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Modern science has still not given us a satisfactory empirical explanation of the increasing complexity in living beings through evolutionary history, though whether or not the complexity increases in biological evolution is a hotly debated topic and no agreed-upon definitions of the complexity exist. Nevertheless, this poses the question when comparing simple prokaryotic cells with more complex eukaryotic cells or comparing these with animals or plants or the most complex phenomena, e.g. consciousness and human language. The question of how life actually came into existence is definitely important in this respect. Assuming the hypothesis that in the beginning of the origins of life evolution had to first involve autocatalytic systems which only subsequently acquired the capacity of genetic heredity, we discuss in the present article the possible emergence of digital, discrete information arising from analogue information stored in the intra and intermolecular interactions throughout the molecular evolution. Explaining the origin of life is perhaps central and the most challenging question in modern science. The results of such debates and investigations might shift current biological paradigms and might also have a momentous significance for modern philosophy in understanding our place in universe.

The self-organization of open reaction systems is closely related to specific mechanisms that allow the export of internally generated entropy from systems to their environment. According to the second law of thermodynamics, systems with effective entropy export to the environment are better internally organized. Therefore, they are in thermodynamic states with low entropy. In this context, we study how self-organization in enzymatic reactions depends on their kinetic reaction mechanisms. Enzymatic reactions in an open system are considered to operate in a non-equilibrium steady state, which is achieved by satisfying the principle of maximum entropy production (MEPP). The latter is a general theoretical framework for our theoretical analysis. Detailed theoretical studies and comparisons of the linear irreversible kinetic schemes of an enzyme reaction in two and three states are performed. In both cases, in the optimal and statistically most probable thermodynamic steady state, a diffusion-limited flux is predicted by MEPP. Several thermodynamic quantities and enzymatic kinetic parameters, such as the entropy production rate, the Shannon information entropy, reaction stability, sensitivity, and specificity constants, are predicted. Our results show that the optimal enzyme performance may strongly depend on the number of reaction steps when linear reaction mechanisms are considered. Simple reaction mechanisms with a smaller number of intermediate reaction steps could be better organized internally and could allow fast and stable catalysis. These could be features of the evolutionary mechanisms of highly specialized enzymes.

Namen publikacije je študentom posredovati osnovna znanja iz področja merskih napak in njihovo uporabo pri analizi fizikalnih meritev na čimbolj jasen, pregleden in sistematičen način. V knjižici so opisani osnovni pristopi risanja in branja diagramov ob upoštevanju napak pri merjenju. Kot učno gradivo je knjižica namenjena študentom prvega letnika fizike pri obveznem predmetu Osnovna merjenja in študentom fizike na študijskem programu Predmetni učitelj pri laboratorijskih vajah iz mehanike. Izkušnje kažejo, da so osnovna znanja iz področja merskih napak in risanja ter analize diagramov z upoštevanjem merskih napak za študij fizike tako pomembna, da je smiselno tej učni snovi dati več poudarka in jo obravnavati zelo sistematično, znanje pa je smiselno utrditi z dodatnimi računskimi primeri. Tem potrebam sledi prvi del te knjižice. V drugem delu je opisanih 7 laboratorijskih vaj, ki jih študentje izvedejo samostojno v fizikalnem laboratoriju.

We investigate the relations between the enzyme kinetic flexibility, the rate of entropy production, and the Shannon information entropy in a steady-state enzyme reaction. All these quantities are maximized with respect to enzyme rate constants. We show that the steady-state, which is characterized by the most flexible enzymatic transitions between the enzyme conformational states, coincides with the global maxima of the Shannon information entropy and the rate of entropy production. This steady-state of an enzyme is referred to as globally optimal. This theoretical approach is then used for the analysis of the kinetic and the thermodynamic performance of the enzyme triose-phosphate isomerase. The analysis reveals that there exist well-defined maxima of the kinetic flexibility, the rate of entropy production, and the Shannon information entropy with respect to any arbitrarily chosen rate constant of the enzyme and that these maxima, calculated from the measured kinetic rate constants for the triose-phosphate isomerase are lower, however of the same order of magnitude, as the maxima of the globally optimal state of the enzyme. This suggests that the triose-phosphate isomerase could be a well, but not fully evolved enzyme, as it was previously claimed. Herein presented theoretical investigations also provide clear evidence that the flexibility of enzymatic transitions between the enzyme conformational states is a requirement for the maximal Shannon information entropy and the maximal rate of entropy production.

The origin of translation is critical for understanding the evolution of life, including the origins of life. The canonical genetic code is one of the most dominant aspects of life on this planet, while the origin of heredity is one of the key evolutionary transitions in living world. Why the translation apparatus evolved is one of the enduring mysteries of molecular biology. Assuming the hypothesis, that during the emergence of life evolution had to first involve autocatalytic systems which only subsequently acquired the capacity of genetic heredity, we propose and discuss possible mechanisms, basic aspects of the emergence and subsequent molecular evolution of translation and ribosomes, as well as enzymes as we know them today. It is possible, in this sense, to view the ribosome as a digital-to-analogue information converter. The proposed mechanism is based on the abilities and tendencies of short RNA and polypeptides to fold and to catalyse biochemical reactions. The proposed mechanism is in concordance with the hypothesis of a possible chemical co-evolution of RNA and proteins in the origin of the genetic code or even more generally at the early evolution of life on Earth. The possible abundance and availability of monomers at prebiotic conditions are considered in the mechanism. The hypothesis that early polypeptides were folding on the RNA scaffold is also considered and mutualism in molecular evolutionary development of RNA and peptides is favoured.

We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.

A new definition of life is proposed and discussed in the present article. It is formulated by modifying and extending NASA's working definition of life, which postulates that life is a "self-sustaining chemical system capable of Darwinian evolution". The new definition includes a thermodynamical aspect of life as a far from equilibrium system and considers the flow of information from the environment to the living system. In our derivation of the definition of life we have assumed the hypothesis, that during the emergence of life evolution had to first involve autocatalytic systems that only subsequently acquired the capacity of genetic heredity. The new proposed definition of life is independent of the mode of evolution, regardless of whether Lamarckian or Darwinian evolution operated at the origins of life and throughout evolutionary history. The new definition of life presented herein is formulated in a minimal manner and it is general enough that it does not distinguish between individual (metabolic) network and the collective (ecological) one. The newly proposed definition of life may be of interest for astrobiology, research into the origins of life or for efforts to produce synthetic or artificial life, and it furthermore may also have implications in the cognitive and computer sciences.

Explaining the emergence of life is perhaps central and the most challenging question in modern science. Within this area of research, the emergence and evolution of the genetic code is supposed to be a critical transition in the evolution of modern organisms. The canonical genetic code is one of the most dominant aspects of life on this planet, and thus studying its origin is critical to understanding the evolution of life, including life’s emergence. In this sense it is possible to view the ribosome as a digital-to-analogue information converter. Why the translation apparatus evolved, is one of the enduring mysteries of molecular biology. Assuming the hypothesis that during the emergence of life evolution had to first involve autocatalytic systems, which only subsequently acquired the capacity of genetic heredity, in the present article we discuss some aspects and causes of the possible emergence of digital, discrete information arising from analogue information realized in the intra- and inter-molecular interactions throughout molecular evolution. How such reverse translation was achieved at a molecular level is still unclear. The results of such debates and investigations might shift current biological paradigms and might also have a momentous significance for modern philosophy in understanding our place in the universe.

Movement of charges during enzyme catalytic cycle may be due to conformational changes, or to fast electron or proton transfer, or to both events. In each case, entropy production can be calculated using Terrel L. Hill's method, if relevant microscopic rate constants are known. When ranked by their evolutionary distance from putative common ancestor, three β-lactamases considered in this study show correspondingly increased catalytic constant, catalytic efficiency, and overall entropy production. The acylation and deacylation steps with concomitant proton shuttles are the most important contributors to overall entropy production. The maximal entropy production requirement for the ES↔EP or EP↔E + P step leads to optimal rate constants, performance parameters, and entropy production values, which are close to those extracted from experiments and also rank in accordance with evolutionary distances. Concurrent maximization of entropy productions for both proton transfer steps revealed that evolvability potential of different β-lactamases is similarly high. These results may have implications in particular for latent potential of β-lactamases to evolve further and in general for selection of optimized enzymes through natural or directed evolution.

The authors developed a mathematical model of arachidonic acid (AA) degradation to prostaglandins (PGs) and leukotrienes (LTs), which are implicated in the processes of inflammation and hypersensitivity to non‐steroidal anti‐inflammatory drugs (NSAIDs). The model focuses on two PGs (PGE(2) and PGD(2)) and one LT (LTC(4)), their % increases and their ratios. Results are compared with experimental studies obtained from non‐asthmatics (NAs), and asthmatics tolerant (ATA) or intolerant (AIA) to aspirin. Simulations are carried out for predefined model populations NA, ATA and three AIA, based on the differences of two enzymes, PG E synthase and/or LTC(4)‐synthase in two states, that is, no‐inflammation and inflammation. Their model reveals that the model population with concomitant malfunctions in both enzymes is the most sensitive to NSAIDs, since the duration and the capacity for bronchoconstriction risk are highest after simulated oral dosing of indomethacin. Furthermore, inflammation prolongs the duration of the bronchoconstriction risk in all AIA model populations, and the sensitivity analysis reveals multiple possible scenarios leading to hypersensitivity, especially if inflammatory processes affect the expression of multiple enzymes of the AA metabolic pathway. Their model estimates the expected fold‐changes in enzyme activities and gives valuable information for further targeted transcriptomic/proteomic and metabolomic studies.

A procedure for maximization of the density of entropy production in a single stationary two-step enzyme reaction is developed. Under the constraints of mass conservation, fixed equilibrium constant of a reaction and fixed products of forward and backward enzyme rate constants the existence of maximum in the density of entropy production is demonstrated. In the state with maximal density of entropy production the optimal enzyme rate constants, the stationary concentrations of the substrate and the product, the stationary product yield as well as the stationary reaction flux are calculated. The test, whether these calculated values of the reaction parameters are consistent with their corresponding measured values, is performed for the enzyme Glucose Isomerase. It is found that calculated and measured rate constants agree within an order of magnitude, whereas the calculated reaction flux and the product yield differ from their corresponding measured values for less than 20 % and 5 %, respectively. This indicates that the enzyme Glucose Isomerase, considered in a non-equilibrium stationary state, as found in experiments using the continuous stirred tank reactors, possibly operates close to the state with the maximum in the density of entropy production.

Aspirin-induced asthma (AIA) is a severe inflammatory disease, which affects aspirin-intolerant patients after ingestion of aspirin or other non-steroidal anti-inflammatory drugs (NSAIDs). In this article, a mathematical model describing arachidonic acid metabolism and its interaction with NSAIDs, is used to study the strategy for safe managing of NSAIDs to AIA patients. Three different AIA patient populations are taken into consideration. First, the values of aspirin and ibuprofen limiting doses that might induce symptoms of AIA are calculated and compared to experimentally observed threshold doses to enlighten which AIA patient population is susceptible to aspirin and ibuprofen. Second, the methodology of NSAID administration is studied on AIA populations susceptible to aspirin and ibuprofen by using 1,000 mg dose of aspirin and 200 or 400 mg dose of ibuprofen followed by PGE(2) analogue dosing. Our model results show that successive doses of PGE(2) analogue applied at appropriate time after aspirin or ibuprofen ingestion would enable administration of both NSAIDs to AIA patients. PGE(2) analogue doses and the corresponding times of their applications are calculated. The model is also used to estimate the duration of symptoms of AIA for different aspirin and ibuprofen doses.

In this paper the 4-state latch bridge model proposed by Rembold and Murphy is expanded; first by incorporation of the analytical expression of Ca2+ dependent MLCK activation from the work of Kato et al. and second, by inclusion of the myosin dephosphorylation based on the Michaelis-Menten kinetics. The analysis of the proposed model and the comparison with the original model results as well as with the experimental data is presented. The model is able to predict the steady-state isometric stress and the myosin phosphorylation in dependence on steady cytosolic [Ca2+] as well as the temporal evolution of the system in dependence on the input Ca2+ signal in the form of biphasic transient, whereby our model results are in several aspects in better agreement with experimental observations.

There have been many attempts to use optimization approaches to study the biological evolution of enzyme kinetics. Our basic assumption here is that the biological evolution of catalytic cycle fluxes between enzyme internal functional states is accompanied by increased entropy production of the fluxes and increased Shannon information entropy of the states. We use simplified models of enzyme catalytic cycles and bioenergetically important free-energy transduction cycles to examine the extent to which this assumption agrees with experimental data. We also discuss the relevance of Prigogine’s minimal entropy production theorem to biological evolution.

The action of different agonists such as acetylcholine on the membrane of airway smooth muscle cells may induce cytosolic Ca(2+) oscillations which can be a part of the Ca(2+) signalling pathway, eventually leading to cell contraction. The aim of the present study is to present a mathematical model of the possible effect of the initial Ca(2+) distribution within the cell on the form and frequency of induced Ca(2+) oscillations. It takes into account intracellular Ca(2+) stores such as sarcoplasmic reticulum and cytosolic proteins as well as Ca(2+) exchange across the plasma membrane. We are able to demonstrate a closer agreement of model predictions with observed Ca(2+) traces for a significantly wider range of parameter values, as was previously reported. We show also that the total cellular Ca(2+) content is an important system parameter especially because of the content in sarcoplasmic reticulum. At a total Ca(2+) increase of about 20%, the oscillation frequency increases by 25%; also, damped oscillations become sustained. Cases are indicated in which such a situation could occur.

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES ↔ EP in a generalized reversible Michaelis–Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES → EP for three types of β-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.

A quantitative high-performance thin-layer chromatographic (HPTLC) method was developed for the analysis of ampicillin in urine. A dioxane—water—n-butanol—formic acid mobile phase system and HPTLC Silica gel 60 F254 as stationary phase were used. Quantitation was realized on a Zeiss PMQ 2 densitometer connected to a Varian A-25 recorder and an Apple II microcomputer or alternatively with an HP 9830A computer and HP 9862A plotter. A good linear range of detection (0.05–1.00 μg) at 480 nm was obtained. Standard statistical methods demonstrated good reproducibility (coefficient of variation is not greater than 3%). The method is appropriate for ampicillin quality control and pharmacokinetic studies.