Why life is complex and — most importantly — what is the origin of the over abundance of complexity in nature? This is a fundamental scientific question which, paraphrasing the late Per Bak, “is screaming to be answered but seldom is even being asked.” In this three-article series, we review recent attempts across several scales to understand the origins of complex biological problems from the perspective of critical phenomena. Following a broad introduction to complexity, criticality and universality in Part 1, to illustrate the approach, three cases will be discussed in Parts 2 and 3; large scale brain dynamics, the characterization of spontaneous fluctuations of proteins, and the physiological complexity of the cell mitochondria network.

Introduction

In the last decade, we have witnessed an escalating interest in complex biological phenomena at all levels including macroevolution, neuroscience at different scales, and molecular biology. Potential progress is of paramount importance, thus we shall examine a bit how we are currently proceeding to carve out these new areas, starting with asking whether biological phenomena are more or less complex than other fundamental problems in physics. The answer is not clear at first, however striking differences exist in the approaches as well as in the sociology of both fields. 

The history of physics records many important efforts in search for universality; large classes of phenomena must be explained in terms of a few fundamental laws. In contrast, biology more often seems to emphasize unique and singular aspects; because not all organisms are alike, there is a large diversity of species, families, etc… such that taxonomy ends up prevailing over integration of knowledge. This apparent uniqueness of each biological phenomena in some cases leads to overspecialization, which may, from time to time, encourage the creation of a sub-discipline for each new group of complex biological phenomena. Of course, this tendency prevents fruitful dialogue between biology and the rest of the sciences, thus leading to an exponential increase of our knowledge about almost nothing, or in other words, to the fragmentation of the biological scientific inquiry into many disconnected “cottage industries.”

The full Interdialogue with Dante Chialvo.

Often it is also argued that biology could not be well-studied by physics, because “the laws of physics are simple but nature is complex.” This is motivated by the assumption that anything that “looks” complex originates from laws that must also be complex. Thus, the idea that has been perpetuated is that the complexity of nature is almost inaccessible, arguing that the diversity and ever changing fluctuations shown by natural objects prevent their study through mathematical tools. In contrast, others such as Leon Glass and Michael C. Mackey called attention to the fact that [1] 

“… if the complex dynamic phenomena that occur in the human body were to arise in some inanimate physical system — let us say in a laser, or liquid helium or a semiconductor — they would be subjected to the most sophisticated experimental and theoretical study.” 

This article series adheres to the spirit of the above quote and aims to illustrate some successful attempts to study complex collective phenomena [2] with approaches borrowed from statistical physics. Rather than going into the details of each of the studies reviewed, the emphasis here will be put on the logic behind adopting this approach to study biological function. Another cautionary note is that we are here preaching for the non-cognoscenti, and as the topic is at the fringe of disciplines, surely physicists and biologists alike will encounter boring passages on their most familiar topics. 

The next sections will progressively introduce the problem of complexity (Section 2) and how its origin can be related to critical phenomena. The examples were chosen with the intention to persuade the reader that the same simple laws apply exactly to very different complex phenomena, a notion known in physics as universality. After defining the issues in Part 1, our own advances in the use of this approach to study complexity in life will be discussed by presenting three problems in Part 2 and 3, starting with the description of our long-going work on brain dynamics [2] in Part 2 . The issue of protein dynamics will then be discussed in Part 3 by reviewing our recent work [3] on the finite size scaling analysis of structural protein data from a large database. After that,  we review an empirical and theoretical analysis [4] able to uncover a critical fusion–fission balance in the mitochondrial network of a cell. The series  concludes with a summary of the main message.

Complexity

Recipe for natural complexity: a bit of order and another bit of disorder

Given the fact that complexity is ubiquitous in nature, it is then natural to wonder about how it is built. It has long been suspected that the answer to this question lies at the border between order and chaos. As denoted in the Frauenfelder [5] illustration of Fig. 1, a bewildering variety of apparently disconnected phenomena — all of them dubbed “complex” — exhibited an intermediate level of order and disorder; including life itself, the brain, languages, proteins, turbulence in fluids, slow dynamics of glasses, to name only a few.

Clearly, something repetitive (as in the case of extreme order) does not seem difficult to explore, as would be the case of a crystalline structure. In the same way, what does change erratically in anarchy, as is the case of the trajectories of the molecules of a gas, does not look complex. On the other hand, something that occasionally stops being monotone (whether in space or in time) surprises us and becomes something intriguing and complex. That fair and balanced mixture of order and disorder, or surprise and boredom, is commonly the letter of presentation of complexity. 

Everyday examples abound. Let us take the case of music where there is a balance between surprise and repetition, avoiding excessive monotony or frequent surprise. Another example, involving spatial aspects, could be fingerprints, all similar and different at the same time. 

The full Interdialogue with Rafael Hurtado.

We could ask ourselves if the complexity of the mixture we observe is related to the complexity of the mechanism that generates it. In other words: must we assume that to manufacture the precise “mixture” that prevails in something complex, requires new and more complex laws than those necessary to generate the extreme order or the disorder? We will show that the same simple laws can explain the simple and the complex.

Phases and Universality

Perhaps being a daily experience, we fail to notice that matter in nature comes to us in a few “phases” or states, for example water, mostly in three. It is important to note that in spite of the great qualitative differences between the three states, exactly the same physical laws govern the behavior of their constituent molecules. A relatively small change, in temperature or pressure, can originate very different collective behaviors of the same molecules. In other words, monumental collective changes – which are reflected as different phases – do not require different molecules, physical laws nor any fundamental change in the laws ruling the “interactions” of the molecules.

Let us inspect the case of water: vapor is a gas at the macroscopic level and if we observe it with a powerful microscope, we could count billions of water molecules moving crazily in any direction (the greater the speed the higher the temperature of the vapor). If we slowly cool this gas, we will see that the same molecules move slower, and that small groupings of the molecules begin to form. This occurs because, as the temperature decreases, the mutual attractions between the molecules begin to overcome the tendency to disorder that the thermal agitation gives to them, so the molecules tend to come together. Soon, the small initial clusters continue to capture other molecules, forming drops of water when the temperature is below 100 degrees centigrade. If the temperature continues to drop, the attractive forces between molecules begin to play an increasingly important role in opposing the thermal agitation and at 0 degrees centigrade, they will be able to produce regular microscopic structures, thus causing the solidification of water into ice. These two changes (condensation or solidification and vice versa) are called in physics “phase changes” or “phase transitions”.

The full Interdialogue with Dante Chialvo.

Not more than a century ago, it was thought that these phase transitions resulted in a replacement of one form of matter for another. For example, steam for water and water for ice, because matter was considered to be continuous. This vision continued until, at the dawn of the twentieth century, it was confirmed that matter was made up of discrete sets of atoms and thus it became clear that despite large qualitative differences in the appearance of the phases, they involve the same molecules changing only their conformation. It is interesting to note that coincidentally, Ramon y Cajal also broke the existing idea that the brain was a syncytium, histologically identifying the synapse and then demonstrating the discrete nature of the nervous system.

Phase transitions occur in all the matter that surrounds us, and its study has been systematized recently in a great variety of collective phenomena that occur whenever a large number of non-linear elements interact. It is known, for example, that the correlations between the parts that make up a system obey statistically identical rules, regardless of whether the constituent elements are neurons, ants, grains of sand or water molecules. 

In all cases, the same theory explains how the system is ordered or disordered, what types of collective behavior can be expected, how stable or unstable they will be, how it can be disturbed, etc. The fact that all these disparate phenomena obey the same laws is what is known in physics as universality.

To accept that the same laws govern and explain apparently very disparate phenomena is a process of generalization not without difficulties. It is enough to imagine Galileo Galilei trying to persuade the theologians that the celestial bodies were governed by the same laws as a vulgar stone or a bird feather. It was obvious that they would protest, “How to pretend that those majestic celestial bodies circulating the heavenly spaces where the gods reign will follow the same rules than these mundane objects?” 

Today, the rationale of using the exact same laws to describe the oscillations of a swing and the evolution of planets in its orbits is easily admitted. Still, only a minority are inclined to accept that the laws of physics must be fundamental to understanding the world of neuroscience. This explains the reluctance to admit that the interactions between a multitude of neurons can trigger collective phenomenologies that are qualitatively equivalent to those we observe, for example, as a product of the interaction between atoms of a metal.

Complexity arises in between order and disorder

To describe the universal scenario of the complexity that emerges at a phase transition, we will consider the prototypical case of magnetization, which is an example of collective phenomena. Fig. 2 shows the behavior of a piece of iron subjected to an external magnetic field as the temperature increases. Without going into much detail, the atoms tend to align their magnetic moments with those of their immediate neighbors. In turn, this tendency to order competes with the agitation that temperature produces. If the temperature is low, the final state of the system will be ordered with all spins oriented in the same direction.

The degree of order–disorder of the system can be followed by choosing the appropriate variable; in this case, it is the magnetization. The magnetization is maximum when order prevails (where the image acquires the configuration that is familiar to us: with a north and a south pole) and vanishes when disorder prevails (when the neighboring magnetic moments are randomly oriented). The examples in the three intermediate panels in Fig. 2 show an instantaneous image of the state of the system, where black/white represents north/south spin orientation. 

It can be seen that at very low temperatures almost all spins coincide, meaning that order prevails; while at very high temperatures, disorder prevails resulting in alternating small neighboring regions with opposite alignments. Although the spatial patterns we see are different, they are homogeneous throughout the system. 

The complexity of these patterns can be evaluated in many ways. For instance, one of them involves algorithmic complexity, estimated by computing the length of the algorithm needed to describe that state. If the pattern to be evaluated is repetitive and homogeneous — as in extreme temperature — then the complexity will be vanishingly small. On the other hand, complexity is expected to be high at temperatures close to the critical point, since the spatial patterns correspond to non-homogeneous and complex mixtures of disorder and order. 

The patterns at the critical temperature show a great deal of heterogeneity: there are black “islands” (indicating a coincidence in the spins orientation) of all sizes, which in turn contain white lagoons, which are also of all sizes. This is contrary to what is observed at the extremes. Close to the critical point there is no preferred size for islands or lagoons – in fact the observed patterns are “scale-free”. 

Scale-invariance also implies the largest complexity because it means the largest number of configurations. This absence of scale results in a continuous function obeying a power law, P(S) ~ 1/S^𝛽, where 𝛽 is the exponent that characterizes the distribution of sizes S. This type of power-law obeying function is distinctive of the behavior of complex systems. It is easily recognized when doing logarithms in both axes, with a straight line being perceived, as illustrated in the bottom central panel of Fig. 2.

Complexity can also be observed in the time domain analyzing the temporal fluctuations of the order parameter. The magnetization as a function of time at both extremes of temperature exhibits very small fluctuations, while close to the critical point shows episodes of apparent calm that are interrupted from time to time by large variations. The variability of the magnetization over time is also scale-free, a consequence of the fact that in complex systems the spatial and temporal dynamics are not independent, they are two sides of the same coin. 

The full Interdialogue with Jorge Pullin.

The universality discussed here suggests that the way in which complexity emerges in the example of magnetization can be seen generically in phase transitions in systems very different from one another. Indeed, many examples can be found in recent peer-reviewed scientific literature, such as in flocks of birds, large groups of neurons, stockbrokers interacting, etc… In the subsequent articles in this series, we will discuss three key examples, including important aspects of cerebral dynamics, proteins and mitochondrial dynamics, all governed by common universal principles.

Complexity is always critical

The preceding paragraphs summarize one of the lessons of statistical physics: complexity and criticality are almost synonymous.

The properties that make a system complex are exactly the same as those exhibited by a system when it approaches the critical point of an order–disorder phase transition (let the reader ignore for the moment how a given system manages to reach criticality.) The main point is that close to the critical point, the spatial patterns exhibit a mixture of order and disorder: not all the microscopic elements of the system do the same, nor does each one behave randomly. In this way, the “repertoire” of patterns that the system is able to exhibit increases. 

Turning to the biological consequences of criticality, note that the combination of collective tendencies of order and disorder is fundamental for the adaptability of any collective. The collective needs a certain regularity to function, but also it must be flexible and variable in order to adapt to changes in its environment. 

For instance, let us consider the case of the brain: If all the neurons behaved suddenly in the same way, we would be witnessing an epileptic attack. In the other extreme, if each neuron behaves randomly, they would be uncorrelated and there would be no exchange of information, making any concerted output impossible. In both cases – extreme order or extreme disorder – it is inconceivable that the brain could function.

Editor’s note: This three-part written-recorded series is based on the original written article, “Life at the Edge: Complexity and Criticality in Biological Function,” which was published under a creative commons license by Acta Physica Polonica B. Read the original article here.