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Register a new userDiscreteness-Induced Transitions in Autocatalytic Systems
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To study the dynamics of chemical processes, we often adopt rate equations to observe the change in chemical concentrations. However, when the number of the molecules is small, the fluctuations cannot be neglected. We often study the effects of fluctuations with the help of stochastic differential equations. Chemicals are composed of molecules on a microscopic level. In principle, the number of molecules must be an integer, which must only change discretely. However, in analysis using stochastic differential equations, the fluctuations are regarded as continuous changes. This approximation can only be valid if applied to fluctuations that involve a sufficiently large number of molecules. In the case of extremely rare chemical species, the actual discreteness of the molecules may critically affect the dynamics of the system. To elucidate the effects of the discreteness, we study an autocatalytic system consisting of several interacting chemical species with a small number of molecules through stochastic particle simulations. We found novel states, which were characterized as an extinction of molecule species, due to the discrete nature of the molecules. We also observed a strong dependence of the chemical concentrations on the size of the system, which was caused by transitions to the novel states.
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To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however, the discreteness in the number of molecules cannot be neglected since the number of molecules must be an integer. This discreteness can be important in biochemical reactions, where the total number of molecules is not significantly larger than the number of chemical species. To elucidate the effects of such discreteness, we study autocatalytic reaction systems comprising several chemical species through stochastic particle simulations. The generation of novel states is observed; it is caused by the extinction of some molecular species due to the discreteness in their number. We demonstrate that the reaction dynamics are switched by a single molecule, which leads to the reconstruction of the acting network structure. We also show the strong dependence of the chemical concentrations on the system size, which is caused by transitions to discreteness-induced novel states.
A self-consistent equation to derive a discreteness-induced stochastic steady state is presented for reaction-diffusion systems. For this formalism, we use the so-called Kuramoto length, a typical distance over which a molecule diffuses in its lifetime, as was originally introduced to determine if local fluctuations influence globally the whole system. We show that this Kuramoto length is also relevant to determine whether the discreteness of molecules is significant or not. If the number of molecules of a certain species within the Kuramoto length is small and discrete, localization of some other chemicals is brought about, which can accelerate certain reactions. When this acceleration influences the concentration of the original molecule species, it is shown that a novel, stochastic steady state is induced that does not appear in the continuum limit. A theory to obtain and characterize this state is introduced, based on the self-consistent equation for chemical concentrations. This stochastic steady state is confirmed by numerical simulations on a certain reaction model, which agrees well with the theoretical estimation. Formation and coexistence of domains with different stochastic states are also reported, which is maintained by the discreteness. Relevance of our result to intracellular reactions is briefly discussed.
Large molecules such as proteins and nucleic acids are crucial for life, yet their primordial origin remains a major puzzle. The production of large molecules, as we know it today, requires good catalysts, and the only good catalysts we know that can accomplish this task consist of large molecules. Thus the origin of large molecules is a chicken and egg problem in chemistry. Here we present a mechanism, based on autocatalytic sets (ACSs), that is a possible solution to this problem. We discuss a mathematical model describing the population dynamics of molecules in a stylized but prebiotically plausible chemistry. Large molecules can be produced in this chemistry by the coalescing of smaller ones, with the smallest molecules, the `food set, being buffered. Some of the reactions can be catalyzed by molecules within the chemistry with varying catalytic strengths. Normally the concentrations of large molecules in such a scenario are very small, diminishing exponentially with their size. ACSs, if present in the catalytic network, can focus the resources of the system into a sparse set of molecules. ACSs can produce a bistability in the population dynamics and, in particular, steady states wherein the ACS molecules dominate the population. However to reach these steady states from initial conditions that contain only the food set typically requires very large catalytic strengths, growing exponentially with the size of the catalyst molecule. We present a solution to this problem by studying `nested ACSs, a structure in which a small ACS is connected to a larger one and reinforces it. We show that when the network contains a cascade of nested ACSs with the catalytic strengths of molecules increasing gradually with their size (e.g., as a power law), a sparse subset of molecules including some very large molecules can come to dominate the system.
We review the mechanism and consequences of the bridging-induced attraction, a generic biophysical principle which underpins some existing models for chromosome organisation in 3-D. This attraction, which was revealed in polymer physics-inspired computer simulations, is a generic clustering tendency arising in multivalent chromatin-binding proteins, and it provides an explanation for the biogenesis of nuclear bodies and transcription factories via microphase separation. Including post-translational modification reactions involving these multivalent proteins can account for the fast dynamics of the ensuing clusters, as is observed via microscopy and photobleaching experiments. The clusters found in simulations also give rise to chromatin domains which conform well with the observation of A/B compartments in HiC experiments.
Recent literatures reported blue-green emission from amyloid fibril as exclusive signature of fibril formation. This unusual visible luminescence is regularly used to monitor fibril growth. Blue-green emission has also been observed in crystalline protein and in solution. However, the origin of this emission is not known exactly. Our spectroscopic study of serum proteins reveals that the blue-green emission is a property of protein monomer. Evidences suggest that semiconductor-like band structure of proteins with the optical band-gap in the visible region is possibly the origin of this phenomenon. We show here that the band structure of proteins is primarily the result of electron delocalization through the peptide chain, rather than through the hydrogen bond network in secondary structure.
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