Abstract — Systems biology is a potential new branch of biology with roots in
many other fields such as biology, physics, mathematics, and computer science. Accordingly,
this is a manifestation of mathematical biology and endeavors to understand
complex systems, such as networks of genes, as interacting systems’
components. In this paper, we analyze
the field from a literature review framework; the author is passive in the
review. Further, we conclude that systems biology is a potential field for
contributing to the new horizons of science, especially biomedical sciences;
also the weakness of systems biology is that it is not commonly mentioned in
traditional books in biology, even recently published. Nonetheless, as the
literature claims, this field might be the bridge for making biology,
especially genetics, a source of ideas and principles for other fields, such as
biomechanics; and simultaneously an example for other fields of biomedical
sciences that mathematics, physics and other branch indeed can enhance those
with new insights and methods.
Keywords—Systems
Biology; Biological Systems; Biological Networks; Gene sharing;
I.
Introduction
‘The all is more than the sum of the
parts.’ This sentence might be tricky for some not endowed with the right
thinking. One might figure it out that some phenomena cannot be overcome, such
as in quantum mechanics (Heisenberg Principle), or some cannot be modeled, such
as the prediction of the sides of a coin in a sequence of tosses, due to not
being feasible. The observation that possibly some phenomena cannot be always
put under the ‘law of action and reaction’ was warmly discussed in one of the
Einstein’s scientific life [1] where he has asked if it is always possible to
predict the outputs of physical systems if one models every part of this phenomena
accurately. Nonetheless, in some cases, not completely new in science, but
neglected intentionally for past scientists under names such as ‘vital forces’,
is the fact that some systems just can be interpreted properly if it is looked
from ‘above.’ This was defended firmly by Capra ([2], [3]); this is sometimes
referred as ‘holistic’ view against ‘reductionism.’ Therefore, the observation
that some systems cannot be tore up for being studied is not a matter of ‘human
limitations’, but rather a question of workings of the systems. Some
properties, termed widely emergent properties, can be just seen with the system
‘at work;’ they disappear when one ‘turns off’ or change the state of some
system’s component.
Regarding the matter of the workings of
complex systems, in biology it has recently formally given this task to a new
branch named Systems Biology (approximately documented in the literature about
2000 with [26], which claims to be the first formal publication, book, in
systems biology; however, the principles is not new). This paper intends to
shed some light on the issue. The current manuscript intends to be a map on the
theme, a short-hand writing in which one can encounter a list of references for
starting out in the theme or even increasing their knowledge; the topic
discussed and references left represents the current author’s points of view
and literature. The paper is far away from exhaustive, but rather informative.
Systems biology is a ‘hot’-scientific field, as points out [26], any attempts
might get obsolete fast. The most notable changes might come into the
application; nonetheless, the principles have been conserved. Systems biology
has emerged as a formal and important field from the necessity to understand
interactions of genes-genes and proteins-proteins; the question is how it comes
out “strange” observations, such as ‘conscious’ in the mind or even the cyclic
beating of the heart from movements of ions. With the explosion of data coming
from the project for mapping the genome, some information was observed to be
missing and this was interaction, the potential last step in the complete
understanding of life from the gene-level podium.
Control Systems Theory (CST) [5] attempts
to understand each part of a plant for controlling; this theory is
highly-dependent on differential equations theory. This is assumed that any
input will trigger some output by interaction between the parts. Moreover, this
is widely applied to complex systems composed of machines, for example; each
part is a complex system by its own, but they are regarded as ‘black box’, it
does not matter how they are inside, but rather how they ‘act’; this is an
‘engineering look of complex systems.’ See that this is a recursive action,
start from a complex problem as start ‘calling’ for the response of other
complex systems inside it until you get some ‘basal’ response; this is possible
because all parts are connected. Further, this is termed up-bottom approach.
In mathematics, complex systems are
analyzed by Bifurcation Theory (BT) [13]. It was observed, in some simple cases
created models, that complex systems might exhibit two or more behavior
depending on the state of the components; the system changes its behavior in
some cases completely different from the previous. The parameters under which
it happens are called bifurcation parameters. Some model cases for bifurcations
was identified and documented in the literature [28]. A system can change from
stable to unstable or from equilibrium as a point to as a cycle, for example.
This can be shown that even negative autoregulation in gene expression can
display those behaviors; negative autoregulation is the simplest network motif
in the theory of transcription network in systems biology analysis [10].
Systems biology is strongly rooted in
network theory for making sense of the all based upon the components integrated,
however it cannot be said that networks makes up the field. Network flows from
optimization theory [16] is strongly dependent on networks, nonetheless, they
work on static networks, which is simpler than the kind of networks under
analysis by systems biology; in systems biology, they are dynamical networks,
with phase portraits; they can be unstable; they can exhibit complex behaviors,
such as bifurcations.
In spite of the fact that little books in
systems biology leave it clear, systems biology just could be possible due to
efforts coming from the long past; works from previous scientists. The question
constantly posed was the applicability of the laws of physics to living matter
[12]; they used to believe that ‘not’, it gave space for concept such as ‘vital
force,’ some just existing in living matter. Nonetheless, this started to be
questioned with creation of simple ‘living’ systems in laboratory via inorganic
matter [4]. This would prove that life is not more than the laws of physics
under certain conditions; this opened space for an explosion of ‘artificial
life’ creation; as points out [4], biologists did not get happy in the first
attempts following successive failures.
Some might say, based upon the following
excerpt [27] that systems biology is just physiology renewed; in some sense it
is, but one needs to be careful with this assumption. Physiology is the study
of living organisms work. Further, it includes the study of proteins, such as how
the shape and electrical properties of proteins allow it to work as sodium
channel for moving ions in and out of the cell; at the other end, it is
concerned with complex processes that depend on the interplay of many widely
separated works in the body. What makes physiology unique among biologists is
that they are always interested in functions and integration; systems biology
takes the word ‘integration’ to the extreme sense of the word. Further, in
physiology, many areas are still poorly understood, such as ‘mind’ coming from
the brain; approaches from systems biology might give us some insights into the
answer. Making use of this passage, D. Noble [8] trained in physiology has
worked a bio-process in the heart for creating the pulses for heartbeats; in
the times when the reductionism was the state of the art, the author highlights
the problems to convince the scientists of his scientific realm on the validity
of the model presented; this was a practice of systems biology, emergent
properties from the integration of proteins.
One quite interesting application of
systems biology is ‘gene sharing’ [6], termed coined by the author [6]. Some
proteins might execute more than one function depending on its current
concentration (gene expression); [6] cites the example that gave rise to the
book in which the same protein from the lens of the eye of birds is expressed
in lower rate in the same organism working as enzyme in biochemical reactions.
Another example is given regarding a second protein working as receptor in the
cell membrane and transcription factors in the nucleus of the same cell. See
that transcription factor is left by the author as ‘ambiguous’ case; some
transcription factor might activate and repress depending in the environment
conditions. This is any example of bifurcation, once the proteins interact for
changing their molecular-function; this interaction makes the systems a
N-dimensional dynamical system, where N is the number of proteins.
Bifurcations in biological systems are
not new at all. In [14] it is studied bifurcations in neurons; as claims the
author, the literature has given too much attention to neurons in networks and
neglecting the specificity of neurons individually, this potential pitfall is
not done in systems biology. It was observed that neurons anatomically
identical might act differently and neurons different in anatomy might act
equally; this is due to bifurcation of the emergent states of the neurons. Note
that the biochemical process that starts with the application of an input
current in neurons and culminate with the spikes of the neuron is
protein-dependent.
Another interesting study of systems
biology is given in [30], by the author of this paper. As defends [29], much
has been discovered in the nature of matter, such as genes and interactions
between proteins, one must take it into account in new theories for
biomechanics. [29] uses the name continuum biomechanics, also used by [31]. Systems biology looks upon protein interaction
for creating the all, whereas continuum biomechanics looks upon the response of
living matter (the all) for creating properties of the biomaterial under
analysis; this studies also the element until the point it is necessary. They
are dual problems: one sees matter from above while the other from the bottom.
 |
Fig. 1.
The two antagonistic, but complementary ways, of studying living
matter [30]. (The letters means: on systems biology box “G- gene; P –
protein; C – Cell”; and on the biomechanics box “M – matter; S –
Structure; C – Components”)
|
Systems biology is a manifestation of mathematical biology. Mathematical biology is the application of mathematical modeling to problems coming from biological sciences, see for example ([20]. [21]). As defends [20], mathematical biology tries to exploit the trivial synergy between biology and mathematics; biology offers difficult problems to mathematics, mathematics offers solutions via models, and biology offers the place for testing the models. Mathematics was not accepted in biology easily [4]; much attempted has failed for establishing what we see nowadays. As [4] points out that the biggest problems came from biologists that insisted in not believing in the power of mathematics; hidden was the concept that biology is somehow too different from other existences for being modeled via mathematics, concepts such as ‘vital forces’ gained place.
Minsky [7] has pointed out the fact that
some systems cannot be understood unless one takes into account the entire
working system. In neuron science [15], it has emergent properties in the
neuronal networks, quite similar to those of genes; neuronal network is also
treated by textbooks in systems biology [10]. This must be noted that the
complexity encountered in biological system is not new, but avoided by previous
scientists; this is seen in the work of the quantum mechanics scientist
Schrödinger [9] by highlighting the potential difficult of reducing complex
systems such as living matter to the simple laws of physics, as it has been
done for centuries in physics. When looking in the genome, systems biology is
not concerned in a single gene, which is the concern of bioinformatics, but
rather in thousands of genes working simultaneously; this creates quite complex
dynamical networks. Emergent properties in neuronal systems are widely studies
in the physics of neural networks ([22], [23], [24]). The most important in
gene expression via networks, as one of the most common application of systems
biology, is the fact that the study of genes as nucleic acid sequences, as it
is done in bioinformatics practices, just provides us with which protein is
expressed, but it gives rises to non information regarding quantity, place and
period of time [32]. This is interesting noting that every cell contains the
same genetic code, but the question is how they are different and the answer is
on the expression patterns. As [4] presents, this dilemma of gene expression by
different cells puzzled scientists for a quite long time; the second puzzle
came from cellular differentiation, with the ‘French flag’ model dominating;
how ‘gene’ knows where they are.
The concept of emergent property is quite
important for systems biology; this is what really gives systems biology a
specific and remarkable place in biomathematics. In Neural networks, this is
widely applied for calculation in computer science [25]; this is hardly seen
some concerned about how it works, it just works. In the body this is similar,
but we have not just networks of neurons, but also proteins for executing
similar tasks [10]; ‘learn’ is not something just from ‘neurons,’ this is in
every piece of our body. In the literature, the concepts of systems biology has
been absorbed via new names, such as systems biomedicine [18] and system
bioinformatics [17]. This is in some sense positive, once results might be
migrated without prejudices, as discussed by [4] potential barrier for
migrating mathematical biology to biomedical sciences.
In the remaining part of the paper, the
author will dissert on some topics. The selection is merely for opening
scientific view, the reader is invited to consult the references left in the
end of the current work for broadening idea or some specific point. The first
set of topics regards the dimensions of systems biology, this is meant, the
scientific field that contributes for the existence of systems biology as an
independent and promising field. As one will likely conclude, the
multidisciplinary nature of systems biology will give it a place in the scientific
realm. The next set of topics is regarded networks of genes, the most popular
documentation of systems biology applications. This might be explained keeping
in mind the high-connectivity in the genetic code, which makes reductionism
impracticable for interesting results. The next is gene sharing, a recent
documented application of systems biological principles; proteins changing
their function based upon concentration or interaction with the environment;
permanent-multifunctional genes. The next section discusses modular look, this
is a guiding principle from systems biology, one ‘neglects’ the nature of
small-systems, one application is the use of network motifs for understanding
complex transcriptional networks. The next is mathematical computational models
in systems biology. Systems biology is highly dependent in computational
practices for getting some results; such as algorithms for simulating networks
of expressing genes, set of nonlinear differential equations. Finally one
reaches the conclusions and final remarks.
II.
The dimensions of Systems Biology
This is presented a scheme below, fig. 2, with
the ‘dimensions’ of systems biology; this is meant the fields that borrow
principles and tools for the existence of systems biology as a well-established
field.
 |
Fig. 2.
The related fields to
systems biology. (Note that some circles
might be claimed as dependent, but this is separated for highlighting their
importance. The dashed circle intends to pinpoint the synergic existence of the
fields by their own)
|
The boxes are explained below.
- Computer Science: the theories from systems biology is connected to complex systems, such as graph theory and nonlinear dynamical systems; analysis of bifurcation theory and simulation-modeling of complex systems. Those cannot be successfully inferred with simple models solved by hand for hypothetical cases. Further, it is desirable the analysis of parameters;
- Bioinformatics: One might claim that bioinformatics is just a sub-area of computer science, but it is not; in spite of the fact it has some dependence. Bioinformatics has concerns on laboratorial experiments and translation to common use. The place of systems biology is to make sense of those data in ‘on-working’; not a single gene, even thousands, see microarrays analysis for example;
- Mathematics: Mathematics nowadays has rooted in almost all fields of sciences and biology is not different. One of those manifestations comes out in systems biology. For examples, gene can have their expression patterns analyzed using nonlinear differential equation. The ‘French flag’ model is the diffusion equation (a partial differential equation, pde). Gene expression is in general noisy (stochastic differential equation);
- Biology: Besides one can claim that biology is the mother of systems biology, this claim might be dangerous; this is the target of systems biology and main body; nonetheless, the principles can be migrated to other fields such as graph theory;
- Physics: Physics goes into systems biology through mainly philosophical principles: the chase of generalization always present in physics. Also as a example of successful case of mathematical exportation, mathematical physics. The instruments for measurement might be applications of physics;
- Chemistry: the nature of controlling networks is mainly chemical; important phenomena such as inclusion of chemicals for changing molecular properties are strongly chemistry in action. See for example chemotaxis;
- Artificial Intelligence: Artificial intelligence offers methods not encountered in pure mathematics, such as neural networks or optimization programming. Further, systems biology might contribute to artificial intelligence;
- Engineering sciences: The concern on understanding to design is also part of systems biology, such as how to recreate the studied phenomena in the hope to prove that they can be reproduced in laboratory.
III.
Feedbacks in biological systems
As presents [4], feedbacks in biological
systems might happens in many levels, such as gene-proteins or organism-gene;
see scheme in fig. 3. Feedbacks is something important for systems biology once
the second step in the development of the ideas coming from the revolution
triggered by the gene discover was the inclusion of feedbacks in the genetic
circuits as idea models.
In system control theory [5], feedbacks is a way
for making systems robust; they might adapt based upon the current states for
future states. This is used for training neural network, in which the feedback
is given by an error function, for example. In biological systems this was
proposed and verified. As points out [8], this increased the role of the
environment in biological systems. The genes does not have all information,
some is adapted to the environment condition via controlling systems endowed
with feedbacks, see fig. 3. This suggested [8] the gene-environment paradigm.
As noted by Savageau [10], not only the gene information is under selection,
also the controlling patterns; repression or activation, as model controlling
patterns.
 |
Fig. 3.
The new approach proposed by systems biology
(second scheme) and the first thinking proposed by first genetic-based
scientists. (Inspired by [8], scheme used
in paper proposed to the same scientific meeting).
|
IV. Networks of genes
When ‘someone’ is ‘hot’, they sweat; the question is how this happens. Bearing in mind that every process in the body is directly or indirectly a function of protein production and protein is produced from gene information; one might ask how that is done. Systems biology has worked on this kind of questions. Those networks are called Sensory Transcription Networks; they ‘sense’ environmental demands and trigger some internal transcription networks. See scheme following, fig. 4.
|
 |
| Fig 4. Transcription networks and the environmental. (The signal are external “forces” such as glucose starvation or light presence. “X” are transcription factors, special set of proteins used for communicating genes. The arrows are flux of something, such as information. Source: inspired [10]). |
The most remarkable observation is that those responses are carried out in networks; genes communicating for some final task. Transcription networks are networks of genes that control gene expression; in general, genes might repress or activate others. In addition, networks touch a second important observed-peculiarity of biological systems: redundancy.
V. Gene Sharing
Gene sharing [6] is a quite interesting
manifestation of the ideas defended by systems biology; the correlations
between elements of a system might create different properties even the system
being the same. It was observed that structural proteins, called crystallins, responsible for transparent
and refractive properties of the cellular lens in the eye also perform
nonrefractive stress-related or metabolic functions (enzymatic) in other
tissues. The difference is in the level of expression of the protein; in the
lens they are expressed in a relative-high level, whereas in the tissue they
are expressed in a low-level. As claims [6], this is not a special case. A second example is a polypeptide that works as ligand when it is in the cellular
membrane or transcription factor when it migrates to the center of the cell. The
author claims that the examples presented are not special cases. The author [6]
attempts to clarify the meaning of gene sharing. For example, the changing of amino
acid sequence is not gene sharing; even if this changes the function of the
final molecular system. Further, in general gene sharing happens in bifurcation
style; the molecular system keeps multifunction being ‘turned off’ under
certain environmental conditions, such as high expression in the case of the
crystallins. Moreover, gene sharing maintains the same gene as root for the
molecular system and in general the primary structure of the molecular system
(sequence of amino acid) is not affected; however, not always this means gene
sharing; splicing and pos-editing of mRNA will not always culminate in gene
sharing.
Gene sharing is a quite good example that
emergent properties exist and that the environment plays central role in the
protein workings. This is possible to demonstrate using simple numerical
simulations at home that simple network motifs such as negative autoregulation
or positive regulation can generate those bifurcation points depending on
parameters values or concentrations; those simulations impose non-protein
property assumptions, just concentration and parameters. Negative
autoregulation is a network motif where a gene represses itself whereas
positive regulation is a network where a gene activates another.
VI. Module look
The brain is a highly-layered system [33].
This was observed that the brain is a set of specialized compartment connected
to each other. The most interesting is that those parts are highly connected
[15]; some has tried to destroy one part in the hope to affect just some
isolated part, but the whole brain is affected [15]. Further, tasks such as
‘thinking’ about works, highly abstracted, requires the activation of most of
all the cortex cerebral, see fig. 5. This is not peculiar from the brain. Genes
have showed similar behavior; this is seen in the attempt to treat one disease
and appearing the well-known side-effects. See scheme following, fig. 6. In gene expression networks,
those elements of the system are called network motifs; highly specialized
sub-graphs of genes. In studies, [10] has demonstrated that complex networks
can be successfully decomposed into those simpler graphs called network motifs.
VII. . Mathematical-computational models in systems biology
The meaning of model is not a commonplace
for biology and mathematics [4]. In fact, in mathematics this is a set of
principles and formulae; while in biology this is a model organism used to make
studies, such as the bacteria C. Coli.
Therefore, this was the first problem encountered by mathematical biologist [4].
But, with the efforts of some scientists, they have achieved some agreements
and today mathematical models are an important part of biological sciences.
Since biological systems are complex systems, the old ‘pen and paper’
mathematics cannot be applied successfully, computer is of high-priority. The
main reason is the problem of finding analytical solution for most of the
problems treated in the literature in a feasible time. Design and application
of algorithms are part of systems biology practices ([19]. [26]). The most
promising models are from computational intelligence ([30], [34]) due to their
nonparametric nature. Another set of models comes from systems control theory
[35]. This is chased parameter approximation via technique from systems control
theory. Numerical simulations, such as Molecular Dynamics and numerical methods
for differential equations are quite important models for systems biology [30].
 |
| Fig 5. The highly interconnected processing of the brain. (Source: adapted from [15]) |
 |
| Fig 6. Organism, scheme (Each irregular shape intends to represent a component, whereas the arrow stands for connections between those components. The dashed arrows are internal connection while the other are external (coming in and out. source: from paper by the author submitted to the same scientific meeting). |
VIII. Conclusions and final remarks
It was surveyed systems biology in the
literature; a passive analysis. Thus, systems biology is a relatively recent
field with roots in physics, biology, mathematics, computer science, and other
fields that endeavors to understand biological systems as small parts
interacting for creating what we ‘see’ and ‘feel’. Further, this is claimed that
some important properties cannot be ‘seen’ unless the entire system under work
is analyzed; all the elements working simultaneously. In addition, it was
discussed some case-examples, such as gene sharing, which is an example
encountered in the literature of proteins that have multifunction depending on
the environment states; this is a bifurcation case. It was discussed as well in
the demand for mathematical-computational models and some principles for
systems biology. Furthermore, models from computational intelligence are
promising models as well numerical methods for differential equations.
Perhaps the world we leave in is a proof
that emergent properties exist and are effective. This might be found out on
the problems encountered by physicists to unite quantum mechanics and classical
mechanics. Non one can say for sure the numerical value for what the classical
mechanical world disappears (the collapse of the wave function) or for which the
quantum mechanical world starts and finishes out. The difficult to explain the
macro-world (classical mechanics) based upon the micro-world (quantum
mechanics) might be because the macro-world is itself an emergent property of
the micro-world. Another supporting point might be for example the nature of
light as posed by Clerk Maxwell [11], light just exists in a definite speed and
interchanges of electric and magnetic fields; light itself is a emergent
property, light disappears if one stops it. Nonetheless, those are just
enforcing point, not representing practices of systems biology.
Regarding the complexity from biological
systems, the author in a paper submitted to the same scientific meeting has
written “…one always needs to be recollected on the difficult to capture
biological laws with the current state of the art of applied sciences, it
cannot be an obstacle, but the reason for improving. Systems biology has taken
this task……..” and this could a guiding principle. Additionally, the potential
weakness of systems biology is that it is still not part of classical textbooks
books in genetics ([36], [37], [38], [39]); this is rarely encountered
mathematical terms such as ‘noise’ in textbook of traditional biology, even
recently written books.
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