Solutions to Exercises
A First Course in Systems Biology
EBERHARD O. VOIT
(with the assistance of I-Chun Chou, Po-Wei Chen,
Sepideh Dolatshahi, Yun Lee, Zhen Qi and Weiwei Yin)
Most exercises in A First Course in Systems Biology are structured to be open-ended and
stimulate self-motivated learning and exploration. As a consequence, they do not have unique
solutions. Some students find this ambiguity uncomfortable and would much rather be assured
that there is one correct solution. However, after a while, they often see that open-ended
questions are much closer to reality, especially with regard to complex phenomena in biology.
Furthermore, students recognize that they can structure their solutions, to some degree, according
to their own preference: Some students like conceptual approaches, others like simulations, yet
others are intrigued by rigorous proofs. Some enjoy trying out multiple changes in model settings
and studying the responses of a system, others would much rather extract the essence of a
problem and try to solve it as concisely as possible, while some prefer to spend their time
screening the literature for experts’ answers or solutions to similar problems. Many students have
asked me: how many simulations do I have to do? Initially, they sometimes do not like my
answer: Before you execute a simulation, make a prediction of what you expect to happen. If
your predictions are consistently correct, at least qualitatively, you may stop. However, if your
predictions are sometimes correct and sometimes false, then there are aspects of the system that
you don’t really understand. You need to keep on simulating, analyzing and interpreting.
Many exercises permit a lot of latitude in terms of breadth and depth, and the instructor
might want to specify the expected length of a report, level of detail of an analysis, and possibly
a specific focus. For instance, if students are asked to explore different visualizations of protein
structures in the Protein Data Bank (PDB), one could ask them to focus on specific proteins that,
for some reason, are of particular interest to the student, class or the program. Some exercises
ask for reports excerpting information from the literature or the Internet. The answers proposed
here usually do not offer as much detail as one might expect from a student, but merely point to
relevant information and highlight important topics. Similarly, the exploration of software
requires hands-on working with the program, and the solutions just provide pointers as to where
and how to start. Again, it might be useful to connect these software questions with a specific
biological question.
The total number of exercises per chapter is probably too high for a typical one-semester
class, but affords the instructor some flexibility in choosing exercises that are deemed most
relevant for the types of students taking the class, their backgrounds in biology, mathematics,
and computing, and the department or program in which the course is taught. Finally, the large
number and variety of exercises, and the inbuilt flexibility in solution strategies, suggest that
some of the proposed solutions could probably be improved. I would be very happy to receive
better solutions and possibly include them in future versions of this solution manual.
,Solutions to Exercises in Chapter 1
1.1. Search the Internet, as well as different dictionaries, for definitions of a “system.”
Extract commonalities among these definitions and formulate your own definition.
Solution:
A good start is an Internet search with “definition of system” as the search term, which leads to a
lot of hits. There is a huge literature about systems, and philosophers considered the concept
even before Aristotle and Plato. The definitions of the term are of course all slightly different,
but many of them have some key features in common. According to these commonalities:
• A system is a group, assemblage, or organized set of several or many parts, elements, objects,
or items.
• The parts are interconnected or interrelated; they regularly interact.
• The parts and their interconnections create a unified or integrated whole that has defined
boundaries; everything outside the boundaries is considered as the environment.
• The interconnections within the system create some functionality.
• The functionality is complex and sometimes emergent, which means that it cannot be
identified in the components alone.
• Systems have structure and behavior.
• Many systems have internal regulators.
• Open systems process input and/or generate output; closed systems do not exchange mass or
energy with the environment.
• Terms sometimes seen as synonyms (at least of some systems) are network; scheme;
complex of methods; set of rules.
• The word “system” comes from Greek and refers to a composition or combined set-up of
several parts.
1.2. Search the Internet for definitions of “systems biology.” Extract commonalities among
these definitions and formulate your own definition.
Solution:
The term “systems biology” is roughly synonymous with “analysis of biological systems.” Thus,
the concept and definition of “systems biology” share much with the generic definitions of
systems in Exercise 1.1, but specifically applied to biology.
A genuine aspect of systems biology is that it is often contrasted to reductionism, that is,
the philosophy, especially in biology, of taking things further and further apart in order to study
the properties of the ultimate components. While systems biology aims to reconstruct systems
from components, the dichotomy between systems biology and reductionism should not be seen
as a competition of what is right and what not, because systems biology would not be able to
function without targeted reductionistic research. At the same time, only knowing the
components is insufficient and requires a complementary phase of reconstruction.
, Other genuine features of system biology include the fact that biological systems
naturally span multiple organizational, spatial, and temporal scales, which are to be integrated in
comprehensive systems studies to explain overall function. Also, the aspect of emerging
properties is usually associated with biological systems. Finally, systems biology is very
interested in dynamics, and some definitions of systems biology declare it as the application of
dynamical systems theory to biological phenomena.
While some authors define systems biology as an extension of molecular and -omics
biology, one should keep in mind that physiology and ecology have been practicing systems
analysis in biology for a long time, and that fields like cybernetics and biomathematics could
also be seen as its precursors. Ultimately, as the text explains, systems biology is really the result
of the confluence of many fields, and this fact should enter its definition.
1.3. List 10 systems within the human body.
Solution:
Obvious examples include:
• the nervous system;
• the gastrointestinal system;
• the cardiovascular system.
However, the human body is full of uncounted “smaller” or less prominent systems, such as:
• the system with which the eye responds to light;
• the system in which neurotransmitters are passed through different brain sections;
• the uptake system with which cells incorporate materials or signals;
• a large number of specific metabolic pathway systems;
• the system of the ribosome that translates mRNA into proteins;
• the many gene regulatory systems that respond to specific situations or demands;
• the information system within the genetic code.
1.4. Exactly what features make the system in Figure 1.10 so much more complicated than
the system in Figure 1.8?
Solution:
The main reason that the system in Figure 1.8 is so much easier to understand than the system in
Figure 1.10 is its linear structure. Our intuition is correct when we say that an increase in E will
hasten the conversion of X into Y and the production of Z. We cannot say by how much, but we
can imagine some type of monotonic response, because there are no counteracting or competing
processes. By contrast, Figure 1.10 contains a logical feedback loop through which changes in Z
feed back on earlier events, which themselves drive the dynamics of Z. Now, there are competing
processes, namely the production of Z (tending to increase Z) and its ultimately inhibitory effect
on this production (tending to diminish Z). These processes are not black or white, on or off, but
depend on numerical features that we cannot really process well in our minds, especially if we
, are interested in quantitative statements. Indeed, we have seen that drastically different responses
of the same system are possible (see Figure 1.11), if the parameter settings are slightly altered. In
particular, it is impossible to intuit the threshold where one behavior switches into a different
behavior. Mathematics and computer simulations often characterize such situations rather easily.
1.5. Imagine that Figure 1.10 represents a system that has become faulty owing to disease.
Describe the consequences of its complexity for any medical treatment strategy.
Solution:
Even if we know the structure of the system, repair mechanisms are not easy to install. For
instance, imagine that one of the processes represented by a green arrow is disrupted. Because of
this disruption, the system is no longer regulated and does not adapt, for instance, to an increased
or decreased input. Thus, a medical treatment of the disrupted system would have to mimic this
control. As a specific example, suppose the model is a very much simplified system regulating
blood sugar. If we had a constant sugar input at just the right concentration, the disrupted system
would function well. However, if the input is increased, more Z is produced, and the disrupted
system cannot do anything about it. Medically, we would thus have to respond to every specific
input with a corresponding reduction, for instance, in E. As diabetics know, they have to take
insulin not continuously but at specific times, in connections with meals, and, ideally, in just the
right amounts, thereby mimicking the natural control system.
In many cases, the structure of a diseased system is not even known, and treatment of a
disrupted system becomes a hit-or-miss strategy. If a feedback system acts very slowly, we might
be able to respond appropriately, but if it acts fast, its control becomes problematic.
1.6. In Figure 1.2, are there control paths along which ABA either activates or inhibits
closure of stomata? If so, list at least one path each. If both paths exist in parallel, discuss
what you expect the effect of an increase in ABA to be on stomata closure.
Solution:
There are indeed positive and negative pathways connecting ABA to the closure system. For
instance, the pathway through RAC1 (center of the graph) and Actin includes two negative
effects, which make the entire pathway positive: If only this pathway were there, then more ABA
would lead to more closure. By contrast, the pathway through pHc (center toward the right) and
KAP (right above closure) contains only one negative signal. Thus, if this pathway were the only
one present, then more ABA would lead to less closure.
The situation that the system contains these two counteracting pathways, along with the
numerous other signals, makes intuitive predictions entirely unreliable. For instance, suppose
only the two pathways mentioned above were present. Without more information, we don’t
know which of the two has a stronger effect. Also, we don’t know whether the two pathways act
with the same speed. It could well be that the faster pathway initially “wins,” but that the slower
pathway has a stronger effect and overcomes the faster pathway after some time, thereby
creating a temporary response. When all pathways shown are active, we have no chance of
making quantitatively correct predictions without a detailed computational model.
