Specificity of Bionoise
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
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:
(generated inside the process or system of interest). It is
the consequence of the inherently random nature of biochemical
(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.
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:
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
is highly probabilistic.
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.
is equally a stochastic process. In translation,
produced by transcription
is decoded by the ribosome
to produce a specific
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.
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
variability among isogenic populations of cells. This is called
spite of identical initial conditions, with time, different cells or
species may evolve along distinct directions).
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
As expected, the
is equally present in biosystems. Its origins are related to:
fluctuations of the
potential-energy of the system due to the existence of thermally
activated processes in proteins (as folding);
the diffusion of
macromolecules in the functional space;
fluctuations in the
surrounding solvent, due to interactions of the protein and the
fluctuations in any
biological rhythm (from cellular to behavioral levels);
voltage fluctuations in
bilayer lipid membranes
of metabolites across biological membranes;
electromagnetic excitation, which is filtered by the biosystem
and gives rise to 1/f noise
(Szendro, Vincze & Szasz)
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
where K and C
are constants depending on the particular system and ω
is the pulsation.
excluding 1/f noise, the
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
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
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
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
then the probability that there are exactly
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
with a standard deviation
. These fluctuations are denoted as
(or particularly in electronics, as
Note that sometimes
This law applies to physical systems with a very limited number of
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.
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.
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.
amplification of weak, under-threshold signals (by
enhanced signal transmission across voltage-dependent ion channels
(actually noise helps transport across membrane ion channels).
enables adaptation if
environmental conditions shift.
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
utilize random fluctuations on the surface to evade host responses.
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.
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”
Leibnitz & M. Koda).
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.
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
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.