In the previous chapter we were concerned with the HI between two solute particles. This has been... more In the previous chapter we were concerned with the HI between two solute particles. This has been considered to be the first and most important step towards the full characterization and understanding of the phenomenon of HI. It should be remembered, however, that the problem of pairwise HI has been isolated as a single factor that contributes to the total "driving force" of very complex biochemical processes. At present we are still far from having a full, or even a satisfactory, knowledge of the pairwise HI phenomenon. Much is left to be done on both the experimental and the theoretical fronts before we may claim that this goal has been reached. Nevertheless, this fact alone should not hinder our efforts to study more complex processes involving HI. The next step that we have in mind is the study of the HI among many simple solute particles in a solvent. This step serves as a bridge leading from the simplest pairwise HI to the enormously more complex biochemical processes. This chapter is devoted to surveying the various experimental sources from which we can obtain information on HI among many solute particles. As in the case of pairwise HI we shall find that information on this subject is rather fragmentary and much more should be done before any reasonably clear view of this field emerges.
Ben-Naim, Arieh, 1934-Cooperativity and regulation in biochemical processes/Arieh Ben-Naim. p. cm... more Ben-Naim, Arieh, 1934-Cooperativity and regulation in biochemical processes/Arieh Ben-Naim. p. cm. Inc1udes bibliographical references and index. ISBN 0-306-46331-8 I. Cooperative binding (Biochemistry) 2. Statistical mechanics. 3. Physical biochemistry. I. Title.
This article provides answers to the two questions posed in the title. It is argued that, contrar... more This article provides answers to the two questions posed in the title. It is argued that, contrary to many statements made in the literature, neither entropy, nor the Second Law may be used for the entire universe. The origin of this misuse of entropy and the second law may be traced back to Clausius himself. More resent (erroneous) "justification" is also discussed.
This lecture is addressed to anyone who has studied thermodynamics. It is more of pedagogical cha... more This lecture is addressed to anyone who has studied thermodynamics. It is more of pedagogical character, rather than a research topic. The main idea is that contrary to what is written in most textbooks, mixing of ideal gases, by itself, does not affect any thermodynamic property of the system. In particular, the entropy of the system does not change when mixing ideal gases. Hence, thermodynamically speaking, mixing, by itself, is a "non-thermodynamic-process.” The process of mixing can be either reversible or irreversible. The same is true for de-mixing processes. The process of assimilation, involving indistinguishable particles is introduced. It is shown that assimilation does affect the entropy of a system. The informational-theoretical aspects of mixing and assimilation are discussed.
We start with reviewing the origin of the idea that entropy and the Second Law are associated wit... more We start with reviewing the origin of the idea that entropy and the Second Law are associated with the Arrow of Time. We then introduced a new definition of entropy based on Shannon’s Measure of Information (SMI). The SMI may be defined on any probability distribution; and therefore it is a very general concept. On the other hand entropy is defined on a very special set of probability distributions. More specifically the entropy of a thermodynamic system is related the probability distribution of locations and velocities (or momenta) of all the particles, which maximized the Shannon Measure of Information. As such, entropy is not a function of time. We also show that the H-function, as defined by Boltzmann is an SMI but not entropy. Therefore, while the H-function, as an SMI may change with time, Entropy, as a limit of the SMI does not change with time.
The International Journal of Physics, Jan 23, 2013
The idea that the hydrophobic effect is the major driving force for processes such as protein fol... more The idea that the hydrophobic effect is the major driving force for processes such as protein folding and protein-protein association has prevailed in the biochemical literature for over half a century. It has recently become clear that the evidence in favor of the hydrophobic paradigm has totally dissipated. The dominance of the hydrophobic effect has been reduced into nothing but a myth. On the other hand, the new paradigm based on a host of hydrophilic effects has emerged. This new paradigm offers simple and straightforward answers to the long sought problems of protein folding and protein-protein association.
Statistical Thermodynamics for Chemists and Biochemists, 1992
Liquids are the most important thermodynamic phase for life, but also other materials like a plas... more Liquids are the most important thermodynamic phase for life, but also other materials like a plasma behave in many aspects like liquids. Liquids are much more difficult to describe in terms of their internal interactions compared to crystals or ideal gases. The problem lies in the irregular distances that determine the potential energy between particles. The structure of liquids can be either simulated by Monte Carlo or molecular dynamics techniques or be approached by integral equation techniques. Integral equation techniques are approximative but computationally inexpensive and not affected by statistical inaccuracies.
Molecular dynamics simulations were used to calculate the force between two simple hydrophilic so... more Molecular dynamics simulations were used to calculate the force between two simple hydrophilic solutes in dilute aqueous solution. The "solutes" were two water molecules in the same relative orientation as the nextnearest neighbors in hexagonal ice I. Both the direct and solvent-induced contributions to the force were calculated as a function of separation distance. The total force between the solutes was found to be most attractive at 5.0 (-1.6 kcal/mol/A). The potential of mean force had a minimum at 4.3 A, which is 0.2 A closer than the next-nearest-neighbor distance in ice. A parallel set of simulations were conducted with the partial charges on the "solutes" removed to examine hydrophobic analogs. In this case, the total force was most attractive at 3.5 A (-0.9 kcal/mol/A), and the minimum of the potential was at the contact distance of 3.2 A. In agreement with earlier predictions, the maximum solvent-induced contribution to the potential was cu. 4 times more negative for the hydrophilic "solutes" than for the hydrophobic ones. These differences are shown to be due predominantly to a solvent water molecule which simultaneously hydrogen bonds to both hydrophilic "solutes". The results support earlier assertions that solvent-induced interactions between polar amino acid residues are more important in protein folding and stability than generally considered.
ABSTRACT The solubilities of methane, ethane, propane and n-butane were measured in aqueous solut... more ABSTRACT The solubilities of methane, ethane, propane and n-butane were measured in aqueous solutions of sodium octanoate of molar concentrations between 0–0.8M. From these measurements we have computed the standard free energies, entropies and enthalpies for the process of transferring the solute molecules from the gaseous phase into the solutions. We found that propane and n-butane behave as expected at, and beyond, the cmc, namely the solubility takes a steep turn upwards. On the other hand, methane and ethane seem to cross the cmc with almost no change in their solubility. A tentative interpretation of this behavior is suggested, based on the competing effects of salting out and solubilization.
Some concepts, such as energy landscape, Gibbs energy landscape, and cooperativity, frequently us... more Some concepts, such as energy landscape, Gibbs energy landscape, and cooperativity, frequently used in the theory of protein folding, are examined exactly in one-dimensional systems. It is shown that much of the confusion that exists regarding these, and other concepts arise from the misinterpretation of Anfinsen's thermodynamic hypothesis.
We present an inventory of factors that determine the stability of proteins. It is shown that the... more We present an inventory of factors that determine the stability of proteins. It is shown that the (true) potential of mean force between pairs of amino acid residues does not belong to this inventory. Therefore, such quantities are not needed for either estimating the stability of a protein or for predicting its structure. It is also shown that the so-called “statistical potential” as derived from the data bank of protein structures is neither the potential nor the potential of mean force for pairs of amino-acid residues. A critical examination of the nonadditivity of the many body potential of the mean force is also presented.
The pair correlation functions for a mixture of two Lennard–Jones particles were computed by both... more The pair correlation functions for a mixture of two Lennard–Jones particles were computed by both the Percus–Yevick equations and by molecular dynamics. The changes in the pair correlation function resulting from changes in the composition of the mixtures are quite unexpected. Essentially, identical changes are obtained from the Percus–Yevick equations and from molecular dynamics simulations. The molecular reason for this unexpected behavior is discussed.
The European Physical Journal Special Topics, 2013
ABSTRACT It is commonly accepted that water plays an essential role in determining both the stabi... more ABSTRACT It is commonly accepted that water plays an essential role in determining both the stability of the 3D structure of protein, as well as speed of the protein folding process. How exactly water does that, is still very controversial. Until recently it was believed that various hydrophobic effects, which originate from the solvent, are the dominant factors. In the first part of this article we discuss the paradigm shift from hydrophobic (HϕO), to a hydrophilic (HϕI) based theory of protein folding. Next, we analyze the types of solvent-induced forces that are exerted on various groups on the protein. We find that the HϕI-HϕI solvent-induced forces are likely to be the strongest. These forces originate from water molecules forming hydrogen-bonded-bridges between two, or more hydrophilic groups attached to the protein. Therefore, it is argued that these forces are also the forces that force the protein to fold, in a short time, along a narrow range of pathways. This paradigm shift brings us, as close as we can hope for, to a solution to the general problem of protein folding.
In (2015), I wrote a book with the same title as this article. The book's subtitle is: "What we k... more In (2015), I wrote a book with the same title as this article. The book's subtitle is: "What we know and what we do not know." On the book's dedication page, I wrote [1]: "This book is dedicated to readers of popular science books who are baffled, perplexed, puzzled, astonished, confused, and discombobulated by reading about Information, Entropy, Life and the Universe." In the first part of this article, I will present the definitions of two central concepts: the "Shannon measure of information" (SMI), in Information Theory, and "Entropy", in Thermodynamics. Following these definitions, I will discuss the framework of their applicability. In the second part of the article, I will examine the question of whether living systems and the entire universe are, or are not within the framework of applicability of the concepts of SMI and Entropy. I will show that much of the confusion that exists in the literature arises because of people's ignorance about the framework of applicability of these concepts.
In the previous chapter we were concerned with the HI between two solute particles. This has been... more In the previous chapter we were concerned with the HI between two solute particles. This has been considered to be the first and most important step towards the full characterization and understanding of the phenomenon of HI. It should be remembered, however, that the problem of pairwise HI has been isolated as a single factor that contributes to the total "driving force" of very complex biochemical processes. At present we are still far from having a full, or even a satisfactory, knowledge of the pairwise HI phenomenon. Much is left to be done on both the experimental and the theoretical fronts before we may claim that this goal has been reached. Nevertheless, this fact alone should not hinder our efforts to study more complex processes involving HI. The next step that we have in mind is the study of the HI among many simple solute particles in a solvent. This step serves as a bridge leading from the simplest pairwise HI to the enormously more complex biochemical processes. This chapter is devoted to surveying the various experimental sources from which we can obtain information on HI among many solute particles. As in the case of pairwise HI we shall find that information on this subject is rather fragmentary and much more should be done before any reasonably clear view of this field emerges.
Ben-Naim, Arieh, 1934-Cooperativity and regulation in biochemical processes/Arieh Ben-Naim. p. cm... more Ben-Naim, Arieh, 1934-Cooperativity and regulation in biochemical processes/Arieh Ben-Naim. p. cm. Inc1udes bibliographical references and index. ISBN 0-306-46331-8 I. Cooperative binding (Biochemistry) 2. Statistical mechanics. 3. Physical biochemistry. I. Title.
This article provides answers to the two questions posed in the title. It is argued that, contrar... more This article provides answers to the two questions posed in the title. It is argued that, contrary to many statements made in the literature, neither entropy, nor the Second Law may be used for the entire universe. The origin of this misuse of entropy and the second law may be traced back to Clausius himself. More resent (erroneous) "justification" is also discussed.
This lecture is addressed to anyone who has studied thermodynamics. It is more of pedagogical cha... more This lecture is addressed to anyone who has studied thermodynamics. It is more of pedagogical character, rather than a research topic. The main idea is that contrary to what is written in most textbooks, mixing of ideal gases, by itself, does not affect any thermodynamic property of the system. In particular, the entropy of the system does not change when mixing ideal gases. Hence, thermodynamically speaking, mixing, by itself, is a "non-thermodynamic-process.” The process of mixing can be either reversible or irreversible. The same is true for de-mixing processes. The process of assimilation, involving indistinguishable particles is introduced. It is shown that assimilation does affect the entropy of a system. The informational-theoretical aspects of mixing and assimilation are discussed.
We start with reviewing the origin of the idea that entropy and the Second Law are associated wit... more We start with reviewing the origin of the idea that entropy and the Second Law are associated with the Arrow of Time. We then introduced a new definition of entropy based on Shannon’s Measure of Information (SMI). The SMI may be defined on any probability distribution; and therefore it is a very general concept. On the other hand entropy is defined on a very special set of probability distributions. More specifically the entropy of a thermodynamic system is related the probability distribution of locations and velocities (or momenta) of all the particles, which maximized the Shannon Measure of Information. As such, entropy is not a function of time. We also show that the H-function, as defined by Boltzmann is an SMI but not entropy. Therefore, while the H-function, as an SMI may change with time, Entropy, as a limit of the SMI does not change with time.
The International Journal of Physics, Jan 23, 2013
The idea that the hydrophobic effect is the major driving force for processes such as protein fol... more The idea that the hydrophobic effect is the major driving force for processes such as protein folding and protein-protein association has prevailed in the biochemical literature for over half a century. It has recently become clear that the evidence in favor of the hydrophobic paradigm has totally dissipated. The dominance of the hydrophobic effect has been reduced into nothing but a myth. On the other hand, the new paradigm based on a host of hydrophilic effects has emerged. This new paradigm offers simple and straightforward answers to the long sought problems of protein folding and protein-protein association.
Statistical Thermodynamics for Chemists and Biochemists, 1992
Liquids are the most important thermodynamic phase for life, but also other materials like a plas... more Liquids are the most important thermodynamic phase for life, but also other materials like a plasma behave in many aspects like liquids. Liquids are much more difficult to describe in terms of their internal interactions compared to crystals or ideal gases. The problem lies in the irregular distances that determine the potential energy between particles. The structure of liquids can be either simulated by Monte Carlo or molecular dynamics techniques or be approached by integral equation techniques. Integral equation techniques are approximative but computationally inexpensive and not affected by statistical inaccuracies.
Molecular dynamics simulations were used to calculate the force between two simple hydrophilic so... more Molecular dynamics simulations were used to calculate the force between two simple hydrophilic solutes in dilute aqueous solution. The "solutes" were two water molecules in the same relative orientation as the nextnearest neighbors in hexagonal ice I. Both the direct and solvent-induced contributions to the force were calculated as a function of separation distance. The total force between the solutes was found to be most attractive at 5.0 (-1.6 kcal/mol/A). The potential of mean force had a minimum at 4.3 A, which is 0.2 A closer than the next-nearest-neighbor distance in ice. A parallel set of simulations were conducted with the partial charges on the "solutes" removed to examine hydrophobic analogs. In this case, the total force was most attractive at 3.5 A (-0.9 kcal/mol/A), and the minimum of the potential was at the contact distance of 3.2 A. In agreement with earlier predictions, the maximum solvent-induced contribution to the potential was cu. 4 times more negative for the hydrophilic "solutes" than for the hydrophobic ones. These differences are shown to be due predominantly to a solvent water molecule which simultaneously hydrogen bonds to both hydrophilic "solutes". The results support earlier assertions that solvent-induced interactions between polar amino acid residues are more important in protein folding and stability than generally considered.
ABSTRACT The solubilities of methane, ethane, propane and n-butane were measured in aqueous solut... more ABSTRACT The solubilities of methane, ethane, propane and n-butane were measured in aqueous solutions of sodium octanoate of molar concentrations between 0–0.8M. From these measurements we have computed the standard free energies, entropies and enthalpies for the process of transferring the solute molecules from the gaseous phase into the solutions. We found that propane and n-butane behave as expected at, and beyond, the cmc, namely the solubility takes a steep turn upwards. On the other hand, methane and ethane seem to cross the cmc with almost no change in their solubility. A tentative interpretation of this behavior is suggested, based on the competing effects of salting out and solubilization.
Some concepts, such as energy landscape, Gibbs energy landscape, and cooperativity, frequently us... more Some concepts, such as energy landscape, Gibbs energy landscape, and cooperativity, frequently used in the theory of protein folding, are examined exactly in one-dimensional systems. It is shown that much of the confusion that exists regarding these, and other concepts arise from the misinterpretation of Anfinsen's thermodynamic hypothesis.
We present an inventory of factors that determine the stability of proteins. It is shown that the... more We present an inventory of factors that determine the stability of proteins. It is shown that the (true) potential of mean force between pairs of amino acid residues does not belong to this inventory. Therefore, such quantities are not needed for either estimating the stability of a protein or for predicting its structure. It is also shown that the so-called “statistical potential” as derived from the data bank of protein structures is neither the potential nor the potential of mean force for pairs of amino-acid residues. A critical examination of the nonadditivity of the many body potential of the mean force is also presented.
The pair correlation functions for a mixture of two Lennard–Jones particles were computed by both... more The pair correlation functions for a mixture of two Lennard–Jones particles were computed by both the Percus–Yevick equations and by molecular dynamics. The changes in the pair correlation function resulting from changes in the composition of the mixtures are quite unexpected. Essentially, identical changes are obtained from the Percus–Yevick equations and from molecular dynamics simulations. The molecular reason for this unexpected behavior is discussed.
The European Physical Journal Special Topics, 2013
ABSTRACT It is commonly accepted that water plays an essential role in determining both the stabi... more ABSTRACT It is commonly accepted that water plays an essential role in determining both the stability of the 3D structure of protein, as well as speed of the protein folding process. How exactly water does that, is still very controversial. Until recently it was believed that various hydrophobic effects, which originate from the solvent, are the dominant factors. In the first part of this article we discuss the paradigm shift from hydrophobic (HϕO), to a hydrophilic (HϕI) based theory of protein folding. Next, we analyze the types of solvent-induced forces that are exerted on various groups on the protein. We find that the HϕI-HϕI solvent-induced forces are likely to be the strongest. These forces originate from water molecules forming hydrogen-bonded-bridges between two, or more hydrophilic groups attached to the protein. Therefore, it is argued that these forces are also the forces that force the protein to fold, in a short time, along a narrow range of pathways. This paradigm shift brings us, as close as we can hope for, to a solution to the general problem of protein folding.
In (2015), I wrote a book with the same title as this article. The book's subtitle is: "What we k... more In (2015), I wrote a book with the same title as this article. The book's subtitle is: "What we know and what we do not know." On the book's dedication page, I wrote [1]: "This book is dedicated to readers of popular science books who are baffled, perplexed, puzzled, astonished, confused, and discombobulated by reading about Information, Entropy, Life and the Universe." In the first part of this article, I will present the definitions of two central concepts: the "Shannon measure of information" (SMI), in Information Theory, and "Entropy", in Thermodynamics. Following these definitions, I will discuss the framework of their applicability. In the second part of the article, I will examine the question of whether living systems and the entire universe are, or are not within the framework of applicability of the concepts of SMI and Entropy. I will show that much of the confusion that exists in the literature arises because of people's ignorance about the framework of applicability of these concepts.
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