Thursday, March 22, 2012

Random events result in order -- how?

Development is ultimately very organized and predictable -- children look like their parents, legs are generally where they belong, and a lion never gives birth to a whale -- but yet another paper describes the randomness of the processes at the cellular level.  How can this be?

The paper is in the April BioEssays; "Genes at work in random bouts", Alexey Golubev.  Golubev says that things that go on inside cells are generally thought to be determined by the interaction of different molecules, which is itself determined by the concentration of those molecules in the cell.  Ordinary differential equations (ODEs) describing all this can be written, and, Golubev says, "ODE solutions may be consistent with oscillatory and/or switch-like changes in molecule levels and, by inference, in cell conditions."  This begins to make intercellular processes sound determined and law-like.

But, the article is basically about the stochastic (random, or probabilistic) events occurring in cells that affect their gene expression patterns, and hence the cycle between cell divisions or the time it takes the cell to express the genes related to its particular tissue  This variation, the author notes, makes stem cells--cells not committed to just one cell-type--plastic and flexible. 

But, as he points out, the idea of molecular concentrations is only true at the level of populations of cells, not in single cells themselves.  There's a lot of randomness in terms of what's going on in single cells, in cell differentiation and cell proliferation, particularly with respect to when genes are turned on or off, and thus which proteins are available, and what happens when. 

The question becomes, then, given all this stochasticity in cellular activity, how development is so organized.  The apparent problem is that once one reaction has taken place, it affects the next reaction, and this includes hierarchical changes such as changes in gene expression in the cell.  Thus, the cell is not just a mix of things, each in large numbers, that will 'even out' over time.  Differences that can be occasioned by chance in a cell can add up. Of course, if the cell continues to detect the same external conditions, its response may adjust so that things do even out.  But it doesn't need to happen. 

On the other hand, most tissues in most organisms are comprised of many cells of the same type.  Each may be experiencing stochastic changes, but their tissue-specific behavior may usually 'even out' because the variation will be slight and in different directions among the cells, so that on average they are doing the same, appropriate, thing.  In unusual circumstances, if this doesn't happen, the organism may be very different from its peers....or  it may not survive.

This perhaps reflects a fundamental property of populations, known as the 'law of large numbers'.  The theory behind this (Ken was just realizing from reading a book called The Taming of Chance (1990, by Ian Hacking, Cambridge Press)), comes from the study of populations of individually differing individuals, whose aggregate behaviors have regular distributions: the 'normal' or bell-shaped--or at least orderly--distributions of stature, incomes, and so many other things.  In another common phrase, they have 'central tendencies.'  Normal meant that most were near the norm.  This statistical idea was worked out over the 18th and 19th century, and raises interesting questions about causation.  Hacking's book shows how people had to learn that causation was not about precisely fore-ordained laws, but about probabilities, and that this applied to society.

The classic cases had to do with things like suicide.  One can't predict who will commit suicide in a given year, or by what means.  But the numbers, and the number who do it by each method, are very similar from year to year in a given population.  Likewise, the life expectancy is an average, and nobody lives exactly that long: some die younger, some older.  So are many social facts like political affiliations and so on.

Why is this?  It is the net, end result of many different individuals each with slightly varying characteristics.  There were many explanations of why this was, that are beyond this post, but in essence there are many contributing factors of diverse kinds, that mostly aren't known, so that a few individuals are exposed to many, others to only a few, but most of us to some 'average' amount of these factors.  The fraction exposed to many such factors is the fraction of individuals who are taller, more intelligent, ...., or who commit suicide.

The law of large numbers is a statistical fact that can be proven mathematically under rather general conditions.  This leads to central tendencies.  That is why population statistics took on a central role in social sciences, where often the underlying causal factors and their specific effects are unknown or hard to estimate accurately.  Social sciences can 'understand' society--at least predict some things about it--without understanding causation in the strict sense.  And in some situations, these things don't work very well--economics is one, in which stability of population outcomes occasionally, at least, takes a quick left-turn.

Probably the same applies to the populations of cells that make up a tissue, and if so this would make the high amount of probabilistic events in cells that would make each cell different, which can lead to a central tendency for the kidney to filter blood is similar ways, and so on.  Because of local differences among cells, different genotypes, and different life-experiences, kidney functions differ among people.  Some are at the extremes and we call that 'disease', but most are roughly near the norm.

Biologists routinely speak of chance, but often act as if they believe that genes 'determine' the organisms the way a program determines what a computer does.  They know about variation in populations, and how, for example, polygenic traits like stature or blood pressure (the darlings of the GWAS world) vary, even if they are driven to enumerate all the underlying causes that vary among individuals in the population.  In a sense, the population concept applied to tissue is of the same sort, and provides another source of variation between genotype and trait.


Arjun said...

Although not directly related to the discussion in the post, regarding the rise of order from seeming disorder I have recently come across a branch of mathematics which may interest you known as Ramsey Theory. "One might summarize the philosophy that lies behind Ramsey theory as follows 'a sufficiently large system, no matter how random, must contain highly organized subsystems.'"(

I find it interesting mainly for its philosophical implications regarding the inevitable existence of order in the universe.

The question remains though (for me, at least)-- to what extent is order 'inherent' in the universe and to what extent is it a product of our consciousnesses in an attempt to organize large sets of data resulting from sense-perceptions?

Ken Weiss said...

This has to do, I think, with the meaning of 'order' in your message. Suppose there are a myriad of things, each unrelated and different, but that the universe is continuous--like forces, or made of molecules that persist. Then, there will be similarity over time and place in the universe: a carbon atom, beam of light, or pull of gravity will vary more or less continuously from one moment to the next.

This doesn't mean the universe is homogeneous. But in any given place or scale etc., statistical patterns result by default, not because there need be any prior, or external, orderer or (as the classical religious argument put it) design.

Of course, this does require that the underlying properties like atoms and forces exist, and they form a lower-level type of order.

At the ultimate philosophical end of the spectrum would be the anthropic principle: in a totally unordered universe, there would not be humans to see and think about it. So there could be totally disordered universes, that we would not be in and hence could not know about.

This also reflect our nature as evolutionary beings, which is really your last paragraph. We evolved to perceive and react to orderly things, because if our ancestors couldn't make sense of things in a competitive universe, they wouldn't have reproduced.

So there may disorder even in our universe, that we're just not equipped to detect. Even 'randomness' is a concept related to 'order', so real disorder could be of some entirely different type.

Given this, to me, the question becomes one about causation: is there truly probabilistic causation (as opposed to causation that, by any measure we happen to have, seems to be probabilistic, such as quantum phenomena and many others), and how can that be?

If coin-flipping machines can be built that make the outcome entirely predictable (it's been done), does that imply that everything else that appears to be probabilistic (or disorderly) is really just our misperception of underlying order?