As we must account for every idle word, so we must for every idle silence.
BENJAMIN FRANKLIN
Saturday 1 April 2017
A Brief history of theistic monism
By Peter Clarke
Tom Chivers' lively description of his interview with neuroscience professor Patrick Haggard highlights the fundamental question of whether brain research undermines our belief in free will and responsibility. Our brains determine our thinking and behaviour, and our neurons obey the laws of physics and chemistry, so how are we different from neural machines? As Tom points out in a second article, a lot depends on how you define free will.
On this issue, philosophers are divided into two camps: “libertarians“and “compatibilists”. For libertarians, free will is almost by definition incompatible with brain determinism. They argue from our experience of making choices that somewhere in the brain there must be indeterminate events. Most modern libertarians, including Robert Kane, invoke Heisenbergian uncertainty as the source of brain indeterminism, despite scepticism among scientists. In contrast, compatibilists argue for a different definition of free will. They make the distinction between external and internal constraints. The difference is illustrated by the following two excuses: “It’s not my fault I broke the window, my brother pushed me”, and “It’s not my fault I broke the window, my brain caused me to do it”.
Few people would accept the second excuse, which seems strange at best. If my brain did not cause me to break the window, I was certainly not responsible, so how can brain causation be an excuse? Of course, simple arguments like this are only a start in a complicated debate, but compatibilists are currently in the majority in claiming that the “varieties of free will worth wanting” (to quote Dennett) do not require indeterminate events in the brain. The debate is by no means over.
Our attitude to the free will question is intimately linked to the dualism-monism debate. Dualists believe that there are two separate entities, soul (or mind) and brain, and most maintain that they somehow interact, following Descartes. Monists deny a separate soul, saying that everything is matter. This links in with the question of free will, because if you believe in a separate nonphysical soul/mind that somehow influences the brain, you must assume that conventional physical and chemical forces do not completely determine brain function.
This debate is sometimes caricatured as a rearguard defense by religious or spiritually minded traditionalists against the attacks of modern science and atheistic philosophy, but there is not such a neat dividing line. The first philosophers to invoke physical indeterminism as necessary for free will were the materialists Epicurus and Lucretius, who denied life after death and supernatural intervention in the world. Judaism was monistic throughout the Old Testament era, and early Christianity appears likewise.
It is true that neo-Platonist dualism was incorporated into the philosophies of many leading Christian thinkers including Augustine, Luther and Calvin, but over the last couple of centuries these were opposed by equally Christian monists such as Joseph Priestley, the nonconformist minister famed for isolating oxygen, who argued that dualism was a contamination of biblical Christianity by Platonic philosophy. Over the last 60 years monistic philosophy of mind has gained ground among Christians because of increasing evidence that the biblical conception of man is monist, not dualist. For example, the Hebrew word Nefesh, traditionally translated as “soul”, does not refer to a separate, Platonic soul and is nowadays usually translated as “being”.
But how can a monistic conception of the mind-brain be reconciled with humanist notions of freedom and responsibility and with a theistic belief in life after death? Several solutions have been proposed, but the dual-aspect monism of protestant neurobiologist-philosopher Donald MacKay is justifiably one of the most influential, as is reflected in the writings of many subsequent theistic monists such as Malcolm Jeeves, Nancey Murphy and Warren Brown. According to MacKay, my subjective conscious experience and an objective neurobiological account of my brain are two complementary views of a single entity. There is no separate Platonic soul that floats out of the brain at death. MacKay couples this dual-aspect monism to a compatibilist approach to free will. Thus, protestant MacKay and atheist Daniel Dennett share common ground as far as the mind-brain relation is concerned.
But how could the inevitable destruction of the brain at death square with any idea of an afterlife? The New Testament does not teach an eternal soul, but a resurrected “spiritual body”. This is not defined precisely, but the idea seems to be that the information structure of the real “me” will somehow be restored into a very different embodiment, just as a poem can retain its essence when copied or a computer programme can be reinstalled on a new computer.
There is still plenty of debate even among theists. Monism and compatibilism dominate among protestant neurobiologists and philosophers, whereas Roman Catholic and Orthodox scholars (e.g. Richard Swinburne) tend to favour dualism. If a line can be drawn through the diversity of opinions, it may be the ancient divide between Aristotelians and Platonists. The monistic view of soul/self as information structure is close to that of Aristotle, whereas the most widespread forms of dualism are neo-Platonist. But there is no neat division between dualistic, libertarian theists and monistic, compatibilist atheists.
Peter G H Clarke is an associate professor of neuroscience at the Département de Biologie cellulaire et de Morphologie at the Université de Lausanne.
Tom Chivers' lively description of his interview with neuroscience professor Patrick Haggard highlights the fundamental question of whether brain research undermines our belief in free will and responsibility. Our brains determine our thinking and behaviour, and our neurons obey the laws of physics and chemistry, so how are we different from neural machines? As Tom points out in a second article, a lot depends on how you define free will.
On this issue, philosophers are divided into two camps: “libertarians“and “compatibilists”. For libertarians, free will is almost by definition incompatible with brain determinism. They argue from our experience of making choices that somewhere in the brain there must be indeterminate events. Most modern libertarians, including Robert Kane, invoke Heisenbergian uncertainty as the source of brain indeterminism, despite scepticism among scientists. In contrast, compatibilists argue for a different definition of free will. They make the distinction between external and internal constraints. The difference is illustrated by the following two excuses: “It’s not my fault I broke the window, my brother pushed me”, and “It’s not my fault I broke the window, my brain caused me to do it”.
Few people would accept the second excuse, which seems strange at best. If my brain did not cause me to break the window, I was certainly not responsible, so how can brain causation be an excuse? Of course, simple arguments like this are only a start in a complicated debate, but compatibilists are currently in the majority in claiming that the “varieties of free will worth wanting” (to quote Dennett) do not require indeterminate events in the brain. The debate is by no means over.
Our attitude to the free will question is intimately linked to the dualism-monism debate. Dualists believe that there are two separate entities, soul (or mind) and brain, and most maintain that they somehow interact, following Descartes. Monists deny a separate soul, saying that everything is matter. This links in with the question of free will, because if you believe in a separate nonphysical soul/mind that somehow influences the brain, you must assume that conventional physical and chemical forces do not completely determine brain function.
This debate is sometimes caricatured as a rearguard defense by religious or spiritually minded traditionalists against the attacks of modern science and atheistic philosophy, but there is not such a neat dividing line. The first philosophers to invoke physical indeterminism as necessary for free will were the materialists Epicurus and Lucretius, who denied life after death and supernatural intervention in the world. Judaism was monistic throughout the Old Testament era, and early Christianity appears likewise.
It is true that neo-Platonist dualism was incorporated into the philosophies of many leading Christian thinkers including Augustine, Luther and Calvin, but over the last couple of centuries these were opposed by equally Christian monists such as Joseph Priestley, the nonconformist minister famed for isolating oxygen, who argued that dualism was a contamination of biblical Christianity by Platonic philosophy. Over the last 60 years monistic philosophy of mind has gained ground among Christians because of increasing evidence that the biblical conception of man is monist, not dualist. For example, the Hebrew word Nefesh, traditionally translated as “soul”, does not refer to a separate, Platonic soul and is nowadays usually translated as “being”.
But how can a monistic conception of the mind-brain be reconciled with humanist notions of freedom and responsibility and with a theistic belief in life after death? Several solutions have been proposed, but the dual-aspect monism of protestant neurobiologist-philosopher Donald MacKay is justifiably one of the most influential, as is reflected in the writings of many subsequent theistic monists such as Malcolm Jeeves, Nancey Murphy and Warren Brown. According to MacKay, my subjective conscious experience and an objective neurobiological account of my brain are two complementary views of a single entity. There is no separate Platonic soul that floats out of the brain at death. MacKay couples this dual-aspect monism to a compatibilist approach to free will. Thus, protestant MacKay and atheist Daniel Dennett share common ground as far as the mind-brain relation is concerned.
But how could the inevitable destruction of the brain at death square with any idea of an afterlife? The New Testament does not teach an eternal soul, but a resurrected “spiritual body”. This is not defined precisely, but the idea seems to be that the information structure of the real “me” will somehow be restored into a very different embodiment, just as a poem can retain its essence when copied or a computer programme can be reinstalled on a new computer.
There is still plenty of debate even among theists. Monism and compatibilism dominate among protestant neurobiologists and philosophers, whereas Roman Catholic and Orthodox scholars (e.g. Richard Swinburne) tend to favour dualism. If a line can be drawn through the diversity of opinions, it may be the ancient divide between Aristotelians and Platonists. The monistic view of soul/self as information structure is close to that of Aristotle, whereas the most widespread forms of dualism are neo-Platonist. But there is no neat division between dualistic, libertarian theists and monistic, compatibilist atheists.
Peter G H Clarke is an associate professor of neuroscience at the Département de Biologie cellulaire et de Morphologie at the Université de Lausanne.
Yet more predarwinian tech takes the witness stand for design.
The Machine that Fuels ATP Synthase
Evolution News & Views
Why do you need oxygen to breathe? Oxygen actually plays a secondary role in the amazing process of respiration. What you really need are protons (hydrogen atoms). For every proton captured from your food, there's an electron needing proper disposal. Oxygen is just an electron receptor at the end of a long chain of processes, driven by molecular machines, that captures protons for fuel. The machines translocate the protons across a membrane, creating a pool of protons that enter the ATP synthase rotor and make it turn (see our animation, "ATP Synthase: The Power Plant of the Cell"). In a sense, the whole job of respiration is to set up a proton gradient in the mitochondrial membrane to serve as fuel for ATP synthase.
A bit of background: The protons turn the rotor in ATP synthase like a carousel or waterwheel. This, in turn, rotates a camshaft to mechanically force ADP and phosphate into ATP in the catalytic center of the motor. The energy from your food (or from sunlight in plants) thus transforms chemical energy to electrical energy to mechanical energy and, finally, to another form of chemical energy. Most of the other processes in the cell use ATP for their energy.
We've heard of the mitochondrion as the "powerhouse" of the eukaryotic cell. That's because it creates the ATP to power everything else. Along its folded inner membranes, called cristae, molecular machines pump protons to one side of the inner membrane where they can be channeled into the "turbines" of ATP synthase. In plants, chloroplasts serve this function, capturing energy from sunlight. Bacteria have the same basic machinery in their inner cell membranes. Since we are eukaryotes, let's look at what's going on in our mitochondria, where thousands of molecular machines are working 24/7 to set up the proton gradient, a literal "voltage" to run your motors.
The first of those machines has a cumbersome name, NADH:ubiquinone oxidoreductase (sometimes NADH dehydrogenase). We can use its nickname "Complex I" for convenience. It's one of five "complexes" in the electron transport chain of respiration (also called oxidative phosphorylation), ending with ATP synthase as Complex V. The last of the molecular machines to be elucidated, Complex I has just been described in unprecedented detail by scientists from the molecular biology laboratory at Cambridge.
For many years, scientists knew the general function of Complex I. Its job is to generate four protons for the proton gradient from each input. It does this by taking electrons from NAD (nicotinamide adenine dinucleotide), a sugar phosphate first described in 1906. The reduced form is called NADH.
Now for some terminology: For historical reasons, removing electrons is called "oxidation", and donating them is called "reduction." Together, these are abbreviated "redox" reactions. But since negative electrons and positive protons are involved, it might help to think of 'reduction' as reducing the number of protons. Oxidizing a molecule leaves it with fewer electrons, resulting in a positive charge -- i.e., with extra protons. Reducing a molecule leaves it with a negative charge, or a reduced number of protons. A proton is the same as a hydrogen ion (H+).
The docking site of Complex I oxidizes NADH to NAD+, passing two captured electrons to a cofactor called ubiquinone. In the process, by passing the electrons through a series of iron-sulfur clusters (Fe-S), the machine pumps four protons through the inner mitochondrial membrane, contributing about 40 percent of the proton gradient needed by ATP synthase. You can watch a simplified animation from NDSU Virtual Cell showing how the complexes move electrons and protons around.
The mitochondrion is where the well-known "citric acid cycle" takes place. Students often hear about the chemistry of life, but not as often about the mechanics. They learn how energy from food is transferred through various molecules to make ATP as we breathe in oxygen and breathe out carbon dioxide and water vapor. That's great to know, but what is more fascinating is how these reactions require machines with moving parts. Let's see what scientists have discovered about Complex I, in terms of its structure and dynamics.
Complex I is a huge enzyme, one of the largest in the cell. In mammals, it has 14 core subunits and 31 "supernumerary" (fancy word for "extra") subunits, adding up to a whopping mass of 980 kilodaltons (kDa). (A Dalton is about the mass of a hydrogen atom; technically, 1/12 the mass of a carbon atom.) Such high mass implies over 7,000 properly-sequenced amino acids. That's one huge machine, considering the average size of an enzyme is about 300-400 amino acids. The bacterial Complex I, lacking many of the supernumerary subunits, is still gigantic, weighing in at 550 kDa.
In appearance, Complex I resembles a boot, with the ankle inside the mitochondrion and the sole anchored in the crista. NAD enters the ankle. The protons exit the sole into the inner membrane. But what actually goes on in this structure? Research published in Nature in 2010 suggested the possibility that the bacterial enzyme moves with an action resembling a piston.
The overall architecture of this large molecular machine is now clear. F-ATPase has been compared to a turbine. In a similar vein, complex I seems to resemble a steam engine, where the energy of the electron transfer is used to move a piston, which then drives, instead of wheels, a set of discontinuous helices. The full mechanistic details remain to be clarified by atomic structures of the membrane domain and the entire complex.
A subsequent paper in Nature in 2014 called the piston-like motion into question, at least for the mammalian version, but it did not rule out smaller-scale motions (called "conformational changes" in the literature).
Now, using cryo-electron microscopy, the Cambridge team has described all 45 subunits of Complex I from bovine mitochondria. In Nature, they mention having found moving parts:
We have located and modelled all 45 subunits, including the 31 supernumerary subunits, to provide the entire structure of the mammalian complex. Computational sorting of the particles identified different structural classes, related by subtle domain movements, which reveal conformationally dynamic regions and match biochemical descriptions of the 'active-to-de-active' enzyme transition that occurs during hypoxia. Our structures therefore provide a foundation for understanding complex I assembly and the effects of mutations that cause clinically relevant complex I dysfunctions, give insights into the structural and functional roles of the supernumerary subunits and reveal new information on the mechanism and regulation of catalysis.
The supernumerary subunits "are central to the structure, stability and assembly of the complex, and some also have regulatory or independent metabolic roles," they say. Some of them may serve a role in anchoring the machine to the membrane. That makes sense if the machine is vibrating from moving parts. What do the dynamic regions do? Later in the paper, they explain:
The two states of mammalian complex I described support the idea that dynamic, flexible regions at the hydrophilic-membrane domain interface are important for coupling ubiquinone reduction to proton translocation.
They go into detail about additional movements in a chain reaction, concluding:
Thus, a cascade of events originating from the ubiquinone-binding cleft may couple ubiquinone reduction and protonation to proton translocation. Although all such mechanisms for complex I are currently hypothetical, cryoEM now provides a powerful tool to study individual trapped conformations or separate mixed states computationally in order to determine how conformational changes are initiated, coordinated and propagated.
Currently, biochemists are limited to catching snapshots of the action. In the future, will they be able to watch Complex I move in real time? That's something to look forward to!
Students are likely to be much more interested in cell biology if they learn about molecular machines with moving parts. Who wants to memorize the chemical reactions in the citric acid cycle when you can watch rotors, pistons and pumps? That's what really goes on. We are privileged to live in a time when these realities are coming to light.
The authors point out two other observations of interest for intelligent design. One is that mutations in these machines cause disease and death; they cannot tolerate much change, meaning that the specificity in the amino acid sequence is vital to the function. That's why they say that the core machinery is "conserved from bacteria to humans."
The other observation is that the machines have to be assembled to work in the first place. It's like Scott Minnich's comment in Unlocking the Mystery of Life that the assembly instructions for the bacterial flagellum are even more complex than the machine itself. A machine needs a plan (encoded in DNA). It needs materials that must be delivered to the right place at the right time, in the right quantities. The parts have to be assembled in a coordinated sequence. Each step requires inspection, so that the cell doesn't waste time building something that won't work. That's true of Complex I and the entire factory of machines in the electron transport chain that make life possible. We see similar requirements in the construction of a house or manufacturing plant. It's Undeniable that we compare these processes and intuitively understand that intelligent causes must have been at work in the design of molecular machines.
Let's end with a look at one more level of organization. We mentioned cristae, the folds in mitochondrial membranes where these machines reside. A paper in the Proceedings of the National Academy of Sciences shows that the machines are arranged on the cristae in such a way as to maximize efficiency. In particular, the ATP synthase engines form V-shaped pairs, offset with respect to neighboring pairs so that their moving parts do not conflict but rather promote their respective operations. The spacing and angular displacement of the pairs, furthermore, results in the characteristic curvature of the cristae, which maximizes the proton gradient by creating local concentrations of protons aimed at the engines.
And this was found in Paramecium.
Evolution News & Views
Why do you need oxygen to breathe? Oxygen actually plays a secondary role in the amazing process of respiration. What you really need are protons (hydrogen atoms). For every proton captured from your food, there's an electron needing proper disposal. Oxygen is just an electron receptor at the end of a long chain of processes, driven by molecular machines, that captures protons for fuel. The machines translocate the protons across a membrane, creating a pool of protons that enter the ATP synthase rotor and make it turn (see our animation, "ATP Synthase: The Power Plant of the Cell"). In a sense, the whole job of respiration is to set up a proton gradient in the mitochondrial membrane to serve as fuel for ATP synthase.
A bit of background: The protons turn the rotor in ATP synthase like a carousel or waterwheel. This, in turn, rotates a camshaft to mechanically force ADP and phosphate into ATP in the catalytic center of the motor. The energy from your food (or from sunlight in plants) thus transforms chemical energy to electrical energy to mechanical energy and, finally, to another form of chemical energy. Most of the other processes in the cell use ATP for their energy.
We've heard of the mitochondrion as the "powerhouse" of the eukaryotic cell. That's because it creates the ATP to power everything else. Along its folded inner membranes, called cristae, molecular machines pump protons to one side of the inner membrane where they can be channeled into the "turbines" of ATP synthase. In plants, chloroplasts serve this function, capturing energy from sunlight. Bacteria have the same basic machinery in their inner cell membranes. Since we are eukaryotes, let's look at what's going on in our mitochondria, where thousands of molecular machines are working 24/7 to set up the proton gradient, a literal "voltage" to run your motors.
The first of those machines has a cumbersome name, NADH:ubiquinone oxidoreductase (sometimes NADH dehydrogenase). We can use its nickname "Complex I" for convenience. It's one of five "complexes" in the electron transport chain of respiration (also called oxidative phosphorylation), ending with ATP synthase as Complex V. The last of the molecular machines to be elucidated, Complex I has just been described in unprecedented detail by scientists from the molecular biology laboratory at Cambridge.
For many years, scientists knew the general function of Complex I. Its job is to generate four protons for the proton gradient from each input. It does this by taking electrons from NAD (nicotinamide adenine dinucleotide), a sugar phosphate first described in 1906. The reduced form is called NADH.
Now for some terminology: For historical reasons, removing electrons is called "oxidation", and donating them is called "reduction." Together, these are abbreviated "redox" reactions. But since negative electrons and positive protons are involved, it might help to think of 'reduction' as reducing the number of protons. Oxidizing a molecule leaves it with fewer electrons, resulting in a positive charge -- i.e., with extra protons. Reducing a molecule leaves it with a negative charge, or a reduced number of protons. A proton is the same as a hydrogen ion (H+).
The docking site of Complex I oxidizes NADH to NAD+, passing two captured electrons to a cofactor called ubiquinone. In the process, by passing the electrons through a series of iron-sulfur clusters (Fe-S), the machine pumps four protons through the inner mitochondrial membrane, contributing about 40 percent of the proton gradient needed by ATP synthase. You can watch a simplified animation from NDSU Virtual Cell showing how the complexes move electrons and protons around.
The mitochondrion is where the well-known "citric acid cycle" takes place. Students often hear about the chemistry of life, but not as often about the mechanics. They learn how energy from food is transferred through various molecules to make ATP as we breathe in oxygen and breathe out carbon dioxide and water vapor. That's great to know, but what is more fascinating is how these reactions require machines with moving parts. Let's see what scientists have discovered about Complex I, in terms of its structure and dynamics.
Complex I is a huge enzyme, one of the largest in the cell. In mammals, it has 14 core subunits and 31 "supernumerary" (fancy word for "extra") subunits, adding up to a whopping mass of 980 kilodaltons (kDa). (A Dalton is about the mass of a hydrogen atom; technically, 1/12 the mass of a carbon atom.) Such high mass implies over 7,000 properly-sequenced amino acids. That's one huge machine, considering the average size of an enzyme is about 300-400 amino acids. The bacterial Complex I, lacking many of the supernumerary subunits, is still gigantic, weighing in at 550 kDa.
In appearance, Complex I resembles a boot, with the ankle inside the mitochondrion and the sole anchored in the crista. NAD enters the ankle. The protons exit the sole into the inner membrane. But what actually goes on in this structure? Research published in Nature in 2010 suggested the possibility that the bacterial enzyme moves with an action resembling a piston.
The overall architecture of this large molecular machine is now clear. F-ATPase has been compared to a turbine. In a similar vein, complex I seems to resemble a steam engine, where the energy of the electron transfer is used to move a piston, which then drives, instead of wheels, a set of discontinuous helices. The full mechanistic details remain to be clarified by atomic structures of the membrane domain and the entire complex.
A subsequent paper in Nature in 2014 called the piston-like motion into question, at least for the mammalian version, but it did not rule out smaller-scale motions (called "conformational changes" in the literature).
Now, using cryo-electron microscopy, the Cambridge team has described all 45 subunits of Complex I from bovine mitochondria. In Nature, they mention having found moving parts:
We have located and modelled all 45 subunits, including the 31 supernumerary subunits, to provide the entire structure of the mammalian complex. Computational sorting of the particles identified different structural classes, related by subtle domain movements, which reveal conformationally dynamic regions and match biochemical descriptions of the 'active-to-de-active' enzyme transition that occurs during hypoxia. Our structures therefore provide a foundation for understanding complex I assembly and the effects of mutations that cause clinically relevant complex I dysfunctions, give insights into the structural and functional roles of the supernumerary subunits and reveal new information on the mechanism and regulation of catalysis.
The supernumerary subunits "are central to the structure, stability and assembly of the complex, and some also have regulatory or independent metabolic roles," they say. Some of them may serve a role in anchoring the machine to the membrane. That makes sense if the machine is vibrating from moving parts. What do the dynamic regions do? Later in the paper, they explain:
The two states of mammalian complex I described support the idea that dynamic, flexible regions at the hydrophilic-membrane domain interface are important for coupling ubiquinone reduction to proton translocation.
They go into detail about additional movements in a chain reaction, concluding:
Thus, a cascade of events originating from the ubiquinone-binding cleft may couple ubiquinone reduction and protonation to proton translocation. Although all such mechanisms for complex I are currently hypothetical, cryoEM now provides a powerful tool to study individual trapped conformations or separate mixed states computationally in order to determine how conformational changes are initiated, coordinated and propagated.
Currently, biochemists are limited to catching snapshots of the action. In the future, will they be able to watch Complex I move in real time? That's something to look forward to!
Students are likely to be much more interested in cell biology if they learn about molecular machines with moving parts. Who wants to memorize the chemical reactions in the citric acid cycle when you can watch rotors, pistons and pumps? That's what really goes on. We are privileged to live in a time when these realities are coming to light.
The authors point out two other observations of interest for intelligent design. One is that mutations in these machines cause disease and death; they cannot tolerate much change, meaning that the specificity in the amino acid sequence is vital to the function. That's why they say that the core machinery is "conserved from bacteria to humans."
The other observation is that the machines have to be assembled to work in the first place. It's like Scott Minnich's comment in Unlocking the Mystery of Life that the assembly instructions for the bacterial flagellum are even more complex than the machine itself. A machine needs a plan (encoded in DNA). It needs materials that must be delivered to the right place at the right time, in the right quantities. The parts have to be assembled in a coordinated sequence. Each step requires inspection, so that the cell doesn't waste time building something that won't work. That's true of Complex I and the entire factory of machines in the electron transport chain that make life possible. We see similar requirements in the construction of a house or manufacturing plant. It's Undeniable that we compare these processes and intuitively understand that intelligent causes must have been at work in the design of molecular machines.
Let's end with a look at one more level of organization. We mentioned cristae, the folds in mitochondrial membranes where these machines reside. A paper in the Proceedings of the National Academy of Sciences shows that the machines are arranged on the cristae in such a way as to maximize efficiency. In particular, the ATP synthase engines form V-shaped pairs, offset with respect to neighboring pairs so that their moving parts do not conflict but rather promote their respective operations. The spacing and angular displacement of the pairs, furthermore, results in the characteristic curvature of the cristae, which maximizes the proton gradient by creating local concentrations of protons aimed at the engines.
And this was found in Paramecium.
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