Andrej Dobovišek

Enzyme kinetics and the maximum entropy production principle.

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.

Role of expression of prostaglandin synthases 1 and 2 and leukotriene C4 synthase in aspirin-intolerant asthma: a theoretical study

Altered expressions of the key enzymes in arachidonic acid (AA) metabolism, prostaglandin synthase 1 and 2 and cysteinyl leukotriene C4 synthase, are of importance in understanding aspirin-induced asthma. We propose a mathematical model of AA metabolism and its interaction with non-steroidal anti-inflammatory drugs (NSAIDs). Model simulations depict the impact of modified expressions of the above enzymes on the time dependent synthesis of cysteinyl leukotrienes and anti-inflammatory prostaglandins before and during NSAID exposure in different model states describing healthy humans as well as aspirin-tolerant and -intolerant asthmatics. The results are compared and evaluated with experimental data taken from the literature. Our results identify the decreased expression of prostaglandin H synthase 1 and increased expression of leukotriene C4 synthase as the key elements in AA metabolism that contribute to increased leukotriene C4 and decreased anti-inflammatory prostaglandins after NSAID dosing in aspirin-intolerant patients. On the other hand, the decreased expression of prostaglandin H synthase 2 implies permanently increased leukotriene C4 and lowers the sensitivity to increased drug doses. The model is used for identification of susceptible patient populations for aspirin and ibuprofen, and for identification of critical aspirin doses that might induce bronchoconstriction.

On the Problem of Formulating Principles in Nonequilibrium Thermodynamics

In this work, we consider the choice of a system suitable for the formulation of principles in nonequilibrium thermodynamics. It is argued that an isolated system is a much better candidate than a system in contact with a bath. In other words, relaxation processes rather than stationary processes are more appropriate for the formulation of principles in nonequilibrium thermodynamics. Arguing that slow varying relaxation can be described with quasi-stationary process, it is shown for two special cases, linear nonequilibrium thermodynamics and linearized Boltzmann equation, that solutions of these problems are in accordance with the maximum entropy production principle.

Maximum Entropy Production and Maximum Shannon Entropy as Germane Principles for the Evolution of Enzyme Kinetics

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.

Mathematical Modelling of Ca 2+ Oscillations in Airway Smooth Muscle Cells

The action of different agonists such as acetylcholine on the membrane of airway smooth muscle cells may induce cytosolic Ca2+ oscillations which can be a part of the Ca2+ 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 Ca2+ distribution within the cell on the form and frequency of induced Ca2+ oscillations. It takes into account intracellular Ca2+ stores such as sarcoplasmic reticulum and cytosolic proteins as well as Ca2+ exchange across the plasma membrane. We are able to demonstrate a closer agreement of model predictions with observed Ca2+ traces for a significantly wider range of parameter values, as was previously reported. We show also that the total cellular Ca2+ content is an important system parameter especially because of the content in sarcoplasmic reticulum. At a total Ca2+ 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.

Energy conservation and maximal entropy production in enzyme reactions

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.

In the Beginning was a Mutualism - On the Origin of Translation

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.

The maximum entropy production requirement for proton transfers enhances catalytic efficiency for β-lactamases

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. Hills 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.

Dynamic model of eicosanoid production with special reference to non-steroidal anti-inflammatory drug-triggered hypersensitivity

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 (PGE2 and PGD2) and one LT (LTC4), 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 LTC4-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.