Untangling Complex Systems, page 38
− k mRNA
dt
TF ni
n
d
i
[
] i + K
i
i
[7.27]
d Y
[ ]
Y
[ ]
= k [
]
tl mRNA − khE
dt
T K
[ ]
M + Y
In [7.27], k and k are the kinetic constants of RNA transcription and translation, respectively. The tr
tl
kinetic constant k is relative to the degradation processes of RNA. Transcription factors, TF , can
d
i
act as either activators ( n
i > 0) or inhibitors ( ni < 0), increasing or reducing the transcription rate of
a gene. The second term of the differential equation relative to Y represents its rate of degradation.
The term E represents a protease that degrades Y; its total concentration is E . Its turnover rate is k , T
h
and its Michaelis constant is K . Note that because binding of TF to DNA is fast and often takes
M
i
seconds to reach the equilibrium, whereas mRNA or protein production take minutes to hours, we
can assume the concentration of bound TF are those of equilibrium. In Figure 7.18, a scheme of the i
protein synthesis mechanism described by equation [7.27] is drawn.
TRY EXERCISE 7.5
The Y protein concentration will reach a steady state value without any oscillations, corresponding
to a homeostatic condition.
The presence of some form of feedback in the kinetics of protein synthesis can give rise to
oscillations. For example, protein Y may inhibit the expression of its gene (see Figure 7.19a). An example is PER protein. It rules certain cellular and high-level biological rhythms having periods
of about 24 hours, the so-called circadian rhythms (from the Latin circa dies, meaning “approxi-
mately a day”), by inhibiting the transcription factors of its own PER gene (Novák and Tyson 2008).
Y
E
S
Translation
Signal
k
TF
mRNA
d
RNAp
Transcription
Gene
Promoter site
FIGURE 7.18 Scheme of the synthesis of protein Y, where the protagonists are transcription factors ( TF ), i
RNA polymerase (RNAp), messenger RNA (mRNA), and protease E.
The Emergence of Temporal Order within a Living Being
183
Y
E
S
Translation
Signal
1
k
0.8
TF
mRNA
d
2
RNAp
Transcription
mRNA 0.4
Gene
0.0 0
1
2
3
4
Promoter site
(a)
(b)
Protein Y
FIGURE 7.19 Synthesis of protein Y with a negative feedback effect on its transcription factor ( TF): scheme of the mechanism in (a) and representative solution7 of the equations [7.28] in (b).
Knowing that PER protein (symbol Y) binds its transcription factor according to the following
chemical equation nY + TF = Y ( TF) and that protease E degrades PER protein, the differential n
equations describing the dynamics of the system are:
d [mRNA]
K n
= k
[
]
trCTF
− k mRNA
dt
Kn + Y n
d
[ ]
[7.28]
d Y
[ ]
[ Y ]
= k [mRNA]− khET
dt
tl
KM +
[ Y ]
C is the total concentration of TF and ( K n/ K n [ Y ] n
+
) represents the fraction of TF not bound to Y.
TF
K n = KD, where K is the dissociation constant for the binding process of Y to TF. The other terms D
have the same meaning seen in equation [7.27].
The nullclines of the non-linear differential equations [7.28] are plotted in Figure 7.19b. The
nullcline labeled as 1 is the locus of points where the rate of mRNA synthesis is exactly balanced by
the rate of mRNA degradation. On the other hand, the nullcline labeled as 2 is the locus of points
where the rate of protein synthesis is balanced by the rate of its degradation. The intersection point
of the two nullclines represents the steady state.
The Jacobian of system [7.28] is
nk
n
n
[ ] −1
trCTF K
Y
− k
ss
d
−
(
2
K n + Y n
[ ] )
J
ss
=
[7.29]
k
hET K
k
M
tl
−
2
( K [ ] )
M + Y ss
Its trace is always negative; its determinant is always positive. When the discriminant, that is
∆ = ( tr( J ))2 − 4 det( J ) = ( k
2 2
n
n−1
n
n 2
d − khET K M (
/ KM + [ Y ] ss) ) − 4 nktlktrCTF K [ Y ss
] /( K + Y
[ ss
] ) , is nega-
tive, the steady state is a stable spiral. Although the system [7.28] may exhibit damped oscillations
on the way to the steady state, sustained oscillations in this simple gene regulatory circuit are
impossible, and Y reaches a homeostatic steady state.
7 The representative solution for the system of differential equations [7.28] plotted in Figure 7.19b has been obtained with the following parameter values: k
tr = kd = 0.1 min−1, CTF = 1, K = 1, n = 2, KM = 1, ktl = 1 min−1, kh = 1, ET = 1
(Novák and Tyson 2008).
184
Untangling Complex Systems
kdy Y
E
1
S
Translation
0.8
Signal
TF
mRNA
RNAp
mRNA 0.4
k
2
Transcription
d
Gene
0.0 0
1
2
3
4
Protein Y
(a)
Promoter site
(b)
FIGURE 7.20 Synthesis of protein Y with a negative feedback effect on its transcription factor ( TF) and a negative feedback effect on its degradation process by protease E: scheme of the mechanism in (a) and representative solution8 of the equations [7.31] in (b).
Undamped oscillations emerge when the negative feedback effect of Y on its gene expression is
accompanied by a positive feedback effect, such as the binding of Y to an allosteric site of protease
E inhibiting the activity of E (see Figure 7.20a):
2 Y + E →
2
←
([ 2 ]/[ ][ ] )
2
Y E with KA = Y E
E Y
. [7.30]
The differential equations describing the dynamics of the system are:
d [mRNA]
K n
= k
[
]
trCTF
− k mRNA
dt
Kn + Y n
d
[ ]
[7.31]
d Y
[ ]
[ Y ]
= k [mRNA]− kdY [ Y ]− khET
dt
tl
K
2
M +
[ Y ]+ KMKA[ Y ]
In these equations, k is the rate constant for an alternative pathway of Y degradation. The nullclines dY
of the non-linear differential equations [7.31] are plotted in Figure 7.20b. The nullcline labeled as 1 is the locus of points where the rate of mRNA synthesis is exactly balanced by the rate of mRNA
degradation. The nullcline labeled as 2 is the locus of points where the rate of protein synthesis is
balanced by the rate of its degradation. The term of positive feedback gives rise to a kink in the
nullcline. The intersection point of the two nullclines represents the steady state.
The Jacobian of the system [7.31] is
nk
n
n
[ ] −1
trCTF K
Y
− k
ss
d
−
(
2
K n + Y n
[ ] ) ss
J =
[7.32]
k
1
(
[ ]2 )
hET K M
− KA Y
k
ss
tl
− k
dY −
2 2
KM
Y
K K Y
( +[ ] +
[ ]
ss
M
A
ss )
8 The representative solution for the system of differential equations [7.31] plotted in Figure 7.20b has been obtained with the following parameter values: ktr = kd = kdY = 0.05 min−1, CTF = 1, K = 1, n = 4, KM = 0.1, ktl = 1 min−1, kh = 1, ET = 1, K K
M
A = 2 (Novák and Tyson, 2008).
The Emergence of Temporal Order within a Living Being
185
(mRNA)n
900
DNA
e
(mRNA)n
(mRNA)
600
c
danc
(mRNA)c
Nucleus
Abun 300
Yn
Yc
( Y) c
( Y) n
0
Cytoplasm
30
60
90
Time
FIGURE 7.21 Mechanism of Y protein synthesis taking into account transport of macromolecules between
the nucleus and the cytoplasm (a). Plot of the sustained oscillations for mRNA and Y in cytoplasm and
nucleus (b).9
Jacobian [7.32] differs from that [7.29] in the Y term. When K is small, the positive feedback effect y
A
is negligible, and the system does not show sustained oscillations. When K is sufficiently large,
A
and the negative feedback loop is sufficiently nonlinear (i.e., the n coefficient is sufficiently large),
tr ( J ) becomes null and det ( J ) > 0. Therefore, the system exhibits a limit cycle, and the net diagram flux for the system becomes qualitatively equivalent to that depicted in Figure 7.9 for glycolysis. The mechanism of negative feedback on gene expression combined with inhibition of protein
degradation has been suggested as a possible source of circadian rhythms in the reaction network
that governs expression of the PER gene in fruit flies (Novák and Tyson 2008). Circadian rhythms
in eukaryotic cells10 have also been modeled by invoking a mechanism involving three or more
components and only a negative feedback loop on gene expression (Novák and Tyson 2008). The
components may be mRNA that is synthesized in the nucleus (mRNA ) and transported into the
n
cytoplasm (mRNA ) where it gets translated into protein which is translocated into the nucleus
c
Yc,
( Y ) and represses the activity of its gene (see Figure 7.21a). The four-variable negative-feedback n
loop oscillates as naturally as a pendulum (see Figure 7.21b).
7.5 BIOLOGICAL RHYTHMS
From the biochemical examples investigated in this chapter, it is evident that living organisms have
a natural tendency to exhibit a mixture of homeostatic and oscillatory behaviors: the more complex
the biological system, the greater the possibilities. In fact, as far as the oscillatory behavior is con-
cerned, outputs of various frequencies, phases, and amplitudes are possible. Multicellular organ-
isms have cells that specialize in different functions depending on the organ they belong. Each type
9 The results plotted in Figure 7.21b have been achieved assuming that mRNA is synthesized in the nucleus ( xn) and transported into the cytoplasm ( xc), where it gets translated into protein ( yc), which is translocated into the nucleus ( yn). If we impose that eps = Vnuc/Vcyt; half-life of mRNA in nucleus = 0.693/kdxn; half-life of protein in cytoplasm = 0.693/kdyc, the differential equations are:
dxn/dt = kdxn*(sig/(1 + yn^p)—xn)—kexport*xn
dxc/dt = eps*kexport*xn—kdxc*xc
dyc/dt = kdyc*(xc − yc)—eps*kimport*yc
dyn/dt = kimport*yc—kdyn*yn/(Km + yn)
The constants appearing in the four differential equations have the following values: sig = 1000, p = 2, kdxn = 10,
kexport = 0.2, kdxc = 0.2, eps = 1, kdyn = 8, kdyc = 0.1, Km = 0.1, kimport = 0.1 (Novák and Tyson 2008).
Initial conditions: xn = 1.0, xc = 30.0, yc = 200.0, yn = 120.0.
10 A eukaryote is an organism whose cells contain a nucleus and other organelles enclosed within membranes.
186
Untangling Complex Systems
of cell triggers specific “clock genes.” In fact, each living being appears as “a house with clocks in
every room and every corner; but, yet in one way or another, they work in an organized way,” as
rightly alleged by Derk-Jan Dijk, director of the Surrey Sleep Research Centre in Guildford (UK).
All the periodic processes occurring at either the cellular, organ, or physiological system levels span
more than ten orders of magnitude of timescale, from hundredths of seconds up to tens of years11
(Goldbeter, 2017). They can be sorted out into three time-domains or rhythms: the (1) circadian,
(2) ultradian, and (3) infradian rhythms. The circadian processes are ruled by the periodic revolu-
tion of the earth around its axis, requiring 24 hours, and determining a significant daily variation
in the intensity and spectral composition of the electromagnetic radiation coming from the sun. The
infradian processes depend on the slower revolution of the moon around our planet (requiring about
one month), or the even slower revolution of the earth around the sun (requiring about one year).
Finally, there are organs and physiological systems that have ultradian rhythms, meaning they work
cyclically, with periods shorter than 24 hours. A list of ultradian, circadian, and infradian processes
found in human beings, is reported in Table 7.1.
Among the ultradian periodic processes, individual neurons detain the record of the fastest cycles
possible. In fact, many nerve cells generate impulses of transmembrane depolarization, followed by
hyperpolarization, in around 1 millisecond or so (for more details, see Chapter 9). Neurons use such impulses as signals that must travel very fast for effective communication. In the human hearth, the
electrical impulses last much longer than in nerve cells. In fact, the heart rate is about 60 beats per
minute, so there is a whole second for the impulse to occur and for the heart to recover before next
beat. Respiratory rhythm requires the cooperation of many nerve cells, peripheral and central, and
it has a frequency of about tenths of Hz. Connected with respiration, there is also the nasal cycle
(Atanasov 2014). Our nose holds two parallel breathing passages that are divided by the septum.
Our two nostrils shift their workload back and forth in a delicate dance called the nasal cycle. At
any moment, most of the air we inhale travels through just one nostril, while a much smaller amount
seeps in through the other. This difference is important because odor-causing chemicals vary in the
amount of time they take to dissolve through the mucus that lines our nasal cavity. The two nasal
cavities are like two chromatographic columns separating and detecting many odor-molecules.
Chemicals that dissolve quickly have the strongest effect in a fast-moving airstream that spreads
them out over as many odor receptors as possible. But compounds that dissolve slowly are more
accessible to smell in a slow-moving airstream.Due to the circadian oscillations of environmental
TABLE 7.1
Periodic Processes in Human Beings at the Organ and
Physiological System Levels Sorted out According to Their
Periods ( T) or Frequencies (ν )
Ultradian Rhythms
Circadian Rhythms
Infradian Rhythms
( T < 24 h)
( T ≈ 24 h)
( T > 24 h)
Nerve cell (ν ≈ 1000 Hz)
Sleep-wake; Hunger
dt
TF ni
n
d
i
[
] i + K
i
i
[7.27]
d Y
[ ]
Y
[ ]
= k [
]
tl mRNA − khE
dt
T K
[ ]
M + Y
In [7.27], k and k are the kinetic constants of RNA transcription and translation, respectively. The tr
tl
kinetic constant k is relative to the degradation processes of RNA. Transcription factors, TF , can
d
i
act as either activators ( n
i > 0) or inhibitors ( ni < 0), increasing or reducing the transcription rate of
a gene. The second term of the differential equation relative to Y represents its rate of degradation.
The term E represents a protease that degrades Y; its total concentration is E . Its turnover rate is k , T
h
and its Michaelis constant is K . Note that because binding of TF to DNA is fast and often takes
M
i
seconds to reach the equilibrium, whereas mRNA or protein production take minutes to hours, we
can assume the concentration of bound TF are those of equilibrium. In Figure 7.18, a scheme of the i
protein synthesis mechanism described by equation [7.27] is drawn.
TRY EXERCISE 7.5
The Y protein concentration will reach a steady state value without any oscillations, corresponding
to a homeostatic condition.
The presence of some form of feedback in the kinetics of protein synthesis can give rise to
oscillations. For example, protein Y may inhibit the expression of its gene (see Figure 7.19a). An example is PER protein. It rules certain cellular and high-level biological rhythms having periods
of about 24 hours, the so-called circadian rhythms (from the Latin circa dies, meaning “approxi-
mately a day”), by inhibiting the transcription factors of its own PER gene (Novák and Tyson 2008).
Y
E
S
Translation
Signal
k
TF
mRNA
d
RNAp
Transcription
Gene
Promoter site
FIGURE 7.18 Scheme of the synthesis of protein Y, where the protagonists are transcription factors ( TF ), i
RNA polymerase (RNAp), messenger RNA (mRNA), and protease E.
The Emergence of Temporal Order within a Living Being
183
Y
E
S
Translation
Signal
1
k
0.8
TF
mRNA
d
2
RNAp
Transcription
mRNA 0.4
Gene
0.0 0
1
2
3
4
Promoter site
(a)
(b)
Protein Y
FIGURE 7.19 Synthesis of protein Y with a negative feedback effect on its transcription factor ( TF): scheme of the mechanism in (a) and representative solution7 of the equations [7.28] in (b).
Knowing that PER protein (symbol Y) binds its transcription factor according to the following
chemical equation nY + TF = Y ( TF) and that protease E degrades PER protein, the differential n
equations describing the dynamics of the system are:
d [mRNA]
K n
= k
[
]
trCTF
− k mRNA
dt
Kn + Y n
d
[ ]
[7.28]
d Y
[ ]
[ Y ]
= k [mRNA]− khET
dt
tl
KM +
[ Y ]
C is the total concentration of TF and ( K n/ K n [ Y ] n
+
) represents the fraction of TF not bound to Y.
TF
K n = KD, where K is the dissociation constant for the binding process of Y to TF. The other terms D
have the same meaning seen in equation [7.27].
The nullclines of the non-linear differential equations [7.28] are plotted in Figure 7.19b. The
nullcline labeled as 1 is the locus of points where the rate of mRNA synthesis is exactly balanced by
the rate of mRNA degradation. On the other hand, the nullcline labeled as 2 is the locus of points
where the rate of protein synthesis is balanced by the rate of its degradation. The intersection point
of the two nullclines represents the steady state.
The Jacobian of system [7.28] is
nk
n
n
[ ] −1
trCTF K
Y
− k
ss
d
−
(
2
K n + Y n
[ ] )
J
ss
=
[7.29]
k
hET K
k
M
tl
−
2
( K [ ] )
M + Y ss
Its trace is always negative; its determinant is always positive. When the discriminant, that is
∆ = ( tr( J ))2 − 4 det( J ) = ( k
2 2
n
n−1
n
n 2
d − khET K M (
/ KM + [ Y ] ss) ) − 4 nktlktrCTF K [ Y ss
] /( K + Y
[ ss
] ) , is nega-
tive, the steady state is a stable spiral. Although the system [7.28] may exhibit damped oscillations
on the way to the steady state, sustained oscillations in this simple gene regulatory circuit are
impossible, and Y reaches a homeostatic steady state.
7 The representative solution for the system of differential equations [7.28] plotted in Figure 7.19b has been obtained with the following parameter values: k
tr = kd = 0.1 min−1, CTF = 1, K = 1, n = 2, KM = 1, ktl = 1 min−1, kh = 1, ET = 1
(Novák and Tyson 2008).
184
Untangling Complex Systems
kdy Y
E
1
S
Translation
0.8
Signal
TF
mRNA
RNAp
mRNA 0.4
k
2
Transcription
d
Gene
0.0 0
1
2
3
4
Protein Y
(a)
Promoter site
(b)
FIGURE 7.20 Synthesis of protein Y with a negative feedback effect on its transcription factor ( TF) and a negative feedback effect on its degradation process by protease E: scheme of the mechanism in (a) and representative solution8 of the equations [7.31] in (b).
Undamped oscillations emerge when the negative feedback effect of Y on its gene expression is
accompanied by a positive feedback effect, such as the binding of Y to an allosteric site of protease
E inhibiting the activity of E (see Figure 7.20a):
2 Y + E →
2
←
([ 2 ]/[ ][ ] )
2
Y E with KA = Y E
E Y
. [7.30]
The differential equations describing the dynamics of the system are:
d [mRNA]
K n
= k
[
]
trCTF
− k mRNA
dt
Kn + Y n
d
[ ]
[7.31]
d Y
[ ]
[ Y ]
= k [mRNA]− kdY [ Y ]− khET
dt
tl
K
2
M +
[ Y ]+ KMKA[ Y ]
In these equations, k is the rate constant for an alternative pathway of Y degradation. The nullclines dY
of the non-linear differential equations [7.31] are plotted in Figure 7.20b. The nullcline labeled as 1 is the locus of points where the rate of mRNA synthesis is exactly balanced by the rate of mRNA
degradation. The nullcline labeled as 2 is the locus of points where the rate of protein synthesis is
balanced by the rate of its degradation. The term of positive feedback gives rise to a kink in the
nullcline. The intersection point of the two nullclines represents the steady state.
The Jacobian of the system [7.31] is
nk
n
n
[ ] −1
trCTF K
Y
− k
ss
d
−
(
2
K n + Y n
[ ] ) ss
J =
[7.32]
k
1
(
[ ]2 )
hET K M
− KA Y
k
ss
tl
− k
dY −
2 2
KM
Y
K K Y
( +[ ] +
[ ]
ss
M
A
ss )
8 The representative solution for the system of differential equations [7.31] plotted in Figure 7.20b has been obtained with the following parameter values: ktr = kd = kdY = 0.05 min−1, CTF = 1, K = 1, n = 4, KM = 0.1, ktl = 1 min−1, kh = 1, ET = 1, K K
M
A = 2 (Novák and Tyson, 2008).
The Emergence of Temporal Order within a Living Being
185
(mRNA)n
900
DNA
e
(mRNA)n
(mRNA)
600
c
danc
(mRNA)c
Nucleus
Abun 300
Yn
Yc
( Y) c
( Y) n
0
Cytoplasm
30
60
90
Time
FIGURE 7.21 Mechanism of Y protein synthesis taking into account transport of macromolecules between
the nucleus and the cytoplasm (a). Plot of the sustained oscillations for mRNA and Y in cytoplasm and
nucleus (b).9
Jacobian [7.32] differs from that [7.29] in the Y term. When K is small, the positive feedback effect y
A
is negligible, and the system does not show sustained oscillations. When K is sufficiently large,
A
and the negative feedback loop is sufficiently nonlinear (i.e., the n coefficient is sufficiently large),
tr ( J ) becomes null and det ( J ) > 0. Therefore, the system exhibits a limit cycle, and the net diagram flux for the system becomes qualitatively equivalent to that depicted in Figure 7.9 for glycolysis. The mechanism of negative feedback on gene expression combined with inhibition of protein
degradation has been suggested as a possible source of circadian rhythms in the reaction network
that governs expression of the PER gene in fruit flies (Novák and Tyson 2008). Circadian rhythms
in eukaryotic cells10 have also been modeled by invoking a mechanism involving three or more
components and only a negative feedback loop on gene expression (Novák and Tyson 2008). The
components may be mRNA that is synthesized in the nucleus (mRNA ) and transported into the
n
cytoplasm (mRNA ) where it gets translated into protein which is translocated into the nucleus
c
Yc,
( Y ) and represses the activity of its gene (see Figure 7.21a). The four-variable negative-feedback n
loop oscillates as naturally as a pendulum (see Figure 7.21b).
7.5 BIOLOGICAL RHYTHMS
From the biochemical examples investigated in this chapter, it is evident that living organisms have
a natural tendency to exhibit a mixture of homeostatic and oscillatory behaviors: the more complex
the biological system, the greater the possibilities. In fact, as far as the oscillatory behavior is con-
cerned, outputs of various frequencies, phases, and amplitudes are possible. Multicellular organ-
isms have cells that specialize in different functions depending on the organ they belong. Each type
9 The results plotted in Figure 7.21b have been achieved assuming that mRNA is synthesized in the nucleus ( xn) and transported into the cytoplasm ( xc), where it gets translated into protein ( yc), which is translocated into the nucleus ( yn). If we impose that eps = Vnuc/Vcyt; half-life of mRNA in nucleus = 0.693/kdxn; half-life of protein in cytoplasm = 0.693/kdyc, the differential equations are:
dxn/dt = kdxn*(sig/(1 + yn^p)—xn)—kexport*xn
dxc/dt = eps*kexport*xn—kdxc*xc
dyc/dt = kdyc*(xc − yc)—eps*kimport*yc
dyn/dt = kimport*yc—kdyn*yn/(Km + yn)
The constants appearing in the four differential equations have the following values: sig = 1000, p = 2, kdxn = 10,
kexport = 0.2, kdxc = 0.2, eps = 1, kdyn = 8, kdyc = 0.1, Km = 0.1, kimport = 0.1 (Novák and Tyson 2008).
Initial conditions: xn = 1.0, xc = 30.0, yc = 200.0, yn = 120.0.
10 A eukaryote is an organism whose cells contain a nucleus and other organelles enclosed within membranes.
186
Untangling Complex Systems
of cell triggers specific “clock genes.” In fact, each living being appears as “a house with clocks in
every room and every corner; but, yet in one way or another, they work in an organized way,” as
rightly alleged by Derk-Jan Dijk, director of the Surrey Sleep Research Centre in Guildford (UK).
All the periodic processes occurring at either the cellular, organ, or physiological system levels span
more than ten orders of magnitude of timescale, from hundredths of seconds up to tens of years11
(Goldbeter, 2017). They can be sorted out into three time-domains or rhythms: the (1) circadian,
(2) ultradian, and (3) infradian rhythms. The circadian processes are ruled by the periodic revolu-
tion of the earth around its axis, requiring 24 hours, and determining a significant daily variation
in the intensity and spectral composition of the electromagnetic radiation coming from the sun. The
infradian processes depend on the slower revolution of the moon around our planet (requiring about
one month), or the even slower revolution of the earth around the sun (requiring about one year).
Finally, there are organs and physiological systems that have ultradian rhythms, meaning they work
cyclically, with periods shorter than 24 hours. A list of ultradian, circadian, and infradian processes
found in human beings, is reported in Table 7.1.
Among the ultradian periodic processes, individual neurons detain the record of the fastest cycles
possible. In fact, many nerve cells generate impulses of transmembrane depolarization, followed by
hyperpolarization, in around 1 millisecond or so (for more details, see Chapter 9). Neurons use such impulses as signals that must travel very fast for effective communication. In the human hearth, the
electrical impulses last much longer than in nerve cells. In fact, the heart rate is about 60 beats per
minute, so there is a whole second for the impulse to occur and for the heart to recover before next
beat. Respiratory rhythm requires the cooperation of many nerve cells, peripheral and central, and
it has a frequency of about tenths of Hz. Connected with respiration, there is also the nasal cycle
(Atanasov 2014). Our nose holds two parallel breathing passages that are divided by the septum.
Our two nostrils shift their workload back and forth in a delicate dance called the nasal cycle. At
any moment, most of the air we inhale travels through just one nostril, while a much smaller amount
seeps in through the other. This difference is important because odor-causing chemicals vary in the
amount of time they take to dissolve through the mucus that lines our nasal cavity. The two nasal
cavities are like two chromatographic columns separating and detecting many odor-molecules.
Chemicals that dissolve quickly have the strongest effect in a fast-moving airstream that spreads
them out over as many odor receptors as possible. But compounds that dissolve slowly are more
accessible to smell in a slow-moving airstream.Due to the circadian oscillations of environmental
TABLE 7.1
Periodic Processes in Human Beings at the Organ and
Physiological System Levels Sorted out According to Their
Periods ( T) or Frequencies (ν )
Ultradian Rhythms
Circadian Rhythms
Infradian Rhythms
( T < 24 h)
( T ≈ 24 h)
( T > 24 h)
Nerve cell (ν ≈ 1000 Hz)
Sleep-wake; Hunger
