base-pair long linkers to form what’s called chromatin. It’s an amazing example of the ingenuity of the natural world.

When it comes to studying enormous DNA systems, not even almighty classical simulations will do. We must turn to coarse-grained modeling. Or as I like to call it, simplifying the complex. These models allow us to simulate the behavior of large systems by using a reduced representation, or pseudo-atoms, to describe groups of atoms rather than individual ones.

In the world of biomolecules, coarse-grained models have been widely used at various granularity levels to represent proteins, nucleic acids, lipid membranes, carbohydrates. By decreasing the degrees of freedom, we can perform much longer simulation of much larger models at the expense of molecular detail.

For example, Nordenskiöld’s group created a novel model of the nucleosome with flexible histone tails and a detailed representation of nucleosomal DNA to study the influence of counterions in intra- and inter-nucleosomal interactions. And they didn’t stop there – they extended the model to a super-coarse-grained representation to examine the aggregation of up to 5000 nucleosomes.

So, here we go. We went from quantum effects of nucleobases, which contain about 20 atoms, to a super large model of thousands of nucleosomes, a system that contains almost a million nucleobases.

So yeah, for a quantum chemist that’s, well, freakin’ massive.

Multiscale Simulations of DNA: Coarse-grained modeling of the nucleosome core particle.
Coarse-grained modeling of the nucleosome core particle. Adapted from Lyubartsev et al. 2015

A final personal touch

Phew, we’ve made it. We have seen some beautiful modeling today. Multiscale simulations of DNA, from the tiny quantum effects in isolated nucleobases, to accurate dynamics and reactivity. We gave up the description of electrons and we have seen that with classical molecular dynamics we can investigate more realistic systems to estimate the effects of mutations and foreign environments. And if that’s not enough, there is always the option to let go of atoms too and embrace coarse graining.

You wanna know learn more? A good place to start is this review article by Prof. Orozco – a legend in the field of DNA simulations.

All this writing about DNA has made me nostalgic about my undergrad research days. I was knee-deep in investigating the proton transfer in the Guanine-Cytosine base pair. First, I ran some semi-empirical quantum calculations to predict the properties of the system, and then I hit the lab armed with a cool technique, spectroelectrochemistry – true story: I was a disaster in the lab. But even with my mishaps, I was riding high on the thrill of discovery. I felt like a goddamn scientist.

And yet, simulating DNA isn’t just an academic pursuit. It’s more like peering through a computational window into the essence of our being.

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