Biomedical subjects

Marcel O Vlad

Publications and source records attributed to Marcel O Vlad.

8 recordsLinked to original sources

PubMed2006

Transition event statistics in genetics and disordered kinetics. Theoretical approaches for extracting rate distributions from experimental data.

We study the analogies between the theory of rate processes in disordered systems and the overdispersed molecular clocks in evolutionary biology. A biological "molecular clock" expresses the statistics of the number of amino acid or nucleotide substitutions during evolution. Random variations of the evolution rates lead to statistical (overdispersed) molecular clocks which are described by random point processes with random substitution rates. We find that the models for overdispersed molecular clocks are equivalent to those of the random-rate or random channel models used in disordered kinetics. The number of transport (reaction) events in disordered kinetics plays the same role as the number of substitution events in molecular biology. We study the connections between the (observed) statistics of the transition events and the statistics of random rate coefficients and random channels; a unified approach is developed which is valid both in molecular biology and in disordered kinetics. We develop methods for extracting statistical information about the variations of rate coefficients from experimental or observed data regarding the fluctuations of the numbers of substitution, reaction, or transport events. For systems with static disorder, the observed statistics of the number of reaction events, expressed in terms of probabilities at a given time or by the cumulants of the number of transition events at a given time, contains the information necessary for evaluating the cumulants or the probability density of the rate coefficients or the density of states for random channel kinetics. For dynamic disorder this is not possible; further information about multitime probability distributions of the reaction events is needed.

Amino Acid Substitution↗

PubMed2005

Exact solutions for the entropy production rate of several irreversible processes.

We investigate thermal conduction described by Newton's law of cooling and by Fourier's transport equation and chemical reactions based on mass action kinetics where we detail a simple example of a reaction mechanism with one intermediate. In these cases we derive exact expressions for the entropy production rate and its differential. We show that at a stationary state the entropy production rate is an extremum if and only if the stationary state is a state of thermodynamic equilibrium. These results are exact and independent of any expansions of the entropy production rate. In the case of thermal conduction we compare our exact approach with the conventional approach based on the expansion of the entropy production rate near equilibrium. If we expand the entropy production rate in a series and keep terms up to the third order in the deviation variables and then differentiate, we find out that the entropy production rate is not an extremum at a nonequilibrium steady state. If there is a strict proportionality between fluxes and forces, then the entropy production rate is an extremum at the stationary state even if the stationary state is far away from equilibrium.

Journal Article↗

PubMed2005

Bioluminescence regenerative cycle (BRC) system: theoretical considerations for nucleic acid quantification assays.

A novel application of bioluminescence for nucleic acid quantification, the bioluminescence regenerative cycle (BRC), is described in theoretical terms and supported by preliminary experimental data. In the BRC system, pyrophosphate (PPi) molecules are released during biopolymerization and are counted and correlated to DNA copy number. The enzymes ATP-sulfurylase and firefly luciferase are employed to generate photons quantitatively from PPi. Enzymatic unity-gain positive feedback is implemented to amplify photon generation and to compensate for decay in light intensity by self-regulation. The cumulative total of photons can be orders of magnitude higher than in typical chemiluminescent processes. A system level theoretical model is developed, taking into account the kinetics of the regenerative cycle, contamination, and detector noise. Data and simulations show that the photon generation process achieves steady state for the time range of experimental measurements. Based on chain reaction theory, computations show that BRC is very sensitive to variations in the efficiencies of the chemical reactions involved and less sensitive to variations in the quantum yield of the process. We show that BRC can detect attomolar quantities of DNA (10(-18) mol), and that the useful dynamic range is five orders of magnitude. Sensitivity is not constrained by detector performance but rather by background bioluminescence caused by contamination by either PPi or ATP (adenosine triphosphate).

Adenosine Triphosphate↗

PubMed2005

Fisher's theorems for multivariable, time- and space-dependent systems, with applications in population genetics and chemical kinetics.

We study different physical, chemical, or biological processes involving replication, transformation, and disappearance processes, as well as transport processes, and assume that the time and space dependence of the species densities are known. We derive two types of Fisher equations. The first type relates the average value of the time derivative of the relative time-specific rates of growth of the different species to the variance of the relative, time-specific rates of growth. A second type relates the average value of the gradient or the divergence of the relative, space-specific rates of growth to the space correlation matrix of the relative, space-specific rates of growth. These Fisher equations are exact results, which are independent of the detailed kinetics of the process: they are valid whether the evolution equations are linear or nonlinear, local or nonlocal in space and/or time and can be applied for the study of a large class of physical, chemical, and biological systems described in terms of time- and/or space-dependent density fields. We examine the implications of our generalized Fisher relations in population genetics, biochemistry, and chemical kinetics (reaction-diffusion systems). We show that there is a connection between the enhanced (hydrodynamic) transport of mutations induced by population growth and space-specific rate vectors: the velocity of enhanced transport is proportional to the product of the diffusion coefficient of the species and the space rate vector; this relation is similar to a fluctuation-dissipation relation in statistical mechanics.

Analysis of Variance↗

PubMed2005

Multiple rate-determining steps for nonideal and fractal kinetics.

We show that the kinetic model of a single rate-determining step in a reaction mechanism can be extended to systems with multiple overall reactions for which the elementary reactions obey nonideal or fractal kinetics. The following assumptions are necessary: (1) The system studied is either closed or open, but no constraints exist preventing the evolution toward equilibrium. (2) Elementary reactions occur in pairs of forward and backward steps. (3) The kinetics of the elementary steps are either nonideal or fractal and are compatible with equilibrium thermodynamics. (4) The number of reaction routes is identical with the number of rate-determining steps. If these hypotheses are valid, then the overall reaction rates can be explicitly evaluated: they have a form similar to the kinetic equations for the elementary reactions and the apparent reaction orders and fractal coefficients can be expressed analytically in terms of the kinetic parameters of the elementary reactions. We derive a set of relationships which connect the equilibrium constants of the reaction routes, the corresponding overall rate coefficients, and the stoichiometric numbers of the rate-determining steps. We also derive a set of generalized Boreskov relations among the apparent activation energies of the forward and backward overall processes, the corresponding reaction enthalpies, and the stoichiometric coefficients of the rate-determining steps. If the elementary reactions obey fractal kinetics, the same is true for the rate-determining steps. The fractal exponents of the forward and backward overall reactions are linear combinations of the fractal exponents of the fractal elementary reactions. Similar to the theory of single rate-determining steps, our approach can be used for selecting suitable reaction mechanisms from experimental data.

Journal Article↗

PubMed2004

Extraction of kinetic information from single-molecule experiments.

We discuss two possible approaches for extracting kinetic information from single-molecule experiments. The first approach is based on computing correlation functions from measured fluorescence signals, and the second on studying the statistics of on and off times of the same fluorescence signal. We show that in both cases it is possible to extract kinetic information about the nature of intramolecular fluctuations of the single molecule. We show that for single-molecule kinetics the intramolecular fluctuations produce stochastic memory effects which lead to new dynamic features that do not exist in traditional chemical kinetics. In particular, we investigate a new type of chemical oscillations in correlation functions observed experimentally by Edman and Rigler (Proc. Natl. Acad. Sci. USA 2000, 97, 8266).

Fluorescence↗

PubMed2004

Response experiments for nonlinear systems with application to reaction kinetics and genetics.

A unified type of response experiment is suggested for complex systems made up of individual species (atoms, molecules, quasi-particles, biological organisms, etc.). We make the following assumptions: (i) some of the species may exist in two forms, labeled and unlabeled, respectively; (ii) the kinetic and transport properties of the labeled and unlabeled species are the same, respectively (neutrality assumption); (iii) the experiment preserves the total input and output fluxes; only the fractions of the labeled compounds in the input and output fluxes are varied. Under these circumstances a linear integral superposition law connects the fractions of labeled species in the input and output fluxes. This linear superposition law is valid for homogeneous and inhomogeneous systems and for systems with intrinsic (hidden) state variables; it arises from the neutrality condition and holds even though the underlying dynamics of the process may be highly nonlinear. Because this response law does not involve the linearization of the evolution equations it has great potential for the analysis of complex physical, chemical, and biological systems. We compare our approach with the linearization techniques used in biochemistry and genetics. We consider a simple reaction network involving replication, transformation, and disappearance steps and study the influence of experimental (measurement) and linearization errors on the evaluated values of rate coefficients. We show that the method involving the linearization of the kinetic equations leads to unpredictable results; because of the interference between measurement and linearization errors, either error compensation or error amplification occurs. Although our approach does not eliminate the effects of measurement errors, it leads to more consistent results. For a broad range of input fractions no error amplification or compensation occurs, and the error range for the rate coefficients is about the same as the error range of the measurements.

Genetics, Medical↗

PubMed2002

Memory effects and oscillations in single-molecule kinetics.

An exactly solvable model for single-molecule kinetics is suggested, based on the following assumptions: (i) A single molecule can exist in different chemical states and the random transitions from one chemical state to another can be described by a local master equation with time-dependent transition rates. (ii) Because of conformational and other intramolecular fluctuations the rate coefficients in the master equation are random functions of time; their stochastic properties are represented in terms of a set of control parameters. We assume that the fluctuating rate coefficients fulfill a separability condition, that is, they are made up of the multiplicative contributions of two factors: (a) a universal factor, which depends on the vector of control parameters and is the same for all chemical transformation processes and (b) process-dependent factors, which depend on the initial and final chemical states of the molecule but are independent of the control parameters. For systems with two chemical states the condition of separability is automatically fulfilled. We introduce an intrinsic time scale, which makes it possible to compute theoretically various experimental observables, such as the correlation functions of the fluorescent signal. We analyze the connections between the condition of separability and detailed balance, and discuss the possible cause of chemical oscillations in single molecule kinetics. We show that the intrinsic dynamics of the molecule, expressed by the fluctuations of the control parameters, may lead to damped oscillations of the correlation functions of the fluorescent signal. The influence of the random fluctuations on the control parameters may be described by a renormalized master equation with nonfluctuating apparent rate coefficients. The apparent rate coefficients do not have to obey a condition of detailed balance, even though the real rate coefficients do obey such a condition. It follows that the renormalized master equation may have damped oscillatory solutions.

Kinetics↗