A model for the evolution of nucleotide polymerase directionality

Background

In all known living organisms, every enzyme that synthesizes nucleic acid polymers does so by adding nucleotide 5′-triphosphates to the 3′-hydroxyl group of the growing chain. This results in the well known directionality of all DNA and RNA Polymerases. The lack of any alternative mechanism, e.g. addition in a direction, may indicate a very early founder effect in the evolution of life, or it may be the result of a selective pressure against such an alternative.

Methodology/Principal Findings

In an attempt to determine whether the lack of an alternative polymerase directionality is the result of a founder effect or evolutionary selection, we have constructed a basic model of early polymerase evolution. This model is informed by the essential chemical properties of the nucleotide polymerization reaction. With this model, we are able to simulate the growth of organisms with polymerases that synthesize either or in isolation or in competition with each other.

Conclusions/Significance

We have found that a competition between organisms with polymerases and polymerases only results in a evolutionarily stable strategy under certain conditions. Furthermore, we have found that mutations lead to a much clearer delineation between conditions that lead to a stable coexistence of these populations and conditions which ultimately lead to success for the form. In addition to presenting a plausible explanation for the uniqueness of enzymatic polymerization reactions, we hope these results also provide an example of how whole organism evolution can be understood based on molecular details.     

A mechanistic model for butyrylcholinesterase.

A plausible mechanism of action of horse serum butyrylcholinesterase is proposed. It includes substrate activation at the level of deacylation. The rate constant for the acylation of the enzyme appears to be much greater than the rate constant for the deacylation, at low substate concentrations. At higher substrate concentrations the rate constants become more similar. No interaction between the four subunits in binding of inhibitors or in the catalysis was observed. There is one esteratic and one anionic site per subunit apparent from labelling studies with [32P]diisopropylfluorophosphate and binding studies with N-methylacridine. Although the tetrametric form of the enzyme appears to be the native one, the monomeric and several other aggregated and dissociated states are catalytically active.     

A mechanistic model for partial preferences

Classic prey optimal foraging model assumes that individual predators are globally omniscient; that is, they have exact knowledge of prey population densities in the environment. This study examines a spatially explicit individual-based model of a one-predator two-prey system where individual predators are assumed to be omniscient only locally, i.e., to know prey population densities only in the range of their perception. Due to local variations in prey numbers, the probability of acceptance of less profitable prey shifts from the zero-one rule to a gradually decreasing function, for which an explicit formula is derived, giving way to partial preferences. A corresponding predator functional response to more profitable prey is shown to have a sigmoid-like form.     

A mechanistic model of photoinhibition

A mechanistic model was developed, to simulate the main facets of photoinhibition in phytoplankton. Photoinhibition is modelled as a time dependent decrease in the initial slope of a photosynthesis versus irradiance curve, related to D1 (photosystem II reaction centre protein) damage and non-photochemical quenching. The photoinhibition model was incorporated into an existing ammonium-nitrate nutrition interaction model capable of simulating photoacclimation and aspects of nitrogen uptake and utilization. Hence the current model can simulate the effects of irradiance on photosynthesis from sub-saturating to inhibitory photon flux densities, during growth on different nitrogen sources and under nutrient stress. Model output conforms well to experimental data, allowing the extent of photoinhibition to be predicted under a range of nutrient and light regimes. The ability of the model to recreate the afternoon depression of photosynthesis and the enhancement of photosynthesis during fluctuating light suggests that these two processes are related to photoinhibition. The model may be used to predict changes in biomass and/or carbon fixation under a wide range of oceanographic situations, and it may also help to explain the progression to dominance of certain algal species, and bloom formation under defined irradiance and nutrient conditions.     

A mechanistic model for quasistatic pulmonary pressure-volume curves for inflation

A mechanistic model of the respiratory system is proposed to understand differences in quasistatic pressure-volume (p-V) curves of the inflation process in terms of the alveolar recruitment and the elastic distension of the wall tissues. In the model, a total respiratory system consists of a large number of elements, each of which is a subsystem of a cylindrical chamber fitted with a piston attached to a spring. The alveolar recruitment is simulated by allowing a distribution of the critical pressure at which an element opens; while the wall distension is represented by the piston displacement. Relations are derived between parameters in the error-function p-V model equation and properties of the mechanistic model The parameters of the model-based p-V equation are determined for clinical data sets of patients with acute respiratory distress syndrome.     

A mechanistic model for genetic machinery of ontogenetic growth

Two different genetic mechanisms can be proposed to explain variation in growth trajectories. The allelic sensitivity hypothesis states that growth trajectory is controlled by the time-dependent expression of alleles at the deterministic quantitative trait loci (dQTL) formed during embryogenesis. The gene regulation hypothesis states that the differentiation in growth process is due to the opportunistic quantitative trait loci (oQTL) through their mediation with new developmental signals. These two hypotheses of genetic control have been elucidated in the literature. Here, we propose a new statistical model for discerning these two mechanisms in the context of growth trajectories by integrating growth laws within a QTL-mapping framework. This model is developed within the maximum-likelihood context, implemented with a grid approach for estimating the genomic positions of the deterministic and opportunistic QTL and the simplex algorithm for estimating the growth curve parameters of the genotypes at these QTL and the parameters modeling the residual (co)variance matrix. Our model allows for extensive hypothesis tests for the genetic control of growth processes and developmental events by these two types of QTL. The application of this new model to an F(2) progeny in mice leads to the detection of deterministic and opportunistic QTL on chromosome 1 for mouse body mass growth. The estimates of QTL positions and effects from our model are broadly in agreement with those by traditional interval-mapping approaches. The implications of this model for biological and biomedical research are discussed.     

A three plus three parameters mechanistic model for viral filtration

Viral filtration is an expensive regulatory requirement in downstream processing of monoclonal antibodies (mAbs). This process step is typically operated with an overdesigned filter in order to account for any batch to batch variability in the filter, as well as the feed characteristics. Here, we propose a simple, six‐parameter mechanistic model for viral filtration where three parameters are membrane‐specific while the other three depend on feed characteristics and membrane‐feed interactions. Viruses are considered as passive particles which are retained by the membrane on the basis of size exclusion. The model envisages that the viral filter contains two kind of pores: virus‐retentive, small‐sized pores and non‐retentive, large‐sized pores. The small‐sized pores get blocked during filtration resulting in decrease in active membrane area, while the large‐sized pores get constricted during filtration. The length of constricted part increases during filtration and contributes to increase in hydraulic resistance of the filter. Rate of these processes (blocking and constriction) are assumed to be proportional to the instantaneous rate of retention of the viral particles. The general nature of the model is validated with the experimental data on viral filtration for four different commercial membranes used in biotech industries as well as different model viruses. The proposed model has been demonstrated to describe the behavior of filters with very good accuracy. The best‐fit model parameter values indicate about the various phenomena that are responsible for differences in the behavior of the membranes as well as change in retention and flux with feed concentration. The proposed model can be used for improving design of virus filters as well as in appropriate sizing of the filters during processing. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1538–1547, 2017     

A general mechanistic model for admixture histories of hybrid populations

Admixed populations have been used for inferring migrations, detecting natural selection, and finding disease genes. These applications often use a simple statistical model of admixture rather than a modeling perspective that incorporates a more realistic history of the admixture process. Here, we develop a general model of admixture that mechanistically accounts for complex historical admixture processes. We consider two source populations contributing to the ancestry of a hybrid population, potentially with variable contributions across generations. For a random individual in the hybrid population at a given point in time, we study the fraction of genetic admixture originating from a specific one of the source populations by computing its moments as functions of time and of introgression parameters. We show that very different admixture processes can produce identical mean admixture proportions, but that such processes produce different values for the variance of the admixture proportion. When introgression parameters from each source population are constant over time, the long-term limit of the expectation of the admixture proportion depends only on the ratio of the introgression parameters. The variance of admixture decreases quickly over time after the source populations stop contributing to the hybrid population, but remains substantial when the contributions are ongoing. Our approach will facilitate the understanding of admixture mechanisms, illustrating how the moments of the distribution of admixture proportions can be informative about the historical admixture processes contributing to the genetic diversity of hybrid populations.     

A combined empirical and mechanistic codon model

The evolutionary selection forces acting on a protein are commonly inferred using evolutionary codon models by contrasting the rate of synonymous to nonsynonymous substitutions. Most widely used models are based on theoretical assumptions and ignore the empirical observation that distinct amino acids differ in their replacement rates. In this paper, we develop a general method that allows assimilation of empirical amino acid replacement probabilities into a codon-substitution matrix. In this way, the resulting codon model takes into account not only the transition-transversion bias and the nonsynonymous/synonymous ratio, but also the different amino acid replacement probabilities as specified in empirical amino acid matrices. Different empirical amino acid replacement matrices, such as secondary structure-specific matrices or organelle-specific matrices (e.g., mitochondria and chloroplasts), can be incorporated into the model, making it context dependent. Using a diverse set of coding DNA sequences, we show that the novel model better fits biological data as compared with either mechanistic or empirical codon models. Using the suggested model, we further analyze human immunodeficiency virus type 1 protease sequences obtained from drug-treated patients and reveal positive selection in sites that are known to confer drug resistance to the virus.     

A mechanistic model of the actin cycle

We have derived a broad, deterministic model of the steady-state actin cycle that includes its major regulatory mechanisms. Ours is the first model to solve the complete nucleotide profile within filaments, a feature that determines the dynamics and geometry of actin networks at the leading edges of motile cells, and one that has challenged investigators developing models to interpret steady-state experiments. We arrived at the nucleotide profile through analytic and numerical approaches that completely agree. Our model reproduces behaviors seen in numerous experiments with purified proteins, but allows a detailed inspection of the concentrations and fluxes that might exist in these experiments. These inspections provide new insight into the mechanisms that determine the rate of actin filament treadmilling. Specifically, we find that mechanisms for enhancing Pi release from the ADP.Pi intermediate on filaments, for increasing the off rate of ADP-bound subunits at pointed ends, and the multiple, simultaneous functions of profilin, make unique and essential contributions to increased treadmilling. In combination, these mechanisms have a theoretical capacity to increase treadmilling to levels limited only by the amount of available actin. This limitation arises because as the cycle becomes more dynamic, it tends toward the unpolymerized state.     

Kinetic studies of dimeric Ncd: evidence that Ncd is not processive

Ncd is a kinesin-related motor protein which drives movement to the minus-end of microtubules. The kinetics of Ncd were investigated using the dimeric construct MC1 (Leu(209)-Lys(700)) expressed in Escherichia coli strain BL21(DE) as a nonfusion protein [Chandra, R., Salmon, E. D., Erickson, H. P., Lockhart, A., and Endow, S. A. (1993) J. Biol. Chem. 268, 9005-9013]. Acid chemical quench flow methods were used to measure directly the rate of ATP hydrolysis, and stopped-flow kinetic methods were used to determine the kinetics of mantATP binding, mantADP release, dissociation of MC1 from the microtubule, and binding of MC1 to the microtubule. The results define a minimal kinetic mechanism, M.N + ATP M.N.ATP M.N.ADP.P N. ADP.P N.ADP + P M.N.ADP M.N + ADP, where N, M, and P represent Ncd, microtubules, and inorganic phosphate respectively, with k(+1) = 2.3 microM(-1) s(-1), k(+2) =23 s(-1), k(+3) =13 s(-1), k(+5)= 0.7 microM(-)(1) s(-)(1), and k(+6) = 3.7 s(-)(1). Phosphate release (k(+4)) was not measured directly although it is assumed to be fast relative to ADP release because Ncd is purified with ADP tightly bound at the active site. ATP hydrolysis occurs at 23 s(-)(1) prior to Ncd dissociation at 13 s(-)(1). The pathway for ATP-promoted detachment (steps 1-3) of Ncd from the microtubule is comparable to kinesin's. However, there are two major differences between the mechanisms of Ncd and kinesin. In contrast to kinesin, mantADP release for Ncd at 3.7 s(-)(1) is the slowest step in the pathway and is believed to limit steady-state turnover. Additionally, the burst amplitude observed in the pre-steady-state acid quench experiments is stoichiometric, indicating that Ncd, in contrast to kinesin, is not processive for ATP hydrolysis.     

A mechanistic mathematical model for the catalytic action of glutathione peroxidase

Abstract

Glutathione peroxidase (GPx) is a well-known seleno-enzyme that protects cells from oxidative stress (e.g., lipid peroxidation and oxidation of other cellular proteins and macromolecules), by catalyzing the reduction of harmful peroxides (e.g., hydrogen peroxide: H₂O₂) with reduced glutathione (GSH). However, the catalytic mechanism of GPx kinetics is not well characterized in terms of a mathematical model. We developed here a mechanistic mathematical model of GPx kinetics by considering a unified catalytic scheme and estimated the unknown model parameters based on different experimental data from the literature on the kinetics of the enzyme. The model predictions are consistent with the consensus that GPx operates via a ping-pong mechanism. The unified catalytic scheme proposed here for GPx kinetics clarifies various anomalies, such as what are the individual steps in the catalytic scheme by estimating their associated rate constant values and a plausible rationale for the contradicting experimental results. The developed model presents a unique opportunity to understand the effects of pH and product GSSG on the GPx activity under both physiological and pathophysiological conditions. Although model parameters related to the product GSSG were not identifiable due to lack of product-inhibition data, the preliminary model simulations with the assumed range of parameters show that the inhibition by the product GSSG is negligible, consistent with what is known in the literature. In addition, the model is able to simulate the bi-modal behavior of the GPx activity with respect to pH with the pH-range for maximal GPx activity decreasing significantly as the GSH levels decrease and H₂O₂ levels increase (characteristics of oxidative stress). The model provides a key component for an integrated model of H₂O₂ balance under normal and oxidative stress conditions.     

A critique of directionality theory

Directionality theory suggests that demographic entropy, defined in a way analogous to thermodynamic entropy, is as important as the Malthusian parameter in determining life history evolution in an age-structured population. In particular, it suggests that entropy should increase in equilibrium species and decrease in opportunistic species. This theory has been applied to explain the evolution of body size and of senescence. It has been claimed recently that this theory has been validated by a simulation study, but it is argued here that this study reveals substantial flaws in directionality theory and that the Malthusian parameter rather than entropy is the appropriate tool in the study of life history evolution.     

A simple,mechanistic model for directional instability during mitotic chromosome movements

During mitosis, chromosomes become attached to microtubules that emanate from the two spindle poles. Thereafter, a chromosome moves along these microtubule "tracks" as it executes a series of movements that bring it to the spindle equator. After the onset of anaphase, the sister chromatids separate and move to opposite spindle poles. These movements are often characterized by "directional instability" (a series of runs with approximately constant speed, punctuated by sudden reversals in the direction of movement). To understand mitosis, it is critical to describe the physical mechanisms that underlie the coordination of the forces that drive directional instability. We propose a simple mechanistic model that describes the origin of the forces that move chromosomes and the coordination of these forces to produce directional instability. The model demonstrates that forces, speeds, and direction of motion associated with prometaphase through anaphase chromosome movements can be predicted from the molecular kinetics of interactions between dynamic microtubules and arrays of microtubule binding sites that are linked to the chromosome by compliant elements.     

A mechanistic model for interference and Allee effect in the predator population

We present the results of simulations in an individual-based model describing spatial movement and predator-prey interaction within a closed rectangular habitat. Movement of each individual animal is determined by local conditions only, so any collective behavior emerges owing to self-organization. It is shown that the pursuit of prey by predators entails predator interference, manifesting itself at the population level as the dependency of the trophic function (individual ration) on predator abundance. The stabilizing effect of predator interference on the dynamics of a predator-prey system is discussed. Inclusion of prey evasion induces apparent cooperation of predators and further alters the functional response, giving rise to a strong Allee effect, with extinction of the predator population upon dropping below critical numbers. Thus, we propose a simple mechanistic interpretation of important but still poorly understood behavioral phenomena that underlie the functioning of natural trophic systems.     

A mechanistic model of the adaptation of phytoplankton photosynthesis

The mechanistic model of the phytoplankton photosynthesis-light intensity relationship by Eilers and Peeters (1988.Ecol. Modelling 42, 199–215) is investigated mathematically. The model is based on the physiological idealization of transition probabilities between states of the photosynthetic factories,PSF. The model was found to have under constant light condition a globally stable unique positive equilibrium, while under periodically varying light (e.g. daily periodicity) there exists a unique globally asymptotically stable periodic solution. Based on this, the adaptation to a change of light intensity is defined as a process by which the state ofPSF converges to an equilibrium. Assuming that phytoplankton regulates its photosynthetic production rate with a certain strategy which maximizes production, two such possible strategies were examined. Both the instantaneous and the integral maximal photosynthetic production were shown to have the same result. With realistic qualitative assumptions of the shape of the dependence of the four model parameters on the light intensity to which phytoplankton is adapted, the numerical values of parameters under both constant and periodically varying conditions are determined by applying Pontryagin's maximum principle.