Physics of Complex Organisms - Introduction

There is nothing in the Universe that does not obey the laws of nature underpinned by the theories of Quantum Mechanics and of Relativity.  Living organisms are no exception - their organization, function and size are all subject to constraints defined by the laws of nature.

There are two distinct regimes that one must distinguish here.  The function of organisms at the molecular level falls in the realm of quantum mechanics and mainly the science of chemical reactions determines this.  Evolution has fine-tuned the chemistry to an extent that it might be fair to say that all organisms share a basic optimized unit of life.  The basic unit of life is the biological cell.  Cells come in a large variety in animals and plants but they all appear to have some fundamental properties that make them self-sufficient like houses are.  (There are some fascinating websites that compare different parts and functions of a house with the organelles of a cell).  A cell is essentially a self-sustaining organism that embodies life as it is defined.  A cell has limitations in what it can achieve but these may be overcome by cells functioning together in the form of multicellular organisms.  There are many different ways that cells can join together and the numbers can get very large indeed - a human body has of the order of a million billion cells! Multi-cellular organisms are like cities where a larger number of houses exist but operate in a well-defined regulated manner to cooperate and flourish.

How cells organize themselves in multi-cellular organisms can, fortunately, be described by classical laws of nature which are much easier to visualize and understand and the physics involved is quite straightforward - it is a macroscopic system.  There are many different ways multi-cellular organisms can be constructed. With time, their design in terms of energy efficiency, strength, functionality etc. would have been optimized by natural selection working within the constraints of the laws of physics and this is what we see in today's successful animals and plants.  Of course, they all will not follow the same design - it is a question of engineering - just as an engineer works with basic materials and/or designs to construct different structures - organisms use a variety of designs and materials too.

A good example is the solution for providing oxygen more efficiently to cells over the whole body of an organism.  Diffusion, convection, circulation, hemoglobin are methods that progressively made it easier to transport oxygen over greater distances to more distant part of the body and making possible the growth in animal size. Artificial red blood cells, recpirocytes, have been proposed that will increase the oxygen carrying capacity of normal red blood cells by 236 times with corresponding increase in human endurance. This is an example where modern technology can enhance animal functionality but still working within the laws of physics.

What appears fundamental to our discussion is the size of the organism. Unfortunately, there is not a unique size for all animals or plants and they come in vastly different shapes and sizes.  For animals, the body density is very nearly 1 gm/cc and instead of the volume and shape, it is equally good to work with organism mass.  In nature we indeed have a very large range in masses; mammals alone range from a few grams for a shrew to many tons for a whale.  What is surprising is that even with this vast range of sizes, most body functions scale smoothly as some power law of body mass (allometric scaling). The relative size of the skeleton, metabolic rates, size of the brain, heart beat rate, life span and many more parameters depend on body mass and vary more or less smoothly from the tiniest to the largest of the mammals.

An interesting example to allude to here is that the heart beat rate varies as -0.25 to the power of mass while the life span varies as +0.25 to the power of the mass.  This means the smaller animal heart beats faster but they do not live as long. The total number of heart beats, equal to the product of heart beat rate and life span, for all mammals is therefore independent of their mass (size). Actually the numbers work out such that we all, from shrews to whales, are allowed about 2 billion heart beats in a lifetime!

To stretch the analogy of cells and houses further, we can think of complex organisms as cities. For efficient operation, cities too have to deliver essential commodities like water, food, energy, information etc. to all buildings just as complex organisms need to supply chemical molecules, oxygen, nerve impulses, remove toxic wastes etc. from each cell, however remote.  A system of some sort of networks must operate to maximize efficiency and smooth operation of the city or the organism.  Networks play a fundamental role in the development of complex organisms and go some way to explain their behaviour. 

How size affects animal structure and function is a fascinating subject and in future blogs, I shall look at many aspects of this topic and attempt to understand the physics involved. 

This I shall do but the next few publications will be on the question of how do we measure the age of the Earth and the Universe and where did all the elements come from!!

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Radio-Isotope Dating: Age of the Earth and Plate Tectonics - Introduction

'The world was created on Sunday, 23^rd October 4004 BC"     …James Ussher, Irish Archbishop of Armagh
'..., this world has neither a beginning nor an end".     …James Hutton (1726 – 1797)

For the past few years, I have been giving an annual seminar to the Glasgow University Nuclear Physics Group on a topic that has something to do with nuclear physics but definitely it would have no overlap with the current research programme of the group.  I am happy to say that this year I chose to talk about radioisotope dating as applied to the determination of the age of the Earth and its contribution in establishing plate tectonics on a firm scientific basis.  With no real background in Geology, it was hard work but rather exciting to get to know better the planet we live on. 

In fact, the impact of radioisotope dating on geology and the way we now see the historic evolution of the Earth can only be described as dramatic.  In 1963, geophysicist John Tuzo-Wilson summarized:  "It will be difficult for most of us to accept that large amounts of what we have written and taught has been erroneous".

To an extent, it is not surprising that geology was in such a mess until about 1950.  There was really no absolute time scale - it was a qualitative subject - not really a proper science. This has a feeling of deja vu.  Physics suffered similar fate for almost 2000 years, biology and medicine are definitely showing signs of new life and are developing real understanding about the basis of diseases and how to cure them.

Geology is the science that deals with the history of the Earth as recorded in the rocks.  The problem has been that there was no clock, and rocks have the habit of moving about, weathering and generally changing in every way possible - typically over geological time scales - over millions of years.  Until radioisotope dating arrived properly, around 1950, only thing we could do was to visually examine rocks and chemically find out the minerals it contained.  A totally unsatisfactory situation which lends to a lot of speculative wacky  hypotheses; and the Church got involved too!

Radioactivity was discovered in 1896 and the first ideas that it can be used to date minerals in rocks came within a decade.  The first results were that many of the rocks were hundreds of millions of years old - imagine the reaction of established geologists who believed that the Earth was no more than 20 million years old.  The Church wanted us to believe that it was a mere 6000 years old.  The literature is still full of young-earth 'scientists' who are spending lot of energy in trying to prove that radioisotope dating is a flawed science and its results are misleading.  These are things that make life unique.

It took 50 years to sort out all the details in radioisotope dating method and it is now possible to say with good certainty that the Earth was created at the same time when the Solar System formed from a nebula 4.67 billion years ago.  The initial Earth was in a molten form and the crust took a few hundred million years to form.  Strictly, the Earth is slightly younger than the Solar System.  Meteorites, remnants of the early structures formed in the Solar Nebula, have proved invaluable to fix the date when the Solar System formed. 

While we are talking about the formation of the Solar System, it might be good to reflect on the age of the Milky Way - our galaxy.  It is considered that stars and galaxies started to form within about 100 to 200 million years after the big bang that created the Universe 13.7 billion years ago.  Independent determination of Be-9 abundance on the oldest stars in globular clusters at the periphery of the Milky Way puts their age at 13.6 +- 0.8 billion years. Therefore, the Solar System is much younger than the Milky Way.

Radioisotope dating provided an absolute clock and it was then possible to date past events as they happened on the Earth.  One of the most remarkable discovery was the confirmation of sea floor spreading and thus establishing the theory of continental drift or plate tectonics on a firm scientific footing.  Over the next few weeks, I shall be discussing some of these subjects from a physicist view point. 

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Paris Climate Agreement - Too Little Too Late - Nations buy time to do nothing for at least 5 more years

I had made a resolution that I shall not comment on the Paris Climate Change Agreement - this was not to be; and I feel compelled to say my bit on an agreement that is not quantitative enough but a restatement of 'good intentions' albeit more cleverly drafted.  
CO2 levels have risen from about 300 ppm to 400 ppm since the Industrial Revolution - a good part coming from human activities of burning fossil fuel and deforestation.  Carbon isotope analysis has confirmed this beyond any doubt whatsoever.  People who claim otherwise are only being silly.  The average Global temperature has already risen by 0.8C and could rise by a total of 2.7C even if all the good intentions of the Paris agreement are delivered.  
It will be good to watch what the oil company share price does over the next few months - I bet that it will not crash as it should if the Paris agreement has any meaning and fossil fuel consumption is reduced.  The share price will vindicate my belief  that nations of the world will not implement what they have promised in Paris yesterday.  

The basic problem is money - Bloomberg analysis says it will cost 16500 Billion dollars to shift energy production from fossil to renewable etc. and the biggest developing economies of China and India will not be inclined to find big monies to correct a problem that USA and Europe caused and who also have greater resources.  It really boils down to sustainability.  The carbon foot print of the developed countries is far greater than the average global foot print.  A large fraction of CO2 emission from China and other developing countries goes to produce and transport goods for consumption in the developed countries.  We have got used to living on cheaply produced goods - no wonder inflation is so hard to materialize in spite of masses of Quantitative Easing by the central banks run by very clever, and very rich, people.  We have mortgaged the welfare of the next few generations already.  The climate change effects of rising sea levels, selective severe droughts and rainfalls, new diseases moving north, frequent extreme events will be just a few extra miseries they will need to cope with.

If we keep burning fossil fuels at the current level then CO2 levels will not come down - they will not be coming down in a hurry anyway as once CO2 is in the atmosphere, it will hang around there for much more than a 100 years.  We are already committed.  Emissions need to be cut - and cut drastically - to limit temperature increase to less than 2C.

General wisdom is to limit what one has to say to an A4 sheet of paper.  I could go on for a few more pages but that will be unwise.

Take care and Bye until the next time... 

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Logarithms - Useful Background to Understand Power Laws in Biological Scaling

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Biological Scaling:  Importance of Size:  Laws of Physics  determine how animals are formed and how they function. Animal bodies are designed to operate under the constraints set by the laws of physics.  Strength of animal bones will determine the maximum mass it can have.  How efficiently heat produced by metabolic activity inside the body may be eliminated, how oxygen is transferred to the blood - these processes have limits set by physics and determine the shape and size and methods that animals use to optimize their bodies.

What is amazing is that many body functions of animals, like metabolic activity, heart size, oxygen consumption etc. follow general laws expressed as some power of their mass, and the same power laws hold over a very wide size range from the tiny shrew to the massive whale.  

I intend to look at biological scaling laws.

It can be sometimes difficult to interpret power laws as they are non-linear functions. Power laws may be expressed in an 'easier to interpret' linear form by using logarithms. Logarithms are not somethings that everybody is totally comfortable with and a short primer on logs might be useful before discussing the subject of scaling laws in more detail.  

In mathematics, we define a function as an operation that changes the value, in a well-defined way, of the quantity it operates on.  For example:

square root is a function is                    sqrt(9) = 3 

tan is a trigonometric function               tan(60) = 1.732

Most frequently used functions are found as hot-buttons on your scientific calculator.

Similarly logarithm is a function, also found as a hot-button (log) on your calculator. 

Logs are useful as they change products to sums, and divisions to differences

                                   log (AB)  = log A + log B

                                   log (A/B) = log A – log B

For a power relation: 
       log (A³) = log (A.A.A) = log A + log A + log A = 3 log A

If                                y = xⁿ            then        log y = n log x

n does not have to be an integer.  It can also be a positive or negative number.

In the case of a power law of the form y = a xⁿ       

we have   log y = log (a xⁿ)  = log a + log (xⁿ) = log a + n log x

You might notice that                        log y = log a + n log x               
is the equation of a straight line when one plots log y along the y-axis and log x along the x-axis.  Thus we have converted a power relation which plots a curve, to a linear relation that will plot a straight line.  Also notice that the slope of the straight line is the exponent n of the power relation and the intercept on the y-axis is log(a). 

The log functions we shall use are to the base 10.  This is what the scientific calculator gives too.   This means that log10 = 1 (you can check it on your calculator)

To understand it better: 

Suppose you take log of number 2. 

It will be a number p such that 2 = 10^p 

Taking logs gives us           log 2 = log (10^p)  = p log10 = p                            since log10 = 1

Using your calculator you will find that p = 0.30103

So you see, logarithms are just another way of writing numbers.  In special situations, the type we shall deal with, logs make the equations simpler to interpret.

In the following, I show how logs change power relations to linear relations:   The XCEL worksheet shows what is plotted in the two graphs that follow: 

(please click on the slide to see its bigger image)

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General Theory of Relativity (Part 2) - a Course for the 'Inquisitive' Layman

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Slides of my talk - continued from Part 1

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