Half Life Chemistry Problems - Nuclear Radioactive Decay Calculations Practice Examples
The kinetics of radioactive decay and radiometric dating || minimoving.info
Special Cases: Long time solutions classification time relationship. Rate- determining step a. No Equilibrium t > tB > tA. B → C b. Transient Equilibrium t > tA > tB. A → B c. Secular Equilibrium. tA >> t > tB. A → B. (c. is case of U-Th decay series). C. No Equilibrium. Daughter is rate-determining step t1/2 (B) > t1/2 (A). 1. Fig. Kinetics. Topics: Radioactive Decay, Second Order Integrated Rate Laws, Kinetics and. Chemical Equilibrium, Introduction to Reaction Mechanisms. Chapter 13 (p , ) and Chapter 17 (p ). Radioactive Decay. The decay of a nucleus is ______ of the number of surrounding nuclei that have decayed. All radioactive decompositions, or decays, follow first-order kinetics. Indeed, radioactive decay is considered to be the classic example of first-order reaction kinetics. This is not surprising because the energy of any molecular collision or interaction is negligible in comparison to the energies involved in nuclear processes.
DNA unwinding and polymerization are complex processes involving many intermediate species in the reactions. Our understanding of these processes is limited because the rates of the reactions or the existence of intermediate species is not apparent without specially designed experimental techniques and data here procedures.
In this chapter we describe how pre-steady state single-turnover measurements analyzed by model-based methods can be used for estimating the elementary rate constants. Using the hexameric helicase and the DNA polymerase from bacteriophage T7 as model systems, we provide stepwise procedures for measuring the kinetics of the reactions they catalyze based on radioactivity and fluorescence.
We also describe analysis of the experimental measurements using click available models and software gfit http: Helicases are motor proteins that use the chemical energy of NTP hydrolysis to separate the strands of double stranded nucleic acids 1 — 4.
Often helicases work in association with other proteins, such as the DNA polymerase or single strand binding proteins to perform their function with a greater efficiency.
Characterization of the nucleic acid unwinding activity involves measurement of the rate and the processivity of the helicase-catalyzed unwinding reaction.
Experimental and computational analysis of DNA unwinding and polymerization kinetics
These unwinding parameters can be used as basic handles to understand the mechanism of unwinding and the role of the helicase in a particular biological process. Measurement of the unwinding rate of helicases as a function of DNA duplex stability provided insights into the continue reading or passive nature of the helicase-catalyzed reaction 5. Measurement of the unwinding rate of phage T7 hexameric helicase in the presence of the DNA polymerase provided insights into the synergistic action of the two motor proteins in DNA replication 6.
In this chapter, we describe assays to measure DNA unwinding catalyzed by the helicase, and DNA polymerization catalyzed by the helicase and polymerase proteins using the hexameric ring-shaped T7 gp4 helicase as our model system. We outline procedures to fit the kinetic data to specific models that provide kinetic parameters such as the rate of DNA unwinding and the rate of nucleotide incorporation during DNA polymerization.
The product of bacteriophage T7 gene gp4 is a ring shaped protein 7 — 9 that has both Http://minimoving.info/hyme/online-hookup-how-to-decline-interest.php unwinding and primase activities T7 gp4 unwinds dsDNA using the strand exclusion model wherein one strand of the dsDNA The Kinetics Of Radioactive Decay And Radiometric Hookup threaded into the central channel of the helicase and the other strand is excluded as the helicase unwinds the dsDNA 13 This strand exclusion model is accepted generally for ring shaped helicases 15 — The other key component of T7 replication complex is gp5 DNA polymerase 18 — Interestingly, the rate of DNA unwinding by T7 gp4 is accelerated by the polymerase and approached the ssDNA translocation rate of the helicase 6.
Kinetics of Radioactive Decay
Accurate measurements of kinetic rates of translocation, unwinding, and polymerization provide both quantitative and qualitative insights about the DNA replication mechanism. Unwinding and polymerization pathways comprise many interacting reaction steps such as substrate binding, catalysis, and conformational changes. The large number of these steps makes their identification and characterization increasingly difficult. Therefore, one prerequisite of a successful experimental design is its ability to decouple the pathway: Most clear results are produced by experiments that measure kinetics of one fully decoupled reaction step.
One strategy to maximize decoupling enabled by recent technological advances involves monitoring reactions occurring with single molecules. These techniques have been successfully applied to both DNA unwinding and polymerization 21 — Unfortunately, only parts of DNA processing pathways can be currently observed at single molecule level, which brings us back to conventional measurement techniques that integrate signals originating from billions of enzyme molecules.
During the course of reaction, as the system reaches a steady state, molecules click the following article enzyme become distributed along the reaction pathway populating all of the reaction species and participating in all reactions simultaneously. Combined signal from such heterogeneous mixture is hard to interpret in terms of individual reaction rates. These problems are overcome by using pre-steady state and single round kinetic techniques.
Pre-steady state kinetic measurements involve synchronization of the system — assembling the reaction mixture in a way that populates only one species of the pathway. This can be done, for example, by withholding a component required for the next reaction step. After the reaction in the synchronized mixture is started, but before it reaches a steady state, the measured signal can be attributed to a few steps that follow the synchronization point.
The pre-steady state period of reaction is quite short due to a natural tendency of molecular systems to lose synchronization. To extend it and to be able to characterize more reaction steps in one experiment, single round conditions can be used. Single round conditions effectively prevent the system from reaching a steady state by allowing each molecule of enzyme The Kinetics Of Radioactive Decay And Radiometric Hookup no more than one molecule of substrate.
In case of an unwinding reaction, this can be achieved by adding a helicase trap at the time of initiation.
An excess of ssDNA can capture free helicase molecules from solution preventing them from re-binding to new substrate molecules. Pre-steady state single round approaches enhance our ability to decouple unwinding and polymerization pathways to measure the rates of their reaction steps. DNA unwinding rates have been measured using both bulk and single molecule techniques 56 Single round conditions simplify interpretation of a bulk kinetic measurement result.
Helicases can processively unwind stretches of dsDNA longer than their binding site.
Therefore an unwinding reaction click here be described as an n-step process and for experiments conducted under single round conditions, the results can be fit with a stepping equation 30 Such analysis of unwinding kinetics data for dsDNA substrates of different lengths can be used for estimating helicase stepping rate and size and for assessing processivity of the helicase; i. Ring-shaped helicases assemble around ssDNA, and assembly is usually a slow step relative to the rate of DNA unwinding.
Therefore, to measure the unwinding rate rather than the assembly rate and to synchronize the reactions, it is important to preassemble the helicase on the DNA substrate prior to reaction start. T7 gp4, like other ring-shaped helicases, binds to the DNA only in the presence of its nucleotide substrate dTTP in the case of T7 gp4.
This makes the preassembly of the helicase on the DNA substrate, without reaction occurring during the assembly period, challenging.
Two types of the unwinding assays are described: They are both all-or-none unwinding assays where unwinding rates are obtained from the kinetics of end product formation, i.
Since the unwinding rate of T7 gp4 is fast, the kinetics are measured using a rapid quenched-flow or a stopped-flow apparatus Fig. Two short DNA strands top and bottom are annealed to generate a duplex region 40 bp, here and ssDNA overhangs at one end.
The kinetics of DNA unwinding is fit to obtain the unwinding rate. When helicase unwinds the dsDNA and the top strand is source away from the dye, the fluorescence increases. The time dependent increase in fluorescence is measured continuously in a stopped-flow apparatus. DNA polymerization rates can be estimated from the individual nucleotide incorporation rates measured using transient state kinetic methods.
DNA polymerases incorporate hundreds to thousands of nucleotides during polymerization in a template-dependent manner, adding one dNMP to the primer at a time and moving with a step-size of one nucleotide.
Each nucleotide is added at a different rate that depends on several factors, not all well understood, one of which is the sequence context around the base to be added. The nucleotide addition rate can be determined accurately using a combination of rapid kinetics, product analysis on a high resolution sequencing gel, and data analysis.
The rapid kinetic methods providing milli seconds time resolution capture the formation and decay of intermediate products, the sequencing gels can resolve the DNA products with a single base resolution, and data analysis extracts the single nucleotide incorporation rate and the polymerase off-rates from the observed kinetics of primer elongation. When the template is single stranded, the polymerase can copy the template without the helicase, but when the template is double stranded, the polymerase requires the helicase to unwind the dsDNA.
The rate of DNA unwinding by the helicase with concomitant DNA synthesis can be measured by the unwinding assays described above The Kinetics Of Radioactive Decay And Radiometric Hookup a replication fork substrate. Alternatively, the kinetics of the reaction can be measured by following the primer extension reaction. We describe methods to obtain the rate of each nucleotide addition in the primer extension reaction.
Kinetics of Nuclear Decay
Replication fork substrates are made by annealing the top and bottom ssDNAs to generate a duplex region 40 bp, here and two ssDNA overhangs. Reaction products are separated by PAGE with single-base resolution to measure the amount of each intermediate. Even the most advanced experimental techniques cannot fully decouple all steps involved in unwinding and polymerization process.
Most experimental observations arise not from one but from multiple simultaneously occurring reactions. Such results do not directly provide a value for any reaction rate or even a confirmation that the reaction step actually takes place. This information can be extracted from the results by applying model-based regression analysis that has the following goals: In this chapter we describe analysis of unwinding and polymerization data using gfitan open source program http: Programming, however, is only involved in creating new models; all analysis tasks in gfit using existing models are performed through graphical user interface and do not require any knowledge of programming or MATLAB environment.
In the following sections we discuss details of the analysis procedure, computational problems that it presents, and the ways to address these problems. Analysis starts with creating a computational model based on existing knowledge about the system. The model should be able to compute simulate a predicted result of each experiment.
The Kinetics Of Radioactive Decay And Radiometric Hookup perform computations, the model uses two kinds of inputs: Although, for any given experiment, conditions and parameters are easily distinguishable, the same variable e. Correctness of a model can never be demonstrated conclusively. However, given certain parameter values, a model may produce simulations closely matching fitting experimental measurements.
Testing if the model is consistent with all the experimental observations, a key step in data analysis, is performed by global curve fitting optimization.
Failure to find a good set of parameter values usually means that the model is not accurate and requires structural changes.
Finding a good fit not only demonstrates consistency, but also provides estimates of parameters. Such result does not conclude the analysis because the estimated parameter values carry little meaning without an indication of their uniqueness and an estimate of their confidence intervals. Restarting optimization many times from randomly selected positions in the parameter space may lead to discovery of alternative parameter sets fitting the data, an indication of low confidence.
Underdetermined parameters may stem from an overly complicated model or from insufficient experimental data. The problem can http://minimoving.info/hyme/hookup-a-hard-to-get-girl.php solved by simplifying the model, The Kinetics Of Radioactive Decay And Radiometric Hookup adding explicit constraints to parameters e.
Although procedures for model-based data analysis are well-established, their practical applications to biological systems present several computational challenges and places rigid requirements on the analysis software. The main function of the software is to provide methods for statistical analysis that operate on experimental data and computational models supplied by the researcher. Biological research projects click here highly dynamic.
Therefore the software should make it easy to modify the model, to include new experiments into global analysis, to change statistical weights, to use same parameter value for multiple experiments, etc. The desired flexibility can be achieved by developing a project-specific analysis program 34although our experience shows that this approach requires frequent modifications of the program code, which slow down the analysis and lead to programming errors.
Computational models are the central parts of the analysis. The models have to simulate a wide range of biological processes and experimental procedures. Ordinary differential equations ODEs is currently the most common method to model biology. However, defining a model strictly as a set of ODEs is unacceptable because some systems have to be simulated with a floating number of ODEs e.
Since simulation is usually the slowest step in the analysis process, it should be performed as efficiently as possible. An analysis procedure may involve 10 3 to 10 8 simulations with different experimental conditions and parameters. To carry out the analysis without human intervention, each output of the model has to be directly comparable with the result of the corresponding experiment.
In short, simulations require accuracy, flexibility, and efficiency.
Many experiments arranged side-by-side to each other can be imported in one operation. Reactions are stopped by rapid mixing with 1. Turn on the mercury lamp and allow it to stabilize to 75V. Humana Press, Inc; Does radioactive decay kinetics andwe.
These requirements can be best met by writing models in a general purpose programming language e.