Tag Archives: computational biology

Modelling from the cell through the individual to the host population

During the lock-down in the UK due to the coronavirus pandemic, I have been reading about viruses and the modelling of them.  It is a multi-disciplinary and multi-scale problem; so, something that engineers should be well-equipped to tackle.  It is a multi-scale because we need to understand the spread of the virus in the human population so that we can control it, we need to understand the process of infection in individuals so that we can protect them, and we need to understand the mechanisms of virus-cell interaction so that we can stop the replication of the virus.  At each size scale, models capable of representing the real-world processes will help us explore different approaches to arresting the progress of the virus and will need to be calibrated and validated against measurements.  This can be represented in the sort of model-test pyramid shown in the top graphic that has been used in the aerospace industry [1-2] for many years [see ‘Hierarchical modelling in engineering and biology’ on March 14th, 2018] and which we have recently introduced in the nuclear fission [3] and fusion [4] industries [see ‘Thought leadership in fusion engineering’ on October 9th, 2019].  At the top of the pyramid, the spread of the virus in the population is being modelled by epidemiologists, such as Professor Neil Ferguson [5], using statistical models based on infection data.  However, I am more interested in the bottom of the pyramid because the particles of the coronavirus are about the same size as the nanoparticles that I have been studying for some years [see ‘Slow moving nanoparticles’ on December 13th, 2017] and their motion appears to be dominated by diffusion processes [see ‘Salt increases nanoparticle diffusion’ on April 22nd, 2020] [6-7].  The first step towards virus infection of a cell is diffusion of the virus towards the cell which is believed to be a relatively slow process and hence a good model of diffusion would assist in designing drugs that could arrest or decelerate infection of cells [8].  Many types of virus on entering the cell make their way to the nucleus where they replicate causing the cell to die, afterwhich the virus progeny are dispersed to repeat the process.  You can see part of this sequence for coronavirus (SARS-COV-2) in this sequence of images. The trafficking across the cytoplasm of the cell to the nucleus can occur in a number of ways including the formation of a capsule or endosome that moves across the cell towards the nuclear membrane where the virus particles leave the endosome and travel through microtubules into the nucleus.  Holcman & Schuss [9] provide a good graphic illustrating these transport mechanisms.  In 2019, Briane et al [10] reviewed models of diffusion of intracellular particles inside living eukaryotic cells, i.e. cells with a nuclear enclosed by a membrane as in all animals.  Intracellular diffusion is believed to be driven by Brownian motion and by motor-proteins including dynein, kinesin and myosin that enable motion through microtubules.  They observed that the density of the structure of cytoplasm, or cytoskeleton, can hinder the free displacement of a particle leading to subdiffusion; while, cytoskeleton elasticity and thermal bending can accelerate it leading to superdiffusion.  These molecular and cellular interactions are happening at disparate spatial and temporal scales [11] which is one of the difficulties encountered in creating predictive simulations of virus-cell interactions.  In other words, the bottom layers of the model-test pyramid appear to be constructed from many more strata when you start to look more closely.  And, you need to add a time dimension to it.  Prior to the coronavirus pandemic, more modelling efforts were perhaps focussed on understanding the process of infection by Human Immunodeficiency Virus (HIV), including by a multi-national group of scientists from Chile, France, Morocco, Russia and Spain [12-14].  However, the current coronavirus pandemic is galvanising researchers who are starting to think about novel ways of building multiscale models that encourage multidisciplinary collaboration by dispersed groups, [e.g. 15].

References

[1] Harris GL, Computer models, laboratory simulators, and test ranges: meeting the challenge of estimating tactical force effectiveness in the 1980’s, US Army Command and General Staff College, May 1979.

[2] Trevisani DA & Sisti AF, Air Force hierarchy of models: a look inside the great pyramid, Proc. SPIE 4026, Enabling Technology for Simulation Science IV, 23 June 2000.

[3] Patterson EA, Taylor RJ & Bankhead M, A framework for an integrated nuclear digital environment, Progress in Nuclear Energy, 87:97-103, 2016.

[4] Patterson EA, Purdie S, Taylor RJ & Waldon C, An integrated digital framework for the design, build and operation of fusion power plants, Royal Society Open Science, 6(10):181847, 2019.

[5] Verity R, Okell LC, Dorigatti I, Winskill P, Whittaker C, Imai N, Cuomo-Dannenburg G, Thompson H, Walker PGT, Fu H, Dighe A, Griffin JT, Baguelin M, Bhatia S, Boonyasiri A, Cori A, Cucunubá Z, FitzJohn R, Gaythorpe K, Green W, Hamlet A, Hinsley W, Laydon D, Nedjati-Gilani G, Riley S, van Elsland S, Volz E, Wang H, Wang Y, Xi X, Donnelly CA, Ghani AC, Ferguson NM, Estimates of the severity of coronavirus disease 2019: a model-based analysis., Lancet Infectious Diseases, 2020.

[6] Coglitore D, Edwardson SP, Macko P, Patterson EA, Whelan MP, Transition from fractional to classical Stokes-Einstein behaviour in simple fluids, Royal Society Open Science, 4:170507, 2017.

[7] Giorgi F, Coglitore D, Curran JM, Gilliland D, Macko P, Whelan M, Worth A & Patterson EA, The influence of inter-particle forces on diffusion at the nanoscale, Scientific Reports, 9:12689, 2019.

[8] Gilbert P-A, Kamen A, Bernier A & Garner A, A simple macroscopic model for the diffusion and adsorption kinetics of r-Adenovirus, Biotechnology & Bioengineering, 98(1):239-251,2007.

[9] Holcman D & Schuss Z, Modeling the early steps of viral infection in cells, Chapter 9 in Stochastic Narrow Escape in Molecular and Cellular Biology, New York: Springer Science+Business Media, 2015.

[10] Braine V, Vimond M & Kervrann C, An overview of diffusion models for intracellular dynamics analysis, Briefings in Bioinformatics, Oxford University Press, pp.1-15, 2019.

[11] Holcman D & Schuss Z, Time scale of diffusion in molecular and cellular biology, J. Physics A: Mathematical and Theoretical, 47:173001, 2014.

[12] Bocharov G, Chereshnev V, Gainov I, Bazhun S, Bachmetyev B, Argilaguet J, Martinez J & Meyerhans A, Human immunodeficiency virus infection: from biological observations to mechanistic mathematical modelling, Math. Model. Nat. Phenom., 7(5):78-104, 2012.

[13] Bocharov G, Meyerhans A, Bessonov N, Trofimchuk S & Volpert V, Spatiotemporal dynamics of virus infection spreading in tissues, PLOS One, 11(12):e)168576, 2016.

[14] Bouchnita A, Bocharov G, Meyerhans A & Volpert V, Towards a multiscale model of acute HIV infection, Computation, 5(6):5010006, 2017.

[15] Sego TJ, Aponte-Serrano JO, Ferrari-Gianlupi J, Heaps S, Quardokus EM & Glazier JA, A modular framework for multiscale spatial modeling of viral infection and immune respons in epithelial tissue, bioRxiv. 2020.

Spatial-temporal models of protein structures

For a number of years I have been working on methods for validating computational models of structures [see ‘Model validation‘ on September 18th 2012] using the full potential of measurements made with modern techniques such as digital image correlation [see ‘256 shades of grey‘ on January 22nd 2014] and thermoelastic stress analysis [see ‘Counting photons to measure stress‘ on November 18th 2015].  Usually the focus of our interest is at the macroscale, for example the research on aircraft structures in the MOTIVATE project; however, in a new PhD project with colleagues at the National Tsing Hua University in Taiwan, we are planning to explore using our validation procedures and metrics [1] in structural biology.

The size and timescale of protein-structure thermal fluctuations are essential to the regulation of cellular functions. Measurement techniques such as x-ray crystallography and transmission electron cryomicroscopy (Cryo-EM) provide data on electron density distribution from which protein structures can be deduced using molecular dynamics models. Our aim is to develop our validation metrics to help identify, with a defined level of confidence, the most appropriate structural ensemble for a given set of electron densities. To make the problem more interesting and challenging the structure observed by x-ray crystallography is an average or equilibrium state because a folded protein is constantly in motion undergoing harmonic oscillations, each with different frequencies and amplitude [2].

The PhD project is part of the dual PhD programme of the University of Liverpool and National Tsing Hua University.  Funding is available in form of a fee waiver and contribution to living expenses for four years of study involving significant periods (perferably two years) at each university.  For more information follow this link.

References:

[1] Dvurecenska, K., Graham, S., Patelli, E. & Patterson, E.A., A probabilistic metric for the validation of computational models, Royal Society Open Society, 5:180687, 2018.

[2] Justin Chan, Hong-Rui Lin, Kazuhiro Takemura, Kai-Chun Chang, Yuan-Yu Chang, Yasumasa Joti, Akio Kitao, Lee-Wei Yang. An efficient timer and sizer of protein motions reveals the time-scales of functional dynamics in the ribosome (2018) https://www.biorxiv.org/content/early/2018/08/03/384511.

Image: A diffraction pattern and protein structure from http://xray.bmc.uu.se/xtal/

Establishing fidelity and credibility in tests & simulations (FACTS)

A month or so ago I gave a lecture entitled ‘Establishing FACTS (Fidelity And Credibility in Tests & Simulations)’ to the local branch of the Institution of Engineering Technology (IET). Of course my title was a play on words because the Oxford English Dictionary defines a ‘fact’ as ‘a thing that is known or proved to be true’ or ‘information used as evidence or as part of report’.   One of my current research interests is how we establish predictions from simulations as evidence that can be used reliably in decision-making.  This is important because simulations based on computational models have become ubiquitous in engineering for, amongst other things, design optimisation and evaluation of structural integrity.   These models need to possess the appropriate level of fidelity and to be credible in the eyes of decision-makers, not just their creators.  Model credibility is usually provided through validation processes using a small number of physical tests that must yield a large quantity of reliable and relevant data [see ‘Getting smarter‘ on June 21st, 2017].  Reliable and relevant data means making measurements with low levels of uncertainty under real-world conditions which is usually challenging.

These topics recur through much of my research and have found applications in aerospace engineering, nuclear engineering and biology. My lecture to the IET gave an overview of these ideas using applications from each of these fields, some of which I have described in past posts.  So, I have now created a new page on this blog with a catalogue of these past posts on the theme of ‘FACTS‘.  Feel free to have a browse!

Hierarchical modelling in engineering and biology

In the 1979 Glenn Harris proposed an analytical hierarchy of models for estimating tactical force effectiveness for the US Army which was represented as a pyramid with four layers with a theatre/campaign simulation at the apex supported by mission level simulations below which was engagement model and engineering models of assets/equipment at the base.  The idea was adopted by the aerospace industry [see the graphic on the left] who place the complete aircraft on the apex supported by systems, sub-systems and components beneath in increasing numbers with the pyramid divided vertically in half to represent physical tests on one side and simulations on the other.  This represents the need to validate predictions from computational models with measurements in the real-world [see post on ‘Model validation‘ on September 18th, 2012]. These diagrams are schematic representations used by engineers to plan and organise the extensive programmes of modelling and physical testing undertaken during the design of new aircraft [see post on ‘Models as fables‘ on March 16th, 2016].  The objective of the MOTIVATE research project is to reduce quantity and increase the quality of the physical tests so that pyramid becomes lop-sided, i.e. the triangle representing the experiments and tests is a much thinner slice than the one representing the modelling and simulations [see post on ‘Brave New World‘ on January 10th, 2018].

At the same time, I am working with colleagues in toxicology on approaches to establishing credibility in predictive models for chemical risk assessment.  I have constructed an equivalent pyramid to represent the system hierarchy which is shown on the right in the graphic.  The challenge is the lack of measurement data in the top left of the pyramid, for both moral and legal reasons, which means that there is very limited real-world data available to confirm the predictions from computational models represented on the right of the pyramid.  In other words, my colleagues in toxicology, and computational biology in general, are where my collaborators in the aerospace industry would like to be while my collaborators in the aerospace want to be where the computational biologists find themselves already.  The challenge is that in both cases a paradigm shift is required from objectivism toward relativism;  since, in the absence of comprehensive real-world measurement data, validation or confirmation of predictions becomes a social process involving judgement about where the predictions lie on a continuum of usefulness.

Sources:

Harris GL, Computer models, laboratory simulators, and test ranges: meeting the challenge of estimating tactical force effectiveness in the 1980’s, US Army Command and General Staff College, May 1979.

Trevisani DA & Sisti AF, Air Force hierarchy of models: a look inside the great pyramid, Proc. SPIE 4026, Enabling Technology for Simulation Science IV, 23 June 2000.

Patterson EA & Whelan MP, A framework to establish credibility of computational models in biology, Progress in Biophysics and Molecular Biology, 129:13-19, 2017.