Shamit Shrivastava
9 min readFeb 20, 2016
Einstein’s approach to statistical physics

Applying Einstein’s Scientific Philosophy to Biological Physics: A revolution waiting to happen

The recent discovery of gravitational waves has yet again put Albert Einstein back in the limelight, as his genius continues to shake our world even a century later. Einstein possessed a keen interest and a deep understanding of physics that spanned a wide range of phenomena. It would be interesting to know how Einstein would have approached developing underlying theories of physical processes that have biological significance. While some aspects of his work have been applied to biological physics, the totality of his unique scientific approach has usually not been applied to biological processes.

In 1919 Einstein published an insightful article “My theory” in the Times London detailing how he approached a physical phenomenon from a theoretical standpoint:

“There are several kinds of theory in physics. Most of them are constructive. These attempt to build a picture of complex phenomena out of some relatively simple proposition. The kinetic theory of gases, for instance, attempts to refer to molecular movement the mechanical, thermal, and diffusional properties of gases. When we say that we understand a group of natural phenomena, we mean that we have found a constructive theory which embraces them.

But in addition to this most weighty group of theories, there is another group consisting of what I call theories of principle. These employ the analytic, not the synthetic method. Their starting point and foundation are not hypothetical constituents, but empirically observed general properties of phenomena, principles from which mathematical formula are deduced of such a kind that they apply to every case which presents itself. Thermodynamics, for instance, starting from the fact that perpetual motion never occurs in ordinary experience, attempts to deduce from this, by analytic processes, a theory which will apply in every case. The merit of constructive theories is their comprehensiveness, adaptability, and clarity; that of the theories of principle, their logical perfection, and the security of their foundation. The theory of relativity is a theory of principle. To understand it, the principles on which it rests must be grasped.”

If one looks at Einstein’s contributions on the nature of radiation, molecular dimensions, Brownian motion, critical opalescence, and the theory of relativity, it is clear that these were all theories of principles. For instance, starting from the phenomenological relation between the color of the radiation emitted from a blackbody and its temperature, Einstein showed that the second law (the principle that perpetual motion never occurs) requires the energy of radiation to be quantized.

Einstein’s approach to statistical physics was in particular shaped by his unique description and intuition for the second law of thermodynamics, which surprisingly is not covered in textbooks on thermodynamics. In the presence of a complete molecular theory (constructive theory) one obtains the macroscopic properties using Boltzmann principle S=klnw, where S is the entropy (which is related to macroscopic properties), k is Boltzmann constant and ln is the natural log of the microscopic distribution function w (obtained from molecular theory). This principle predicts the relationship between the likelihood of a certain configuration of a system and its entropy and is the foundation of all teleological statistical mechanics approaches. However, Einstein was highly critical of this approach. In his 1910 paper on critical opalescence, Einstein argued

“In order to be able to calculate w, one needs a complete theory (perhaps a complete molecular mechanical theory) of the system under consideration. Given this kind of approach, it, therefore, seems questionable whether Boltzmann’s principle by itself has any meaning whatsoever, i.e., without a complete molecular mechanical theory, or any other theory that completely represents the elementary process (elementary theory). If not supplemented by an elementary or — to put it differently- considered from a phenomenological point of view equation S=klnw appears devoid of content.”

As an alternative, Einstein proposed the inversion of Boltzmann's principle w=e^(S/k) which he employed to great success. Using this approach, one starts from an experimentally obtained formulation of S (phenomenology) and the second law of thermodynamics and deduces the nature of microscopic distribution function (likelihood of different configurations of a system). As one can see the second law comes a priori in this approach while any microscopic or molecular description of the system under investigation is derived from it and hence comes a posteriori. This is reasonably counterintuitive for someone with a background in biological sciences where the role of molecules and their structures not only dominate the language of scientific discourse but also motivates the development of new tools and the experimental approach intended to further the present state of knowledge. Especially since the advent of molecular biology we have become accustomed to picturing molecules as intricate machines where understanding their motion (snapshots) during a phenomenon is equated with the physical understanding of the phenomenon. Although imperative from a constructive point of view, such a presupposition can also be misleading in a thermodynamic framework, where the efficiency of a machine, say an engine, is determined by the changes in the state of the working fluid during a cycle while the structural details of the engine are inconsequential. Moreover to develop a complete constructive theory based on molecular biology for complex biological systems would be nearly impossible. And without the security of foundation of a theory of principles, one is very likely to make wrong assumptions or propositions. On the other hand, Einstein’s approach to physics can provide an alternative theoretical approach to tackle some of the most challenging problems in the biological sciences. I have had the fortune of being part of such an effort by Dr. Konrad Kaufmann and Prof. Matthias Schneider where we are trying to apply Einstein’s approach in the context of biological membranes (interfaces) in living systems.

Protein and lipids (fats) among other molecules self-assemble in an aqueous environment to form semi-permeable bilayer structures that are ubiquitous in biology. It is well accepted that protein and lipid self-assembly is a direct consequence of the second law of thermodynamics. Cells are packed with these membranes or interfaces, forming organelles and structures such as the outer periphery of a cell. In fact, by some estimates, more than 70% of the inter-cellular water is of interfacial nature which has very different properties than the freely diffusing bulk water. An interface can be treated as a thermodynamic system decoupled from the bulk as it has its own specific heat and hence entropy — a fact incidentally underlined by Einstein in his very first publication in 1901! Once the entropy of the interface is established, it has two direct consequences for the interface that can be deduced purely mathematically;

1. Ion Channels — Fluctuation-dissipation theorem: A system that is thermodynamically stable has positive susceptibilities (any perturbation generates a restorative force). Then Einstein’s inversion of Boltzmann principle requires that spontaneous, reversible and quantized perturbation — fluctuations — in all microscopic measurements of the system (membrane) have to exist. The variance of the fluctuation amplitude is related analytically to the second derivative of the entropy of the interface and hence to its macroscopic susceptibilities based on thermodynamic identities (heat capacity to variance in enthalpy fluctuations, compressibility to variance in area fluctuations, capacitance to variance in charge fluctuations etc). How does this relate to a biological phenomenon? Suppose we put a pair of electrode across a semipermeable membrane in an aqueous medium. The second law requires that spontaneous current fluctuation appears in the recorded traces. However, in the case of the membrane being a part of this circuit, electrical fluctuations imply random and spontaneous opening of the membrane through which a charge carrier (usually an ion) can go through. This phenomenon is known as “ion-channels” and is at the core of the present understanding of biological signaling. Note that Einstein’s approach makes no predictions as well as assumptions about the structural or molecular nature of the pore (whether its lipid or protein etc.), rather it provides quantitative estimates of the amplitude and variance of resulting current fluctuations and their timescales derived mathematically from the second law of thermodynamics. On the other hand molecular biology attempts at explaining these “channel events” through hypothesized conformational changes in specific protein structures. Indeed, experiments on pure lipid bilayer show such channel like events in absence of channel proteins and the measured traces are indistinguishable from those measured on biological membranes (timescales, frequency, and amplitude) [1]. This doesn’t mean that proteins don’t play a role in channel formation, it means that they are not consequential for a general theory that explains the phenomenology of channel formation. As Newton eloquently wrote in Rules of Reasoning in Philosophy,

We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the same natural effects we must, so far as possible, assign the same causes“.

It cannot be overstated that a theory of principles is not necessarily contradictory to a molecular approach (constructive theory), it is rather complimentary. However, if a hypothesized constitutive element of the constructive theory is found in contradiction with the theory of principle the hypothesized constitutive element will have to be dropped as it would amount to a violation of second law of thermodynamics.

2. Signaling — Propagation of Information: Conservation laws (mass, momentum, and entropy) of the interface and the second law of thermodynamics require propagation of macroscopic perturbations which can be observed in all macroscopic measurements of the system. For simplicity, a membrane can be approximated as a compressible continuum with zero viscosity and thermal conductivity. Then there will be lossless propagation of information at the velocity of sound in the medium which is related to the second derivative of the entropy potential (compressibility) of the interface. Therefore a perturbation at one end of a cellular membrane, resulting either from an external influence (electrical, mechanical or chemical) or intrinsic fluctuations (changes in protein conformation) can propagate along the membrane to the other end potentially influencing the conformational state of another protein, thus establishing a signaling pathway. While more complexity needs to be factored in for quantitative accuracy of such signaling, conceptually such waves can redefine our understanding of biological signaling and communication in biology from cellular to organ level, including the brain. Indeed propagating macroscopic perturbations that can be observed in all macroscopic measurements of the plasma membrane (electrical, mechanical, optical, chemical, thermal, magnetic etc) have been long known to facilitate communication in our nervous systems and are known as Action Potentials. Now the question remains, do the nerve impulses represent a phenomenon that is purely based on dynamics of electrical circuits as established by Hodgkin and Huxley, for which they received the 1963 Nobel in physiology and is one of the most successful theories in Biological Sciences. Or is there more to it at a much deeper level which is revealed when Einstein’s scientific philosophy is applied to this phenomenon in its entirety, starting from no assumptions but the second law of thermodynamics.

Figure 1. Nonlinear electromechanical pulse measured experimentally in a pure lipid interface. The nonlinear nature of the excitation (threshold, all — or — none) and biphasic nature of the pulse shape were two key features that contributed to the development of the Hodgkin and Huxley model. For the electromechanical pulse recorded in a pure lipid interface as predicted by Einstein’s approach, the two features result entirely from the physical state of the lipid interface and the boundary conditions. Apart from that the amplitude (50–100mV), timescale (200ms) and velocity (~1 m/s) all have the right order of magnitude compared to nerve impulses measured in living systems. For details please see[2].

Clearly, this is a highly controversial topic and the views presented here are only those of a small but growing minority. Applying Einstein’s approach to biological systems makes a testable prediction regarding channels as well as pulse propagation and both are related to the second derivate of the interfacial entropy. These predictions need to be consistent with every single established experimental fact (and not the interpretation! ) on nerve pulse propagation. It is already consistent with electro-mechano-opto-thermal (yes they have all the components and not just electrical) nature of the nerve impulse phenomenon as opposed to purely electrical nature of the Hodgkin and Huxley model. Again in pure lipid films with no ion-channel proteins, pulses, as predicted by Einstein’s approach, have been shown to exist experimentally and they look strikingly similar to nerve impulses, have similar time scales and velocities, have a threshold for excitation (all — or — none) and saturation of amplitude.

Apart from addressing the scientific realism of a particular phenomenon, a scientific theory is more useful and successful if it simplifies certain real-world challenges. In this sense, Hodgkin and Huxley model will continue to be an essential mathematical tool for basic calculations in neurosciences, as it has been for past few decades, specifically in fields like molecular biology that employ a bottom-up approach in understanding systems. However system-level problems, especially that deal with understanding the effects of external fields on the nervous systems, for example research on acute trauma / brain injury (concussion and blast waves), or therapeutic effects of ultrasound and shock waves (drug delivery, sonoporation, permeabilizing blood-brain barrier etc) will be better served by the top-down nature of the proposed thermodynamic approach. The conservation equations that are at the core of the thermodynamic model of nerve pulse propagation can easily incorporate such external fields, which is not trivial in the case of Hodgkin and Huxley model. Ultimately, both approaches and the respective communities will need to work synergistically for any meaningful progress of biological sciences and not be afraid of one another as this tends to be the biggest obstacle in any scientific revolution.

Further reading “Action Potentials are all in one: The false dichotomy of electrical vs mechanical

References (Open Archive)

  1. B. Wunderlich, C. Leirer, A.-L. Idzko, U.F. Keyser, A. Wixforth, V.M. Myles, T. Heimburg, M.F. Schneider. Phase state dependent current fluctuations in pure lipid membrane. Biophysical Journal Volume 96, Issue 11, p4592–4597, 3 June 2009
  2. Shamit Shrivastava and Matthias F. Schneider Evidence for two-dimensional solitary sound waves in a lipid controlled interface and its implications for biological signalling. Journal of Royal Society Interface 18 June 2014.DOI: 10.1098/rsif.2014.0098
Shamit Shrivastava

Biophysics of sound in membranes and its applications. Post Doctoral Researcher, Engineering Sciences, University of Oxford, UK