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Two-state Trajectory
A two-state trajectory (also termed two-state time trajectory or a trajectory with two states) is a dynamical signal that fluctuates between two distinct values: ON and OFF, open and closed, +/-, etc. Mathematically, the signal X(t) has, for every t, either the value X(t)=c_\mathrm or X(t)=c_\mathrm. In most applications, the signal is stochastic; nevertheless, it can have deterministic ON-OFF components. A completely deterministic two-state trajectory is a square wave. There are many ways one can create a two-state signal, e.g. flipping a coin repeatedly. A stochastic two-state trajectory is among the simplest stochastic processes. Extensions include: three-state trajectories, higher discrete state trajectories, and continuous trajectories in any dimension. Two state trajectories in biophysics, and related fields Two state trajectories are very common. Here, we focus on relevant trajectories in scientific experiments: these are seen in measurements in chemistry, physics, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two State Trajectory
A two-state trajectory (also termed two-state time trajectory or a trajectory with two states) is a dynamical signal that fluctuates between two distinct values: ON and OFF, open and closed, +/-, etc. Mathematically, the signal X(t) has, for every t, either the value X(t)=c_\mathrm or X(t)=c_\mathrm. In most applications, the signal is stochastic; nevertheless, it can have deterministic ON-OFF components. A completely deterministic two-state trajectory is a square wave. There are many ways one can create a two-state signal, e.g. flipping a coin repeatedly. A stochastic two-state trajectory is among the simplest stochastic processes. Extensions include: three-state trajectories, higher discrete state trajectories, and continuous trajectories in any dimension. Two state trajectories in biophysics, and related fields Two state trajectories are very common. Here, we focus on relevant trajectories in scientific experiments: these are seen in measurements in chemistry, physics, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deterministic System
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state. at In physics Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly. In |
Square Wave
A square wave is a non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. In an ideal square wave, the transitions between minimum and maximum are instantaneous. The square wave is a special case of a pulse wave which allows arbitrary durations at minimum and maximum amplitudes. The ratio of the high period to the total period of a pulse wave is called the duty cycle. A true square wave has a 50% duty cycle (equal high and low periods). Square waves are often encountered in electronics and signal processing, particularly digital electronics and digital signal processing. Its stochastic counterpart is a two-state trajectory. Origin and uses Square waves are universally encountered in digital switching circuits and are naturally generated by binary (two-level) logic devices. Square waves are typically generated by metal–oxide–semiconductor fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-molecule Experiment
A single-molecule experiment is an experiment that investigates the properties of individual molecules. Single-molecule studies may be contrasted with measurements on an ensemble or bulk collection of molecules, where the individual behavior of molecules cannot be distinguished, and only average characteristics can be measured. Since many measurement techniques in biology, chemistry, and physics are not sensitive enough to observe single molecules, single-molecule fluorescence techniques (that have emerged since the 1990s for probing various processes on the level of individual molecules) caused a lot of excitement, since these supplied many new details on the measured processes that were not accessible in the past. Indeed, since the 1990s, many techniques for probing individual molecules have been developed. The first single-molecule experiments were patch clamp experiments performed in the 1970s, but these were limited to studying ion channels. Today, systems investigated using ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Force Spectroscopy
Force spectroscopy is a set of techniques for the study of the interactions and the binding forces between individual molecules. These methods can be used to measure the mechanical properties of single polymer molecules or proteins, or individual chemical bonds. The name "force spectroscopy", although widely used in the scientific community, is somewhat misleading, because there is no true matter-radiation interaction. Techniques that can be used to perform force spectroscopy include atomic force microscopy, optical tweezers, magnetic tweezers, acoustic force spectroscopy, microneedles, and biomembranes. Force spectroscopy measures the behavior of a molecule under stretching or torsional mechanical force. In this way a great deal has been learned in recent years about the mechanochemical coupling in the enzymes responsible for muscle contraction, transport in the cell, energy generation (F1-ATPase), DNA replication and transcription (polymerases), DNA unknotting and unwindi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ion Channel
Ion channels are pore-forming membrane proteins that allow ions to pass through the channel pore. Their functions include establishing a resting membrane potential, shaping action potentials and other electrical signals by gating the flow of ions across the cell membrane, controlling the flow of ions across secretory and epithelial cells, and regulating cell volume. Ion channels are present in the membranes of all cells. Ion channels are one of the two classes of ionophoric proteins, the other being ion transporters. The study of ion channels often involves biophysics, electrophysiology, and pharmacology, while using techniques including voltage clamp, patch clamp, immunohistochemistry, X-ray crystallography, fluoroscopy, and RT-PCR. Their classification as molecules is referred to as channelomics. Basic features There are two distinctive features of ion channels that differentiate them from other types of ion transporter proteins: #The rate of ion transport t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. Almost all metabolic processes in the cell need enzyme catalysis in order to occur at rates fast enough to sustain life. Metabolic pathways depend upon enzymes to catalyze individual steps. The study of enzymes is called ''enzymology'' and the field of pseudoenzyme analysis recognizes that during evolution, some enzymes have lost the ability to carry out biological catalysis, which is often reflected in their amino acid sequences and unusual 'pseudocatalytic' properties. Enzymes are known to catalyze more than 5,000 biochemical reaction types. Other biocatalysts are catalytic RNA molecules, called ribozymes. Enzymes' specificity comes from their unique three-dimensional structures. Like all catalysts, enzymes increase the react ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Dot
Quantum dots (QDs) are semiconductor particles a few nanometres in size, having optical and electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanotechnology. When the quantum dots are illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conductance band. The excited electron can drop back into the valence band releasing its energy as light. This light emission (photoluminescence) is illustrated in the figure on the right. The color of that light depends on the energy difference between the conductance band and the valence band, or the transition between discrete energy states when band structure is no longer a good definition in QDs. In the language of materials science, nanoscale semiconductor materials tightly confine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enzymes
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. Almost all metabolic processes in the cell need enzyme catalysis in order to occur at rates fast enough to sustain life. Metabolic pathways depend upon enzymes to catalyze individual steps. The study of enzymes is called ''enzymology'' and the field of pseudoenzyme analysis recognizes that during evolution, some enzymes have lost the ability to carry out biological catalysis, which is often reflected in their amino acid sequences and unusual 'pseudocatalytic' properties. Enzymes are known to catalyze more than 5,000 biochemical reaction types. Other biocatalysts are catalytic RNA molecules, called ribozymes. Enzymes' specificity comes from their unique three-dimensional structures. Like all catalysts, enzymes increase the reaction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Förster Resonance Energy Transfer
Förster resonance energy transfer (FRET), fluorescence resonance energy transfer, resonance energy transfer (RET) or electronic energy transfer (EET) is a mechanism describing energy transfer between two light-sensitive molecules (chromophores). A donor chromophore, initially in its electronic excited state, may transfer energy to an acceptor chromophore through nonradiative dipole–dipole coupling. The efficiency of this energy transfer is inversely proportional to the sixth power of the distance between donor and acceptor, making FRET extremely sensitive to small changes in distance. Measurements of FRET efficiency can be used to determine if two fluorophores are within a certain distance of each other. Such measurements are used as a research tool in fields including biology and chemistry. FRET is analogous to near-field communication, in that the radius of interaction is much smaller than the wavelength of light emitted. In the near-field region, the excited chromophore em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduced Dimensions Form
In biophysics and related fields, reduced dimension forms (RDFs) are unique on-off mechanisms for random walks that generate two-state trajectories (see Fig. 1 for an example of a RDF and Fig. 2 for an example of a two-state trajectory). It has been shown that RDFs solve two-state trajectories, since only one RDF can be constructed from the data, where this property does not hold for on-off kinetic schemes, where many kinetic schemes can be constructed from a particular two-state trajectory (even from an ideal on-off trajectory). Two-state time trajectories are very common in measurements in chemistry, physics, and the biophysics of individual molecules (e.g. measurements of protein dynamics and DNA and RNA dynamics, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
