Untangling complex syste.., p.39

Untangling Complex Systems, page 39

 

Untangling Complex Systems
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Human ovulation

  (circalunar)

  Heart beating (ν ≈ 1 Hz)

  Bowel movements

  Respiration (ν ≈ 0.3 Hz)

  Body temperature

  Seasonal mutations

  (circannual)

  Nasal cycle ( T ≈ 2.8 h)

  Blood pressure

  11 Magicicada species spend most of their 13-year or 17-year lives underground feeding on the roots of trees in the United States. After 13 or 17 years, mature cicada nymphs emerge in the springtime, synchronously and in tremendous numbers.

  The adults are active for about four to six weeks, and they reproduce. Then, the lifecycle is complete, the eggs have been laid, and the adult cicadas disappear for another 13 or 17 years.

  The Emergence of Temporal Order within a Living Being

  187

  light and temperature, many signaling and cellular metabolic processes, having intrinsic periods

  of about 24 hours, tend to entrain with the day-night cycle. There is a central pacemaker that gives

  human body a sense of the time of day: the suprachiasmatic nucleus, a group of 10,000 or so neu-

  rons in the hypothalamus, located at the very bottom of the brain, deep within the skull. It is the

  blue light absorbed by melanopsin (a protein present in the ganglion cells of our retina) that pro-

  vides the primary cue for the entrainment of our circadian rhythms.12 In the presence of daily light that is particularly rich in blue, excitatory signals are sent to the suprachiasmatic nucleus, which

  prevents the pineal gland from producing melatonin, the hormone that induces to sleep (Eisenstein

  2013). Light-dark entrainment of the suprachiasmatic nucleus synchronizes peripheral oscillators

  throughout the entire body and controls the pace of variation of other physiological responses,

  such as body temperature, blood pressure, blood levels of hormones, appetite, and gut motility that

  induces bowel movements. The peripheral oscillators may be phase-shifted by physical activity or

  by altering meal times, but the light seems to be the most crucial determinant of rhythms driven by

  the suprachiasmatic nucleus. Of course, for humans and all the other creatures living outside the

  equatorial zones, the seasonal change in the daily pattern of light/dark exposure has repercussion

  on the peripheral oscillators. Hence, circannual rhythms are present in sleep, mood, reproduction,

  diseases, and deaths for humans (Swaab et al. 1996). In other living species, circannual rhythms

  may be more relevant, because they involve relevant processes such as migration, hibernation, or

  flowering, to make just a few examples (Gwinner 1986).

  Finally, despite the common belief that our mental health and other behaviors, such as the men-

  strual cycle, are modulated by the phase of the moon, is persistent, there is no convincing evidence

  that human biology is in any way regulated by the lunar cycle (Foster and Roenneberg 2008).

  7.6 AMPLIFICATION AND ADAPTATION IN REGULATORY

  AND SENSORY SYSTEMS

  Two relevant additional properties of the biological sensing and regulatory systems are amplifica-

  tion and adaptation. Amplification is the ability to generate amplified responses to low levels of

  stimuli. Adaptation is the ability to adapt to constant backgrounds of stimuli (Koshland et al. 1982).

  Specific signals, such as light of low intensity, a faint sound, the aroma due to a few odor molecules,

  do not have the energy to generate a behavioral response and must be amplified within the organ-

  ism. When we talk about amplification of a signal, we may mean two distinct events: (1) magnitude

  amplification and (2) sensitivity amplification.

  7.6.1 magniTude amPlificaTion

  Magnitude amplification is the production of some output molecules far higher than the elementary

  particles of the stimulus; it trusts in chain reactions. For example, in vision, the absorption of one

  photon can be amplified almost 5,000-fold and becomes perceptible. The first step in human vision

  is the absorption of one photon by the chromophore of the photoreceptor protein rhodopsin, which

  is 11- cis retinal. The excited state of 11- cis retinal isomerizes to all- trans retinal (see Figure 7.22) in 200 fs and with a quantum yield of Φ = 0.67. The isomerization is so fast that is vibrationally

  coherent (Wang et al. 1994).

  The isomerization of retinal induces conformational rearrangement of the protein embedding

  the chromophore. The rhodopsin assumes a signaling state that has a lifetime of about 50 ms. One

  “activated” rhodopsin has the power of activating about 800 G-proteins. Like “activated” rhodop-

  sin, an activated G-protein has a brief lifetime where it can interact with phosphodiesterase (PDE)

  12 Blind people, who do not have cones and rods to orient themselves spatially, are still able to orient temporally if they are provided with melanopsins in the ganglion cells.

  188

  Untangling Complex Systems

  gy

  S 1

  200 fs

  onic enerctrEle

  hv

  CH

  CH

  O

  3

  3

  CH3

  CH3

  H

  CH

  All -trans retinal

  S

  3

  0

  CH

  CH

  3

  CH3

  3

  Reaction coordinate

  11

  1

  2

  12

  CH

  H

  3

  3C

  11-cis retinal

  O

  H

  FIGURE 7.22 Scheme of the first step of human vision: the ultrafast photo-isomerization of 11- cis retinal to all- trans retinal.

  and activates it. The latter occurs without any amplification. One activated PDE can catalyze

  the breakdown of more than one molecule of 3′,5′-cyclic guanosine monophosphate (cGMP) to

  5′-guanosine monophosphate (5′-GMP). Usually, six cGMP molecules are converted to 5′-GMP

  by each activated PDE. Regarding the number of molecules, the absorption of one photon has been

  amplified about 800 × 6 = 4800-fold. Activation of one rhodopsin molecule takes ≈4800 cGMP

  molecules out of circulation. They are not anymore available to maintain the cGMP-gated Na+

  channels open, and about 200 Na+ channels close, which is ≈2% of the total number of ion chan-

  nels in a photoreceptor rod cell. Closing 2% of the channels reduces the ionic current, flowing

  inside the cell, by 2%. The corresponding voltage change across the membrane is ≈1 mV hyper-

  polarization (it means the interior becomes more negative than the exterior). The absorption of

  just one photon determines an electrical effect felt throughout the entire rod. The photo-induced

  hyperpolarization of the photosensitive cell reduces the rate of the release of the neurotransmitter

  glutamate (Oyster 1999).

  7.6.2 sensiTiviTy amPlificaTion

  The sensitivity amplification refers to the percentage change in response compared to the percentage

  change in the stimulus. Three types of mechanisms for sensitivity amplification have been uncovered.

  One involves a stimulus-protein interaction that is allosteric with a large Hill coefficient. Such interac-

  tions are ultrasensitive, with positive cooperativity. A second mechanism for obtaining high sensitivity

  amplification is to have the same effector at several steps in a pathway. In principle, if an effector S

  participates in n elementary steps of a multistep pathway, we might expect that the rate of the overall

  chemical transformation is proportional to [ S] n. A third mechanism, shown in Figure 7.23, involves the interconversion of a key enzyme in active ( I ) and inactive ( I ) forms by the cyclic coupling of covalent a

  i

  modification and de-modification reactions. An example of modification and de-modification are the

  phosphorylation and dephosphorylation reactions, already mentioned in this chapter.

  Assuming that the concentration of ATP is maintained at a constant level that is several orders

  of magnitude higher than the substrate enzymes, the reactions for the interconversion of I to I and i

  a

  vice versa can be written as follows:

  The Emergence of Temporal Order within a Living Being

  189

  K

  E

  Es

  i + s

  Ea

  ATP

  ADP

  ka

  Ii

  Ia

  ki

  Pi

  H2O

  KRe

  Ri + e

  Ra

  FIGURE 7.23 A cyclic phosphorylation and dephosphorylation of enzyme I catalyzed by two distinct

  enzymes, E (a protein kinase) and R (a protein phosphatase), respectively; s represents a stimulus and e is an effector for R.

  Ka

  E

   →

  

  ka

  (

  )

  a + Ii

  EaIi

  Ea + Ia

  ← 

  

   →

  

  [7.33]

  Ki

  R

   →

  

  ki

  (

  )

  a + I a

  RaIa

  Ra + I

  ← 

  

   →

  

  i

  At the stationary state, ka[( EaIi)] = ki[( RaIa)]. We make the following assumptions. First, the equilibria in the formation of the enzyme-effector and enzyme-enzyme complexes are reached very fast.

  Second, the concentrations of the enzyme-enzyme complexes are negligible compared to the con-

  centrations of the active and inactive enzymes. Third, the concentrations of s and e are at constant

  levels for any signaling state. It derives that, at the stationary state,

  k

  [ ][ ]

  [ ][ ]

  aKa Ea

  Ii = kiKi Ra Ia [7.34]

  From the mass balances for E and R and the assumptions listed above, we obtain (for the meaning

  of the symbols, see also Figure 7.23)

   K [ ][ ] 

  

  [ ][ ] 

  Es s

  E

  KRe e R

  [ E

  tot

  ]

  tot

  [ ]

  a = 

  

   and R = 

   [7.35]

  K

  

  a

  

  

  

  [ ]

  

  [ ]

  Es s + 1 

  KRe e +1 

  From the equations [7.34], [7.35], and the assumption that [ I]

  ]

  ], a steady-state expression

  tot ≈ [ Ia + [ Ii

  for the fraction of the modified interconvertible enzyme is:

  [ I ]

  [ ]

  a

  kaKa Ea

  [ I] = k [ ]

  [ ]

  i Ki Ra + kaKa E

  tot

  a

  [7.36]

  =

  1

  k K

  KRe e R

  [ ]

  i i

  t

  1+

  [ ][ ] oot

  KEs s +

  (

  1

  1 )(

  )

  kaKa

  KRe[ e]+

  KEs[ s][ E] tot

  The high sensitivity amplification of an interconvertible enzyme derives from the fact that any one

  of the ten terms in equation [7.36] can be altered by allosteric interaction with one or more allosteric

  effectors. The curves in Figure 7.24 show the enormous indirect effect of the signal [ s] on the fractional activation of the interconvertible enzyme. Curves A and B have been obtained maintaining fixed K

  Es

  and with two-fold changes of the other parameters, favoring the activation of I (the numerical values

  190

  Untangling Complex Systems

  1.0

  1.0

  C

  0.8

  0.8

  B

  A

  0.6

  0.6

  [ Ia]

  [ Ea]

  [ I] tot

  [ E] tot

  0.4

  0.4

  0.2

  0.2

  0.0

  0.0

  –3

  –2

  –1

  0

  1

  2

  log[ s]

  FIGURE 7.24 Ratios of activated interconvertible enzyme I and E as a function of [ s] (plotted in logarithmic scale). Curve A and B refer to I and they have been obtained with K

  Es = 1 (in both A and B); KRe = 1 (in A) and

  ½ (in B); k K

  K

  a a = 1 (in A) and 2 (in B); ki i = 1 (in A) and ½ (in B), [ E] tot = 1 (in A) and 2 (in B); [ R] tot = 1 (in A) and ½ (in B), [ e] = 1 (in A) and ½ (in B). The dashed grey curve C refers to enzyme E.

  of the parameters are listed in the caption of Figure 7.24) (Stadtman and Chock 1977). Such changes promote a significant upward shift (from 0.66 to 0.98) of the ratio [ Ia] [I] tot, and a downward shift in the concentration of the stimulus s required to produce 50% of the activation of the interconvertible enzyme (log[s] drops from 0.0016 in A to −1.67 in B). It is noteworthy that even in the more

  unfavorable conditions of curve A, the concentrations of s required to activate indirectly the intercon-

  vertible enzyme, when the ratio [ Ia] [ I ] tot is less than 0.5, are less than those required for comparable activations of the converter enzyme E (compare curve A with the dashed grey curve C).

  The results shown in Figure 7.24 demonstrate the high sensitivity amplification offered by a

  monocyclic cascade system (whose mechanism is depicted in Figure 7.23) consisting of two oppo-

  sitely directed “converter” enzymes that catalyze the interconversion of a single interconvertible

  enzyme. It has been demonstrated that bicyclic and multicyclic cascade systems are endowed with

  considerably greater amplification potential (Chock and Stadtman 1977). The great amplification

  potential stems from the fact the response of the last interconvertible enzyme in a cascade to a pri-

  mary stimulus, caused by the allosteric interaction of an effector to the first converter enzyme in the

  cascade, is a multiplicative function of various parameters in the cascade.

  7.6.3 adaPTaTion

  A highly sensitive amplification system would cause problems because living beings are almost

  constantly bombarded by stimuli, which could saturate the sensory system. The organism prevents

  this by the adaptation that tends to inactivate the sensing apparatus. There are two possible adap-

  tive responses to changes in stimuli. They are (I) absolute and (II) partial adaptation. In absolute

  adaptation after a transient response, the system adapts absolutely. This behavior happens when a

  stimulus s (see Figure 7.25a) activates the rate of formation ( v ) of the response regulator X rapidly f

  and the rate of X decomposition ( v ) slowly (see Figure 7.25b). A change in s produces a transient d

  signal that adapts absolutely as shown in Figure 7.25c. When s is unchanging, even though present at a high level, it does not trigger any response. Absolute adaptation occurs in sensory systems that

  must detect small changes such as in the visual system and bacterial chemotaxis (Koshland 1980).

  The response regulator could be a small molecule or a combination of small molecules, a protein, a

  combination of proteins or a protein-ligand complex.

  The Emergence of Temporal Order within a Living Being

  191

  s

  s

  Stimulu

  Stimulu

  0

  0

  (a)

  Time

  (d)

  Time

  s

  V

  s

  te

  f

  V

  V

  d

  te

  f

  Ra

  Ra

  Vd

  0

  0

  (b)

  Time

  (e)

  Time

  X

  X

  tor

  tor

  la

  la

  gu

  gu

  onse re

  onse re

  Resp

  Resp

  0

  0

  (c)

  Time

  (f)

  Time

  FIGURE 7.25 Behavior of an absolute adaptive system (left column: graphs a, b, and c) and a partial adaptive

  system (right column: graphs d, e, and f).

  In some systems, absolute adaptation may not be needed. For example, hormones provide stimuli

  from one cell to another. After a short period of stimulation, the hormone level reduces because it

  is no longer produced in the primary organ and is washed away from the bloodstream. In such case,

  the partial adaptation can provide a large initial signal that is partially damped to prevent excessive

  stimulation. Partial adaptation occurs when X inhibits the rate of its decomposition through a slow

  feedback action (see Figure 7.25d–f).

  From Figure 7.25 it is evident that the adaptation action eliminates the ability to detect absolute levels of stimuli, but only in order to increase sensitivity to percentage changes in the background

  over a wide range of background intensities.

  7.7 KEY QUESTIONS

  • Why are proteins so important for cells?

  • Describe the possible mechanisms of enzyme-substrate interactions.

  • Describe the features of allosteric proteins.

  • What is the power of the Maximum Entropy Method?

 

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