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Specificity of Bionoise

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Specificity of Bionoise
 

  1. Background

In any linear electronic system (and equally in some non-linear systems), noise is perceived as a destructive phenomenon that perturbs system operation by corrupting data. By contrast, in biology all systems are non-linear and noise appears to have a constructive role. As in the case of electronics, we can distinguish two main categories of noise:

  • Intrinsic noise (generated inside the process or system of interest). It is the consequence of the inherently random nature of biochemical reactions.

  • Extrinsic noise (either arising from environment or being coupled from nearby processes or systems). As an example of coupling between two processes, consider the production of proteins. They result in short bursts of variable number of molecules that occur at random time intervals. Since production of one protein is conditioned by the existence of another protein that acts as a promoter, fluctuations are coupled from one process to another and may be eventually amplified by the existing positive feedback paths.

  1. Classification

Noise is ubiquitous at any level in a living system. In mesoscopic biology, thermal and concentration fluctuations are dominant. Here is a non-exhaustive list of processes generating various types of noise:

  • Biochemical reactions are all stochastic. To occur, a chemical reaction requires that the reactants come close enough to each other and remain in contact for a while. But molecules are submitted to Brownian movement in their environment. Due to this, a molecule collides with other molecules and receives (or looses) energy that can be temporarily stocked in (or removed from) rotational and vibrational states. Its movement is damped by the viscosity of the fluid. All these phenomena generate fluctuations in local temperature, the rate of reaction and finally the number of produced molecules. The quantitative description of this set of fluctuations is called biochemical noise.

  • Gene expression is highly probabilistic. Transcription in eukaryotic cells occurs in short pulses of mRNA interspersed by long periods of inactivity of indeterminate duration. During transcription, a DNA sequence is read by RNA polymerase, which produces a complementary, antiparallel RNA strand. This implies binding to the promoter region of the gene, and stay for as long as it takes to produce a full transcript. Nevertheless, the binding mechanism itself is probabilistic because of Brownian motion of molecules and secondly because during transcription the probability of promoter recognition is proportional to the concentration of transcription factor (TF), which is inherently fluctuating.

    Translation is equally a stochastic process. In translation, mRNA produced by transcription is decoded by the ribosome to produce a specific amino acid chain, or polypeptide, that will later fold into an active protein. However, the number of ribosomes, the mRNA degradation, and the cellular environment are described by fluctuating quantities. Because gene products from a single network can control either their own expression or the production of a protein in another network, feedback can increase stochasticity.

    Under identical initial conditions (such as concentrations of chemical species, temperature, pressure etc.), the noise affecting gene expression has been shown to produce qualitatively different outcomes, resulting in variability among isogenic populations of cells. This is called phenotypic noise (i.e., in spite of identical initial conditions, with time, different cells or species may evolve along distinct directions).

  • Imperfect timing in both biochemical reactions and gene expression is another factor producing fluctuations in the number of resulting molecules. Timing is paramount to a series of discontinuous processes such as promoter recognition, effective transcription of the gene, RNA splicing if required and finally, translation, in the case of proteins. However, only by chance their timing could be perfect and in practical situations random delays induce fluctuations from one process to the next one.

  • As expected, the 1/fα noise is equally present in biosystems. Its origins are related to:

  1. fluctuations of the potential-energy of the system due to the existence of thermally activated processes in proteins (as folding);

  2. the diffusion of macromolecules in the functional space;

  3. fluctuations in the surrounding solvent, due to interactions of the protein and the hydration water;

  4. fluctuations in any biological rhythm (from cellular to behavioral levels);

  5. voltage fluctuations in bilayer lipid membranes during electroporation;

  6. channel-facilitated transport of metabolites across biological membranes;

  7. environmental white-noise electromagnetic excitation, which is filtered by the biosystem and gives rise to 1/f noise (Szendro, Vincze & Szasz)

  1. Comments

  • The noise power spectrum G(w) of biochemical reactions has a characteristic feature: it is constant at low frequencies and proportional to at high frequencies. Thus, it is always possible to define a Lorentzian function (i.e., a single-peaked function that decays gradually on each side of the peak) to model it.

    On the other hand, the mechanism of noise produced in gene expression is single- or multiple-shot processes. Again, a single-shot noise process is modelled by a Lorentzian function. Its corresponding mathematical expression has the form:

    where K and C are constants depending on the particular system and ω is the pulsation.

    Therefore, excluding 1/f noise, the spectrum of biologically relevant noise tends to be Lorentzian rather than white.

    The powerful of the description by means of Lorentzian functions is the possibility to differentiate between a nonequilibium steady state and an equilibrium system, by examining the differences between a noise power spectrum and its corresponding one-term Lorentzian (Chen Y.,  http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1473677/pdf/biophysj00749-0099.pdf ).

  • At the cell level, the number of molecules involved in biochemical reactions, as well as in gene expression, is very low. Hence, the Poisson distribution fits well the stochastic processes. According to Wikipedia: a Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time, if these events occur with a known average rate and are independently of the time since the last event. Note that Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume. If the expected number of occurrences in this interval is λ, then the probability that there are exactly k occurrences is:

    Poisson noise. The parameter λ is not only the mean value of the number of occurrences per unit time, but also its variance . Thus, the number of observed occurrences fluctuates about its mean λ with a standard deviation . These fluctuations are denoted as Poisson noise (or particularly in electronics, as shot noise). Note that sometimes λ is called noise intensity.

     

  1. Schrödinger's law

This law applies to physical systems with a very limited number of particles.

Concerning the phenotypic noise, it is known that in living cells DNA, RNA, and proteins can be present (and are active) at a few copies per cell. On the other hand, a huge number of cellular biochemical reactions involve a very limited number of molecules (usually tens to hundreds).

According to Schrödinger: in any statistical experiment involving n identical particles, the degree of inaccuracy to be expected in any physical law is inversely proportional to square root of the number of particles.

By extension, any fluctuation can be regarded as an “inaccuracy” with respect to its mean value and therefore the intensity of the generated noise is inversely proportional to the square-root of n. Hence, at mesoscopic scale, due to a reduced population of particles, even small fluctuations in one parameter give rise to a noise much more intense as expected.

For instance, in the case of genetic regulatory networks (GNR) many molecules that control their operation act at extremely low intracellular concentrations. As a result, even small fluctuations generated by stochastic promoter activation, promoter deactivation, random mRNA production and protein degradation cause large random variation in the instantaneous concentration of each molecular species in each cell.

     

  1. Effects of noise

All biosystems are open, non-linear, dissipative, and they are in a dynamic equilibrium with their environment. They are self-organized. In this context, noise has a positive role, including:

  • Generation of errors in DNA replication, leading to mutation and evolution.

  • Noise-induced amplification of weak, under-threshold signals (by stochastic resonance).

  • Noise enhanced signal transmission across voltage-dependent ion channels (actually noise helps transport across membrane ion channels).

  • Phenotypic noise enables adaptation if environmental conditions shift.

  • Any chemical reaction has an activation barrier which is crossed with the help of thermal noise.

  • Noise in intracellular reaction dynamics drives the selection of actively growing states among all possible cellular states (Kaneko & Furusawa).

  • Pathogenic organisms utilize random fluctuations on the surface to evade host responses. The gene expression variability and the accompanying noise make the cell flexible and help it to adapt to varying environmental conditions.

  • Brownian noise plays a dominant role in the molecular motors operation. Molecular motors move along the cytoskeleton and transport proteins from the place where they were fabricated to the place where they are needed. They are fuelled by the chemical energy obtained from the hydrolysis of ATP. Thermal noise is essential to transform chemical energy into mechanical energy.

  • It is admitted that Brownian noise destroy temporal and spatial patterns; however, in out-of-equilibrium nonlinear biosystems noise can produce new ordered behaviours (by inducing synchronization/coherence in chemical and biological systems).

  • Attractors are stable states to which system converges. Noise is essential for switching from attractor to attractor. Attractor selection is driven by the inherent noise in gene expression. It is admitted that “attractor selection dynamically switches between a “deterministic mode”, where the system converges to its nearest attractor and a “random mode”, where the potential landscape is flattened by the activity term” (K. Leibnitz & M. Koda).

  • Many systems (as chemical reactions, society of living organisms and neurons) perform coordination by means of phase synchronization of their local oscillators. It has been found that the common noise to which all individuals are submitted can induce stable phase synchronization in large populations.

  • Noise is paramount to the operation of any excitable system. Without noise, the excitable system delivers no output at all, while too much noise induces a noisy output. For an appropriate noise intensity, the behaviour of the system becomes regular. This is the phenomenon of coherence resonance.

  • etc.

     

  1. Conclusion

Noise has a rather positive role in biological systems, very likely due to the “intelligent” way in which living systems are exploiting it. During millions of years of evolution, those organisms not able to efficiently use noise were very likely naturally eliminated.

 

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