Tag Archives: particles

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].


[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.

Slow moving nanoparticles

Random track of a nanoparticle superimposed on its image generated in the microscope using a pin-hole and narrowband filter.

A couple of weeks ago I bragged about research from my group being included in a press release from the Royal Society [see post entitled ‘Press Release!‘ on November 15th, 2017].  I hate to be boring but it’s happened again.  Some research that we have been performing with the European Union’s Joint Research Centre in Ispra [see my post entitled ‘Toxic nanoparticles‘ on November 13th, 2013] has been published this morning by the Royal Society Open Science.

Our experimental measurements of the free motion of small nanoparticles in a fluid have shown that they move slower than expected.  At low concentrations, unexpectedly large groups of molecules in the form of nanoparticles up to 150-300nm in diameter behave more like an individual molecule than a particle.  Our experiments support predictions from computer simulations by other researchers, which suggest that at low concentrations the motion of small nanoparticles in a fluid might be dominated by van der Waals forces rather the thermal motion of the surrounding molecules.  At the nanoscale there is still much that we do not understand and so these findings will have potential implications for predicting nanoparticle transport, for instance in drug delivery [e.g., via the nasal passage to the central nervous system], and for understanding enhanced heat transfer in nanofluids, which is important in designing systems such as cooling for electronics, solar collectors and nuclear reactors.

Our article’s title is ‘Transition from fractional to classical Stokes-Einstein behaviour in simple fluids‘ which does not reveal much unless you are familiar with the behaviour of particles and molecules.  So, here’s a quick explanation: Robert Brown gave his name to the motion of particles suspended in a fluid after reporting the random motion or diffusion of pollen particles in water in 1828.  In 1906, Einstein postulated that the motion of a suspended particle is generated by the thermal motion of the surrounding fluid molecules.  While Stokes law relates the drag force on the particle to its size and fluid viscosity.  Hence, the Brownian motion of a particle can be described by the combined Stokes-Einstein relationship.  However, at the molecular scale, the motion of individual molecules in a fluid is dominated by van der Waals forces, which results in the size of the molecule being unimportant and the diffusion of the molecule being inversely proportional to a fractional power of the fluid viscosity; hence the term fractional Stokes-Einstein behaviour.  Nanoparticles that approach the size of large molecules are not visible in an optical microscope and so we have tracked them using a special technique based on imaging their shadow [see my post ‘Seeing the invisible‘ on October 29th, 2014].


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. doi:

More uncertainty about matter and energy


When I wrote about wave-particle duality and an electron possessing the characteristics of both matter and energy [see my post entitled ‘Electron uncertainty’ on July 27th, 2016], I dodged the issue of what are matter and energy.  As an engineer, I think of matter as being the solids, liquids and gases that are both manufactured and occur in nature.  We should probably add plasmas to this list, as they are created in an increasing number of engineering processes, including power generation using nuclear fission.  But maybe plasmas should be classified as energy, since they are clouds of unbounded charged particles, often electrons.   Matter is constructed from atoms and atoms from sub-atomic particles, such as electrons that can behave as particles or waves of energy.  So clearly, the boundary between matter and energy is blurred or fuzzy.  And, Einstein’s famous equation describes how energy and matter can be equated, i.e. energy is equal to mass times the speed of light squared.

Engineers tend to define energy as the capacity to do work, which is fine for manufactured or generated energy, but is inadequate when thinking about the energy of sub-atomic particles, which probably is why Feynman said we don’t really know what energy is.  Most of us think about energy as the stuff that comes down an electricity cable or that we get from eating a banana.  However, Evelyn Pielou points out in her book, The Nature of Energy, that energy in nature surrounds us all of the time, not just in the atmosphere or water flowing in rivers and oceans but locked into the structure of plants and rocks.

Matter and energy are human constructs and nature does not do rigid classifications, so perhaps we should think about a plant as a highly-organised localised zone of high density energy [see my post entitled ‘Fields of flowers‘ on July 8th, 2015].  We will always be uncertain about some things and as our ability to probe the world around us improves we will find that we are no longer certain about things we thought we understood.  For instance, research has shown that Bucky balls, which are spherical fullerene molecules containing sixty carbon atoms with a mass of 720 atomic mass units, and so seem to be quite substantial bits of matter, exhibit wave-particle duality in certain conditions.

We need to learn to accept uncertainty and appreciate the opportunities it presents to us rather than seek unattainable certainty.

Note: an atomic mass unit is also known as a Dalton and is equivalent to 1.66×10-27kg


Pielou EC, The Energy of Nature, Chicago: The University of Chicago Press, 2001.

Arndt M, Nairz O, Vos-Andreae J, Keller C, van der Zouw G & Zeilinger A, Wave-particle duality of C60 molecules, Nature 401, 680-682 (14 October 1999).


Electron uncertainty

daisyMost of us are uncomfortable with uncertainty.  Michael Faraday’s ability to ‘accept the given – certainties and uncertainties’ [see my post entitled ‘Steadiness and placidity’ on July 18th, 2016] was exceptional and perhaps is one reason he was able to make such outstanding contributions to science and engineering.  It has been said that his ‘Expts. on the production of Electricity from Magnetism, etc. etc.’ [Note 148 from Faraday’s notebooks] on August 29th 1831  began the age of electricity.  Electricity is associated with the flow of electric charge, which is often equated with the flow of electrons and electrons are subatomic particles with a negative elementary charge and a mass that is approximately 1/1836 atomic mass units.  A moving electron, and it is difficult to find a stationary one, has wave-particle duality – that is, it simultaneously has the characteristics of a particle and a wave.  So, there is uncertainty about the nature of an electron and most of us find this concept difficult to handle.

An electron is both matter and energy.  It is a particle in its materialisation as matter but a wave in its incarnation as energy.  However, this is probably too much of a reductionist description of a systemic phenomenon.  Nevertheless let’s stay with it for a moment, because it might help elucidate why the method of measurement employed in experiments with electrons influences whether our measurements reflect the behaviour of a particle or a wave.  Perhaps when we design our experiments from an energy perspective then electrons oblige by behaving as waves of energy and when we design from a matter perspective then electrons materialise as particles.

All of this leads to a pair of questions about what is matter and what is energy?  But, these are enormous questions, and even the Nobel Laureate Richard Feynman said ‘in physics today, we have no knowledge of what energy is’, so I’m going to leave them unanswered.  I’ve probably already riled enough physicists with my simplistic discussion.

Note: an atomic mass unit is also known as a Dalton and is equivalent to 1.66×10-27kg


Hamilton, J., A life of discovery: Michael Faraday, giant of the scientific revolution. New York: Random House, 2002.

Pielou EC, The Energy of Nature [the epilogue], Chicago: The University of Chicago Press, 2001.