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Applied Longitudinal Data Analysis Modeling Change And Event Occurrence

Supramolecular Chirality in Self-Assembled Systems

THE homochirality of natural amino acids and sugars remains a puzzle for theories of the chemical origin of life1–18. In 1953 Frank7 proposed a reaction scheme by which a combination of autocatalysis and inhibition in a system of replicating chiral molecules can allow small random fluctuations in an initially racemic mixture to tip the balance to yield almost exclusively one enantiomer. Here we show experimentally that autocatalysis in a chemical reaction can indeed enhance a small initial enantiomeric excess of a chiral molecule. When a 5-pyrimidyl alkanol with a small (2%) enantiomeric excess is treated with diisopropylzinc and pyrimidine-5-car-boxaldehyde, it undergoes an autocatalytic reaction to generate more of the alkanol. Because the reaction involves a chiral catalyst generated from the initial alkanol, and because the catalytic step is enantioselective, the enantiomeric excess of the product is enhanced. This process provides a mechanism by which a small initial imbalance in chirality can become overwhelming.

Asymmetric autocatalysis and amplification of enantiomeric excess of a chiral molecule

Over the past thirty years, a new systemic conception of life has emerged at the forefront of science. New emphasis has been given to complexity, networks, and patterns of organisation, leading to a novel kind of 'systemic' thinking. This volume integrates the ideas, models, and theories underlying the systems view of life into a single coherent framework. Taking a broad sweep through history and across scientific disciplines, the authors examine the appearance of key concepts such as autopoiesis, dissipative structures, social networks, and a systemic understanding of evolution. The implications of the systems view of life for health care, management, and our global ecological and economic crises are also discussed. Written primarily for undergraduates, it is also essential reading for graduate students and researchers interested in understanding the new systemic conception of life and its implications for a broad range of professions - from economics and politics to medicine, psychology and law.

The Systems View of Life: A Unifying Vision

The phase-field method has become an important and extremely versatile technique for simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface approach, it allows us to study the evolution of arbitrary complex grain morphologies without any presumption on their shape or mutual distribution. It is also straightforward to account for different thermodynamic driving forces for microstructure evolution, such as bulk and interfacial energy, elastic energy and electric or magnetic energy, and the effect of different transport processes, such as mass diffusion, heat conduction and convection. The purpose of the paper is to give an introduction to the phase-field modeling technique. The concept of diffuse interfaces, the phase-field variables, the thermodynamic driving force for microstructure evolution and the kinetic phase-field equations are introduced. Furthermore, common techniques for parameter determination and numerical solution of the equations are discussed. To show the variety in phase-field models, different model formulations are exploited, depending on which is most common or most illustrative.

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An introduction to phase-field modeling of microstructure evolution

I Historical Roots: From Heat Engines to Cosmology
1 Basic Concepts and the Law of Gases
2 The First Law of Thermodynamics
3 The Second Law of Thermodynamics and the Arrow of Time
4 Entropy in the Realm of Chemical Reactions

II Equilibrium Thermodynamics
5 Extremum Principles and General Thermodynamics Relations
6 Basic Thermodynamics of Gases, Liquids and Solids
7 Thermodynamics of Phase Change
8 Thermodynamics of Solutions
9 Thermodynamics of Chemical Transformations
10 Fields and Internal Degrees of Freedom
11 Thermodynamics of Radiation

III Fluctuations and Stability
12 The Gibbs Stability Theory
13 Critical Phenomena and Configurational Heat Capacity
14 Entropy Productions, Fluctuations and Small Systems

IV Linear Nonequilibrium Thermodynamics
15 Nonequilibrium Thermodynamics: The Foundations
16 Nonequilibrium Thermodynamics: The Linear Regime
17 Nonequilibrium Stationary State and Their Stability: Linear Regime

V Order Through Fluctuations
18 Nonlinear Thermodynamics
19 Dissipative Structures
20 Elements of Statistical Thermodynamics
21 Self-Organization and Dissipative Structures in Nature

Modern Thermodynamics: From Heat Engines to Dissipative Structures

Sodium chlorate (NaClO3) crystals are optically active although the molecules of the compound are not chiral. When crystallized from an aqueous solution while the solution is not stirred, statistically equal numbers of levo (L) and dextro (D) NaClO3 crystals were found. When the solution was stirred, however, almost all of the NaClO3 crystals (99.7 percent) in a particular sample had the same chirality, either levo or dextro. This result represents an experimental demonstration of chiral symmetry breaking or total spontaneous resolution on a macroscopic level brought about by autocatalysis and competition between L- and D-crystals.

https://science.sciencemag.org/content/sci/250/4983/975.full.pdf

Chiral Symmetry Breaking in Sodium Chlorate Crystallization

It has long been known that Earth's biochemistry is overwhelmingly dissymmetric or chiral1–4. In model chemical systems5–7 that spontaneously evolve to a state dominated by either the L or the D enantiomer, parity violation in β-decay and that attributable to weak neutral currents (WNC) in molecules8,9 is thought to be too small to have any significant influence on the emergent chirality10,11. Other conceivable systematic chiral influences are generally even weaker12–14. We show here that there is a simple and extremely sensitive mechanism by which a minute but systematic chiral interaction, no stronger than the WNC interaction in amino acids, can, over a period of ∼15,000 yr, determine which enantiomer will dominate. Such a mechanism is especially interesting when considering the origins of terrestrial biochemistry, particularly in view of the work by Mason and Tranter15, who found that it is the terrestrially dominant L amino acids that are favoured by the WNC interaction.

Weak neutral currents and the origin of biomolecular chirality

During the past decade, chirally autocatalytic systems that exhibit unusual and interesting phenomena, such as spontaneous chiral symmetry breaking and stochastic behavior, have been identified. In this Account we outline the context in which chiral autocatalysis is of interest, summarize recent advances, and discuss our current understanding of the underlying kinetics and mechanisms. In addition, we note some fundamental aspects of amplification of enantiomeric excess and sensitivity of symmetry breaking transitions to asymmetric factors.

Dilip K. Kondepudi

Papers

Modern Thermodynamics: From Heat Engines to Dissipative Structures

Chiral Symmetry Breaking in Sodium Chlorate Crystallization

Weak neutral currents and the origin of biomolecular chirality

Chiral autocatalysis, spontaneous symmetry breaking, and stochastic behavior.

The Handedness of the Universe