Tag Archives: 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.

More laws of biology

Four years ago I wrote a post asking whether there were any fundamental laws of biology that are sufficiently general to apply beyond the context of life on Earth [‘Laws of biology?‘ on January 16th, 2016].  I suggested Dollo’s law that diversity and complexity increases in evolutionary systems; the Hardy-Weinberg law about allele and genotype frequencies remaining constant from generation to generation; and the Michaelis-Menten law governing enzymatic reactions.  Recently, I came across a simpler statement of the laws of biology proposed by Edward O.Wilson.  He states that the first law of biology is all entities and processes of life are obedient to the laws of physics and chemistry; and the second law is all evolution, beyond minor random perturbations due to high mutation rates and random fluctuations in the number of competing genes, is due to natural selection.  It seems likely that these simpler laws will be universally applicable; however, until we find evidence of extra-terrestrial life, they will remain untestable in a universal context unlike the laws of physics.

Source:

Edward O. Wilson, Letters to a Young Scientist, Liveright Pub. Co., NY, 2013.

 

 

Citizens of the world

Last week in Liverpool, we hosted a series of symposia for participants in a dual PhD programme involving the University of Liverpool and National Tsing Hua University, in Taiwan, that has been operating for nearly a decade.  On the first day, we brought together about dozen staff from each university, who had not met before, and asked them to present overviews of their research and explore possible collaborations using as a theme: UN Sustainable Development Goal No.11: Sustainable Cities and Communities.  The expertise of the group included biology, computer science, chemistry, economics, engineering, materials science and physics; so, we had wide-ranging discussions.  On the second and third day, we connected a classroom on each campus using a video conferencing system and the two dozen PhD students in the dual programme presented updates on their research from whichever campus they are currently resident.  Each student has a supervisor in each university and divides their time between the two universities exploiting the expertise and facilities in the two institutions.

The range of topics covered in the student presentations was probably even wider than on the first day; extending from deep neural networks, through nuclear reactor technology, battery design and three-dimensional cell culturing to policy impacts on households.  One student spoke about the beauty of mathematical equations she is working on that describe the propagation of waves in lattice structures; while, another told us about his investigation of the causes of declining fertility rates across the world.  Data from the UN DESA Population Division show that live births per woman in the Americas & Europe have already fallen below the 2.1 required to sustain the population, while it is projected to fall below this level in south-east Asia within the next five years and in the world by 2060.  This made me think that perhaps the Gaia principle, proposed by James Lovelock, is operating and that human population is self-regulating as it interacts with constraints imposed by the Earth though perhaps not in a fashion originally envisaged.

 

Laws of biology?

daisyMany people are familiar with Newton’s Laws of Motion and, perhaps aware of the existence of the laws of thermodynamics. These are fundamental laws of physics upon which much of our engineered world is built. But, are there corresponding fundamental laws of biology? The question is important because we need to understand the interaction of engineered products and services with the biological world (including us) because, as John Caputo has suggested, a post-humanist world is coming into existence as the boundary between humans and technology is eroded.

So, back to laws of biology.  It is challenging to identify predictive statements about the biological world that are generally applicable. Elliott Sober argued that there are no exceptionless laws in biology. However, others would point to Dollo’s law that states evolution is irreversible, which sounds like a form of the second law of thermodynamics: entropy increases in all real processes. Indeed, McShea and Brandon have written a book entitled ‘Biology’s First Law: the tendency for diversity and complexity to increase in evolutionary systems’ which sounds even more like the second law of thermodynamics.

There are other candidates such as the Hardy-Weinberg law that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences; maybe this is corollary of Dollo’s law?   Or, the Michaelis-Menten rate law that governs enzymatic reactions. But, are there any biological laws that are sufficiently general to apply beyond the context of life on Earth?  Answers via comments, please!

Sources:

Caputo JD. Truth: philosophy in transit. London: Penguin, 2013.

Sober, E., Philosophy of biology, Boulder CO: Westview Press, 1993.

Sober, E., Philosophy in biology, in the Blackwell Companion to Philosophy, 2nd edition, edited by Nicholas Bunnin & E.P. Tsui-James, Blackwell Publishers Ltd, 2006.

McShea, D.W. & Brandon, R., Biology’s first law: the tendency for diversity and complexity to increase in evolutionary systems, Chicago: Chicago University Press, 2010.