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16.6: Introduction to Control Systems - Biology


What you’ll learn to do: Describe the nervous, endocrine, reproductive, and sensory systems

The first set of body systems we’ll learn about have been grouped together as the “control systems.” It is important to remember that this isn’t a hard-and-fast categorization: we’ve simply grouped these systems together to help you organize your learning. These control systems all function in roles that control the signals that direct your body’s actions.


Introduction

Each somatic cell in the body generally contains the same DNA. A few exceptions include red blood cells, which contain no DNA in their mature state, and some immune system cells that rearrange their DNA while producing antibodies. In general, however, the genes that determine whether you have green eyes, brown hair, and how fast you metabolize food are the same in the cells in your eyes and your liver, even though these organs function quite differently. If each cell has the same DNA, how is it that cells or organs are different? Why do cells in the eye differ so dramatically from cells in the liver?

Whereas each cell shares the same genome and DNA sequence, each cell does not turn on, or express, the same set of genes. Each cell type needs a different set of proteins to perform its function. Therefore, only a small subset of proteins is expressed in a cell. For the proteins to be expressed, the DNA must be transcribed into RNA and the RNA must be translated into protein. In a given cell type, not all genes encoded in the DNA are transcribed into RNA or translated into protein because specific cells in our body have specific functions. Specialized proteins that make up the eye (iris, lens, and cornea) are only expressed in the eye, whereas the specialized proteins in the heart (pacemaker cells, heart muscle, and valves) are only expressed in the heart. At any given time, only a subset of all of the genes encoded by our DNA are expressed and translated into proteins. The expression of specific genes is a highly regulated process with many levels and stages of control. This complexity ensures the proper expression in the proper cell at the proper time.

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    1.1. A Motivating Example¶

    Before beginning writing, the authors of this book, like much of the work force, had to become caffeinated. We hopped in the car and started driving. Using an iPhone, Alex called out “Hey Siri”, awakening the phone’s voice recognition system. Then Mu commanded “directions to Blue Bottle coffee shop”. The phone quickly displayed the transcription of his command. It also recognized that we were asking for directions and launched the Maps application (app) to fulfill our request. Once launched, the Maps app identified a number of routes. Next to each route, the phone displayed a predicted transit time. While we fabricated this story for pedagogical convenience, it demonstrates that in the span of just a few seconds, our everyday interactions with a smart phone can engage several machine learning models.

    Imagine just writing a program to respond to a wake word such as “Alexa”, “OK Google”, and “Hey Siri”. Try coding it up in a room by yourself with nothing but a computer and a code editor, as illustrated in Fig. 1.1.1 . How would you write such a program from first principles? Think about it… the problem is hard. Every second, the microphone will collect roughly 44000 samples. Each sample is a measurement of the amplitude of the sound wave. What rule could map reliably from a snippet of raw audio to confident predictions (< ext, ext>) on whether the snippet contains the wake word? If you are stuck, do not worry. We do not know how to write such a program from scratch either. That is why we use machine learning.

    Fig. 1.1.1 Identify a wake word. ¶

    Here is the trick. Often, even when we do not know how to tell a computer explicitly how to map from inputs to outputs, we are nonetheless capable of performing the cognitive feat ourselves. In other words, even if you do not know how to program a computer to recognize the word “Alexa”, you yourself are able to recognize it. Armed with this ability, we can collect a huge dataset containing examples of audio and label those that do and that do not contain the wake word. In the machine learning approach, we do not attempt to design a system explicitly to recognize wake words. Instead, we define a flexible program whose behavior is determined by a number of parameters. Then we use the dataset to determine the best possible set of parameters, those that improve the performance of our program with respect to some measure of performance on the task of interest.

    You can think of the parameters as knobs that we can turn, manipulating the behavior of the program. Fixing the parameters, we call the program a model. The set of all distinct programs (input-output mappings) that we can produce just by manipulating the parameters is called a family of models. And the meta-program that uses our dataset to choose the parameters is called a learning algorithm.

    Before we can go ahead and engage the learning algorithm, we have to define the problem precisely, pinning down the exact nature of the inputs and outputs, and choosing an appropriate model family. In this case, our model receives a snippet of audio as input, and the model generates a selection among (< ext, ext>) as output. If all goes according to plan the model’s guesses will typically be correct as to whether the snippet contains the wake word.

    If we choose the right family of models, there should exist one setting of the knobs such that the model fires “yes” every time it hears the word “Alexa”. Because the exact choice of the wake word is arbitrary, we will probably need a model family sufficiently rich that, via another setting of the knobs, it could fire “yes” only upon hearing the word “Apricot”. We expect that the same model family should be suitable for “Alexa” recognition and “Apricot” recognition because they seem, intuitively, to be similar tasks. However, we might need a different family of models entirely if we want to deal with fundamentally different inputs or outputs, say if we wanted to map from images to captions, or from English sentences to Chinese sentences.

    As you might guess, if we just set all of the knobs randomly, it is unlikely that our model will recognize “Alexa”, “Apricot”, or any other English word. In machine learning, the learning is the process by which we discover the right setting of the knobs coercing the desired behavior from our model. In other words, we train our model with data. As shown in Fig. 1.1.2 , the training process usually looks like the following:

    Start off with a randomly initialized model that cannot do anything useful.

    Grab some of your data (e.g., audio snippets and corresponding (< ext, ext>) labels).

    Tweak the knobs so the model sucks less with respect to those examples.

    Repeat Step 2 and 3 until the model is awesome.

    Fig. 1.1.2 A typical training process. ¶

    To summarize, rather than code up a wake word recognizer, we code up a program that can learn to recognize wake words, if we present it with a large labeled dataset. You can think of this act of determining a program’s behavior by presenting it with a dataset as programming with data. That is to say, we can “program” a cat detector by providing our machine learning system with many examples of cats and dogs. This way the detector will eventually learn to emit a very large positive number if it is a cat, a very large negative number if it is a dog, and something closer to zero if it is not sure, and this barely scratches the surface of what machine learning can do. Deep learning, which we will explain in greater detail later, is just one among many popular methods for solving machine learning problems.


    Introduction to Systems Thinking

    System. We hear and use the word all the time. “There’s no sense in trying to buck the system,” we might say. Or, “This job’s getting out of control, I’ve got to establish a system.” Whether you are aware of it or not, you are a member of many systems – a family, a community, a church, a company. You yourself are a complex biological system comprising many smaller systems. And every day, you probably interact with dozens of systems, such as automobiles, retail stores, the organization you work for, etc. But what exactly is a system? How would we know one if we saw one, and why is it important to understand systems? Most important, how can we manage our organizations more effectively by understanding systems?

    This volume explores these questions and introduces the principles and practice of a quietly growing field: systems thinking. With roots in disciplines as varied as biology, cybernetics, and ecology, systems thinking provides a way of looking at how the world works that differs markedly from the traditional reductionistic, analytic view. Why is a systemic perspective an important complement to analytic thinking? One reason is that understanding how systems work – and how we play a role in them – lets us function more effectively and proactively within them. The more we understand systemic behavior, the more we can anticipate that behavior and work with systems (rather than being controlled by them) to shape the quality of our lives.

    It’s been said that systems thinking is one of the key management competencies for the 21st century. As our world becomes ever more tightly interwoven globally and as the pace of change continues to increase, we will all need to become increasingly “system-wise.” This volume gives you the language and tools you need to start applying systems thinking principles and practices in your own organization.


    Tools

    Monotone control systems

    . stems. 1 Introduction One of the most important classes of dynamical systems in theoretical biology is that of monotone systems . Among the classical references in this area are the textbook by Smith =-=[26]-=- and the papers [14, 15] by Hirsh and [25] by Smale. Monotone systems are those for which trajectories preserve a partial ordering on states. They include the subclass of cooperative systems (see e.g.

    Stability of continuous-time distributed consensus algorithms

    . imilar mild conditions on the coupling topology suffice to draw conclusions about the overall system behavior. A possible contribution in this direction could come from the theory of monotone systems =-=[41, 42]-=-. The model studied in the present paper is, in fact, a monotone, cooperative system—an observation which we have not explicitly exploited in the present paper. It may be interesting to investigate ho.

    On the Global Convergence of Stochastic Fictitious Play

    Human sperm competition

    . iting fallout of this result was to the study of three-dimensional competitive systems to 2 H.L. Smith which much of the classical Poincaré-Bendixson theory has been extended [22], [23], [24], [42], =-=[43]-=-, [53], [58]. The work of deMottoni and Schiaffino [10] must also be mentioned here for while it dealt with a specific system, the periodic Lotka-Volterra model of two-species competition, its results.

    Positive and Negative Circuits in Dynamical Systems

    Traveling wave fronts of reaction-diffusion systems with

    Some new directions in control theory inspired by systems biology

    . an order-preservation property for flows (see below for more details). The concept represents a generalization of the notion of monotone autonomous system studied by Hirsch, Smale, Smith, and others =-=[22, 23, 24, 25]-=-. It can often be verified by simply studying the “sign structure” of an incidence graph associated to the Jacobian of the dynamics in other words, by simply inspecting which connections in a diagram.

    Multi-stability in monotone input/output systems

    . are those for which flows preserve a suitable partial ordering on states. The work reported here is grounded upon the rich and elegant theory of monotone dynamical systems (see the textbook by Smith =-=[27]-=- as well as papers such as [17, 16] by Hirsch and [25] by Smale), which provides results on generic convergence to equilibria, and, more generally, on the precise characterization of omega limit sets.

    A Petri net approach to the study of persistence in chemical reaction networks

    . isingly, research by many, notably by Clarke [10], Horn and Jackson [29, 30], Feinberg [18, 19, 20], and many others in the context of complex balancing and deficiency theory, and by Hirsch and Smith =-=[41, 26]-=- and many others including the present authors [2, 17, 3, 9] in the context of monotone systems, has resulted in the identification of rich classes of chemical network structures for which such robust.

    Molecular systems biology and control

    . s to xi(t) < yi(t) for every coordinate i = 1, . . . , n. What matters is that strongly monotone systems are very well-behaved in a dynamical sense. According to a beautiful result of Moe Hirsch (cf. =-=[51, 50, 83, 52]-=-), almost every bounded solution of such a system converges to the set of equilibria. By “almost any” one means every solution except for a measure-zero set of initial conditions, or, in a different v.


    Contents

    Endothermy vs. ectothermy Edit

    Thermoregulation in organisms runs along a spectrum from endothermy to ectothermy. Endotherms create most of their heat via metabolic processes, and are colloquially referred to as warm-blooded. When the surrounding temperatures are cold, endotherms increase metabolic heat production to keep their body temperature constant, thus making the internal body temperature of an endotherm more or less independent of the temperature of the environment. [5] One metabolic activity, in terms of generating heat, that endotherms are able to do is that they possess a larger number of mitochondria per cell than ectotherms, enabling them to generate more heat by increasing the rate at which they metabolize fats and sugars. [6] Ectotherms use external sources of temperature to regulate their body temperatures. They are colloquially referred to as cold-blooded despite the fact that body temperatures often stay within the same temperature ranges as warm-blooded animals. Ectotherms are the opposite of endotherms when it comes to regulating internal temperatures. In ectotherms, the internal physiological sources of heat are of negligible importance the biggest factor that enables them to maintain adequate body temperatures is due to environmental influences. Living in areas that maintain a constant temperature throughout the year, like the tropics or the ocean, has enabled ectotherms to develop a wide range of behavioral mechanisms that enable them to respond to external temperatures, such as sun-bathing to increase body temperature, or seeking the cover of shade to lower body temperature. [6] [5]

    Ectotherms Edit

    Ectothermic cooling Edit

    • Vaporization:
        of sweat and other bodily fluids.
      • Increasing blood flow to body surfaces to maximize heat transfer across the advective gradient.
      • Losing heat by being in contact with a colder surface. For instance:
        • Lying on cool ground.
        • Staying wet in a river, lake or sea.
        • Covering in cool mud.
        • Releasing heat by radiating it away from the body.

        Ectothermic heating (or minimizing heat loss) Edit

        • Convection:
          • Climbing to higher ground up trees, ridges, rocks.
          • Entering a warm water or air current.
          • Building an insulated nest or burrow.
          • Conduction:
            • Lying on a hot surface.
            • Lying in the sun (heating this way is affected by the body's angle in relation to the sun).
            • Folding skin to reduce exposure.
            • Concealing wing surfaces.
            • Exposing wing surfaces.
            • Changing shape to alter surface/volume ratio.
            • Inflating the body.

            To cope with low temperatures, some fish have developed the ability to remain functional even when the water temperature is below freezing some use natural antifreeze or antifreeze proteins to resist ice crystal formation in their tissues. [7] Amphibians and reptiles cope with heat gain by evaporative cooling and behavioral adaptations. An example of behavioral adaptation is that of a lizard lying in the sun on a hot rock in order to heat through radiation and conduction.

            Endothermy Edit

            An endotherm is an animal that regulates its own body temperature, typically by keeping it at a constant level. To regulate body temperature, an organism may need to prevent heat gains in arid environments. Evaporation of water, either across respiratory surfaces or across the skin in those animals possessing sweat glands, helps in cooling body temperature to within the organism's tolerance range. Animals with a body covered by fur have limited ability to sweat, relying heavily on panting to increase evaporation of water across the moist surfaces of the lungs and the tongue and mouth. Mammals like cats, dogs and pigs, rely on panting or other means for thermal regulation and have sweat glands only in foot pads and snout. The sweat produced on pads of paws and on palms and soles mostly serves to increase friction and enhance grip. Birds also counteract overheating by gular fluttering, or rapid vibrations of the gular (throat) skin. Down feathers trap warm air acting as excellent insulators just as hair in mammals acts as a good insulator. Mammalian skin is much thicker than that of birds and often has a continuous layer of insulating fat beneath the dermis. In marine mammals, such as whales, or animals that live in very cold regions, such as the polar bears, this is called blubber. Dense coats found in desert endotherms also aid in preventing heat gain such as in the case of the camels.

            A cold weather strategy is to temporarily decrease metabolic rate, decreasing the temperature difference between the animal and the air and thereby minimizing heat loss. Furthermore, having a lower metabolic rate is less energetically expensive. Many animals survive cold frosty nights through torpor, a short-term temporary drop in body temperature. Organisms, when presented with the problem of regulating body temperature, have not only behavioural, physiological, and structural adaptations but also a feedback system to trigger these adaptations to regulate temperature accordingly. The main features of this system are stimulus, receptor, modulator, effector and then the feedback of the newly adjusted temperature to the stimulus. This cyclical process aids in homeostasis.

            Homeothermy compared with poikilothermy Edit

            Homeothermy and poikilothermy refer to how stable an organism's deep-body temperature is. Most endothermic organisms are homeothermic, like mammals. However, animals with facultative endothermy are often poikilothermic, meaning their temperature can vary considerably. Most fish are ectotherms, as most of their heat comes from the surrounding water. However, almost all fish are poikilothermic.

            By numerous observations upon humans and other animals, John Hunter showed that the essential difference between the so-called warm-blooded and cold-blooded animals lies in observed constancy of the temperature of the former, and the observed variability of the temperature of the latter. Almost all birds and mammals have a high temperature almost constant and independent of that of the surrounding air (homeothermy). Almost all other animals display a variation of body temperature, dependent on their surroundings (poikilothermy). [8]

            Brain control Edit

            Thermoregulation in both ectotherms and endotherms is controlled mainly by the preoptic area of the anterior hypothalamus. [9] Such homeostatic control is separate from the sensation of temperature. [9]

            In birds and mammals Edit

            In cold environments, birds and mammals employ the following adaptations and strategies to minimize heat loss:

            1. Using small smooth muscles (arrector pili in mammals), which are attached to feather or hair shafts this distorts the surface of the skin making feather/hair shaft stand erect (called goose bumps or pimples) which slows the movement of air across the skin and minimizes heat loss.
            2. Increasing body size to more easily maintain core body temperature (warm-blooded animals in cold climates tend to be larger than similar species in warmer climates (see Bergmann's Rule))
            3. Having the ability to store energy as fat for metabolism
            4. Have shortened extremities
            5. Have countercurrent blood flow in extremities – this is where the warm arterial blood travelling to the limb passes the cooler venous blood from the limb and heat is exchanged warming the venous blood and cooling the arterial (e.g., Arctic wolf[10] or penguins [11][12] )

            In warm environments, birds and mammals employ the following adaptations and strategies to maximize heat loss:

            1. Behavioural adaptations like living in burrows during the day and being nocturnal
            2. Evaporative cooling by perspiration and panting
            3. Storing fat reserves in one place (e.g., camel's hump) to avoid its insulating effect
            4. Elongated, often vascularized extremities to conduct body heat to the air

            In humans Edit

            As in other mammals, thermoregulation is an important aspect of human homeostasis. Most body heat is generated in the deep organs, especially the liver, brain, and heart, and in contraction of skeletal muscles. [14] Humans have been able to adapt to a great diversity of climates, including hot humid and hot arid. High temperatures pose serious stresses for the human body, placing it in great danger of injury or even death. For example, one of the most common reactions to hot temperatures is heat exhaustion, which is an illness that could happen if one is exposed to high temperatures, resulting in some symptoms such as dizziness, fainting, or a rapid heartbeat. [15] [16] For humans, adaptation to varying climatic conditions includes both physiological mechanisms resulting from evolution and behavioural mechanisms resulting from conscious cultural adaptations. [17] [18] The physiological control of the body's core temperature takes place primarily through the hypothalamus, which assumes the role as the body's "thermostat". [19] This organ possesses control mechanisms as well as key temperature sensors, which are connected to nerve cells called thermoreceptors. [20] Thermoreceptors come in two subcategories ones that respond to cold temperatures and ones that respond to warm temperatures. Scattered throughout the body in both peripheral and central nervous systems, these nerve cells are sensitive to changes in temperature and are able to provide useful information to the hypothalamus through the process of negative feedback, thus maintaining a constant core temperature. [21] [22]

            There are four avenues of heat loss: evaporation, convection, conduction, and radiation. If skin temperature is greater than that of the surrounding air temperature, the body can lose heat by convection and conduction. But, if air temperature of the surroundings is greater than that of the skin, the body gains heat by convection and conduction. In such conditions, the only means by which the body can rid itself of heat is by evaporation. So, when the surrounding temperature is higher than the skin temperature, anything that prevents adequate evaporation will cause the internal body temperature to rise. [23] During intense physical activity (e.g. sports), evaporation becomes the main avenue of heat loss. [24] Humidity affects thermoregulation by limiting sweat evaporation and thus heat loss. [25]

            Thermogenesis occurs in the flowers of many plants in the family Araceae as well as in cycad cones. [26] In addition, the sacred lotus (Nelumbo nucifera) is able to thermoregulate itself, [27] remaining on average 20 °C (36 °F) above air temperature while flowering. Heat is produced by breaking down the starch that was stored in their roots, [28] which requires the consumption of oxygen at a rate approaching that of a flying hummingbird. [29]

            One possible explanation for plant thermoregulation is to provide protection against cold temperature. For example, the skunk cabbage is not frost-resistant, yet it begins to grow and flower when there is still snow on the ground. [26] Another theory is that thermogenicity helps attract pollinators, which is borne out by observations that heat production is accompanied by the arrival of beetles or flies. [30]

            Some plants are known to protect themselves against colder temperatures using antifreeze proteins. This occurs in wheat (Triticum aestivum), potatoes (Solanum tuberosum) and several other angiosperm species. [7]

            Animals other than humans regulate and maintain their body temperature with physiological adjustments and behavior. Desert lizards are ectotherms and so unable to metabolically control their temperature but can do this by altering their location. They may do this, in the morning only by raising their head from its burrow and then exposing their entire body. By basking in the sun, the lizard absorbs solar heat. It may also absorb heat by conduction from heated rocks that have stored radiant solar energy. To lower their temperature, lizards exhibit varied behaviors. Sand seas, or ergs, produce up to 57.7 °C (135.9 °F), and the sand lizard will hold its feet up in the air to cool down, seek cooler objects with which to contact, find shade or return to their burrow. They also go to their burrows to avoid cooling when the sun goes down or the temperature falls. Aquatic animals can also regulate their temperature behaviorally by changing their position in the thermal gradient. [31]

            Animals also engage in kleptothermy in which they share or even steal each other's body warmth. In endotherms such as bats [32] and birds (such as the mousebird [33] and emperor penguin [34] ) it allows the sharing of body heat (particularly amongst juveniles). This allows the individuals to increase their thermal inertia (as with gigantothermy) and so reduce heat loss. [35] Some ectotherms share burrows of ectotherms. Other animals exploit termite mounds. [36] [37]

            Some animals living in cold environments maintain their body temperature by preventing heat loss. Their fur grows more densely to increase the amount of insulation. Some animals are regionally heterothermic and are able to allow their less insulated extremities to cool to temperatures much lower than their core temperature—nearly to 0 °C (32 °F). This minimizes heat loss through less insulated body parts, like the legs, feet (or hooves), and nose.

            Different species of Sonoran Desert Drosophila will exploit different species of cacti based on the thermotolerance differences between species and hosts. For example, Drosophila mettleri is found in cacti like the Saguaro and Senita these two cacti remain cool by storing water. Over time, the genes selecting for higher heat tolerance were reduced in the population due to the cooler host climate the fly is able to exploit.

            Some flies, such as Lucilia sericata, lay their eggs en masse. The resulting group of larvae, depending on its size, is able to thermoregulate and keep itself at the optimum temperature for development.

            Hibernation, estivation and daily torpor Edit

            To cope with limited food resources and low temperatures, some mammals hibernate during cold periods. To remain in "stasis" for long periods, these animals build up brown fat reserves and slow all body functions. True hibernators (e.g., groundhogs) keep their body temperatures low throughout hibernation whereas the core temperature of false hibernators (e.g., bears) varies occasionally the animal may emerge from its den for brief periods. Some bats are true hibernators and rely upon a rapid, non-shivering thermogenesis of their brown fat deposit to bring them out of hibernation.

            Estivation is similar to hibernation, however, it usually occurs in hot periods to allow animals to avoid high temperatures and desiccation. Both terrestrial and aquatic invertebrate and vertebrates enter into estivation. Examples include lady beetles (Coccinellidae), [38] North American desert tortoises, crocodiles, salamanders, cane toads, [39] and the water-holding frog. [40]

            Daily torpor occurs in small endotherms like bats and hummingbirds, which temporarily reduces their high metabolic rates to conserve energy. [41]

            Normal human temperature Edit

            Previously, average oral temperature for healthy adults had been considered 37.0 °C (98.6 °F), while normal ranges are 36.1 to 37.8 °C (97.0 to 100.0 °F). In Poland and Russia, the temperature had been measured axillarily (under the arm). 36.6 °C (97.9 °F) was considered "ideal" temperature in these countries, while normal ranges are 36.0 to 36.9 °C (96.8 to 98.4 °F). [ citation needed ]

            Recent studies suggest that the average temperature for healthy adults is 36.8 °C (98.2 °F) (same result in three different studies). Variations (one standard deviation) from three other studies are:

            • 36.4–37.1 °C (97.5–98.8 °F)
            • 36.3–37.1 °C (97.3–98.8 °F) for males,
              36.5–37.3 °C (97.7–99.1 °F) for females
            • 36.6–37.3 °C (97.9–99.1 °F) [42]

            Measured temperature varies according to thermometer placement, with rectal temperature being 0.3–0.6 °C (0.5–1.1 °F) higher than oral temperature, while axillary temperature is 0.3–0.6 °C (0.5–1.1 °F) lower than oral temperature. [43] The average difference between oral and axillary temperatures of Indian children aged 6–12 was found to be only 0.1 °C (standard deviation 0.2 °C), [44] and the mean difference in Maltese children aged 4–14 between oral and axillary temperature was 0.56 °C, while the mean difference between rectal and axillary temperature for children under 4 years old was 0.38 °C. [45]

            Variations due to circadian rhythms Edit

            In humans, a diurnal variation has been observed dependent on the periods of rest and activity, lowest at 11 p.m. to 3 a.m. and peaking at 10 a.m. to 6 p.m. Monkeys also have a well-marked and regular diurnal variation of body temperature that follows periods of rest and activity, and is not dependent on the incidence of day and night nocturnal monkeys reach their highest body temperature at night and lowest during the day. Sutherland Simpson and J.J. Galbraith observed that all nocturnal animals and birds – whose periods of rest and activity are naturally reversed through habit and not from outside interference – experience their highest temperature during the natural period of activity (night) and lowest during the period of rest (day). [8] Those diurnal temperatures can be reversed by reversing their daily routine. [46]

            In essence, the temperature curve of diurnal birds is similar to that of man and other homoeothermal animals, except that the maximum occurs earlier in the afternoon and the minimum earlier in the morning. Also, the curves obtained from rabbits, guinea pigs, and dogs were quite similar to those from man. [8] These observations indicate that body temperature is partially regulated by circadian rhythms.

            Variations due to human menstrual cycles Edit

            During the follicular phase (which lasts from the first day of menstruation until the day of ovulation), the average basal body temperature in women ranges from 36.45 to 36.7 °C (97.61 to 98.06 °F). Within 24 hours of ovulation, women experience an elevation of 0.15–0.45 °C (0.27–0.81 °F) due to the increased metabolic rate caused by sharply elevated levels of progesterone. The basal body temperature ranges between 36.7–37.3 °C (98.1–99.1 °F) throughout the luteal phase, and drops down to pre-ovulatory levels within a few days of menstruation. [47] Women can chart this phenomenon to determine whether and when they are ovulating, so as to aid conception or contraception.

            Variations due to fever Edit

            Fever is a regulated elevation of the set point of core temperature in the hypothalamus, caused by circulating pyrogens produced by the immune system. To the subject, a rise in core temperature due to fever may result in feeling cold in an environment where people without fever do not.

            Variations due to biofeedback Edit

            Some monks are known to practice Tummo, biofeedback meditation techniques, that allow them to raise their body temperatures substantially. [48]

            It has been theorized that low body temperature may increase lifespan. In 2006, it was reported that transgenic mice with a body temperature 0.3–0.5 °C (0.5–0.9 °F) lower than normal mice lived longer than normal mice. [49] This mechanism is due to overexpressing the uncoupling protein 2 in hypocretin neurons (Hcrt-UCP2), which elevated hypothalamic temperature, thus forcing the hypothalamus to lower body temperature. Lifespan was increased by 12% and 20% for males and females, respectively. The mice were fed ad libitum. [50] [51] The effects of such a genetic change in body temperature on longevity is more difficult to study in humans in 2011, the UCP2 genetic alleles in humans were associated with obesity. [52]

            There are limits both of heat and cold that an endothermic animal can bear and other far wider limits that an ectothermic animal may endure and yet live. The effect of too extreme a cold is to decrease metabolism, and hence to lessen the production of heat. Both catabolic and anabolic pathways share in this metabolic depression, and, though less energy is used up, still less energy is generated. The effects of this diminished metabolism become telling on the central nervous system first, especially the brain and those parts concerning consciousness [53] both heart rate and respiration rate decrease judgment becomes impaired as drowsiness supervenes, becoming steadily deeper until the individual loses consciousness without medical intervention, death by hypothermia quickly follows. Occasionally, however, convulsions may set in towards the end, and death is caused by asphyxia. [54] [53]

            In experiments on cats performed by Sutherland Simpson and Percy T. Herring, the animals were unable to survive when rectal temperature fell below 16 °C (61 °F). [53] At this low temperature, respiration became increasingly feeble heart-impulse usually continued after respiration had ceased, the beats becoming very irregular, appearing to cease, then beginning again. Death appeared to be mainly due to asphyxia, and the only certain sign that it had taken place was the loss of knee-jerks. [54]

            However, too high a temperature speeds up the metabolism of different tissues to such a rate that their metabolic capital is soon exhausted. Blood that is too warm produces dyspnea by exhausting the metabolic capital of the respiratory centre [ citation needed ] heart rate is increased the beats then become arrhythmic and eventually cease. The central nervous system is also profoundly affected by hyperthermia and delirium, and convulsions may set in. Consciousness may also be lost, propelling the person into a comatose condition. These changes can sometimes also be observed in patients suffering from an acute fever. [ citation needed ] Mammalian muscle becomes rigid with heat rigor at about 50 °C, with the sudden rigidity of the whole body rendering life impossible. [54]

            H.M. Vernon performed work on the death temperature and paralysis temperature (temperature of heat rigor) of various animals. He found that species of the same class showed very similar temperature values, those from the Amphibia examined being 38.5 °C, fish 39 °C, reptiles 45 °C, and various molluscs 46 °C. [ citation needed ] Also, in the case of pelagic animals, he showed a relation between death temperature and the quantity of solid constituents of the body. In higher animals, however, his experiments tend to show that there is greater variation in both the chemical and physical characteristics of the protoplasm and, hence, greater variation in the extreme temperature compatible with life. [54]

            Arthropoda Edit

            The maximum temperatures tolerated by certain thermophilic arthropods exceeds the lethal temperatures for most vertebrates. [55]

            The most heat-resistant insects are three genera of desert ants recorded from three different parts of the world. The ants have developed a lifestyle of scavenging for short durations during the hottest hours of the day, in excess of 50 °C (122 °F), for the carcasses of insects and other forms of life which have succumbed to heat stress. [56]

            In April 2014, the South Californian mite Paratarsotomus macropalpis has been recorded as the world's fastest land animal relative to body length, at a speed of 322 body lengths per second. Besides the unusually great speed of the mites, the researchers were surprised to find the mites running at such speeds on concrete at temperatures up to 60 °C (140 °F), which is significant because this temperature is well above the lethal limit for the majority of animal species. In addition, the mites are able to stop and change direction very quickly. [55]

            Spiders like Nephila pilipes exhibits active thermal regulation behavior. [57] During high temperature sunny days, it aligns its body with the direction of sunlight to reduce the body area under direct sunlight. [57]


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            Results

            We first defined all reachable states of a Boolean network with control applied at the beginning and then removed the control input from the system. This exactly mimics the situation of modifying one node or a group of nodes in the network initially and examining the response. We then extended the reachability to controllability.

            Determining reachability using graphical approach

            For a n-node Boolean network, an integrated state represents the status of n variables in the network. All together there are 2 n integrated states, representing each possible status of the n nodes. An integrated state is denoted as (e_<2^>^) , j=1,2, ⋯ ,2 n , in which (e_<2^>^) means the j th column of 2 n ×2 n identity matrix. A graphical representation, time transition diagram, was proposed to illustrate the transition among the integrated states. Each node of the time transition diagram corresponds to one integrated state (e_<2^>^) of a dynamic network. A directed edge from (e_<2^>^) to (e_<2^>^) , j,k=1,2, ⋯ ,2 n , indicates temporal transitions from an integrated state (e_<2^>^) to an integrated state (e_<2^>^) . The directed edge also represents that the j th column in the transition matrix is (e_<2^>^) . The transition matrix of a Boolean network is calculated using semi-tensor product, and each column of the transition matrix is a vector (e_<2^>^) . From the left to the right, each column of the transition matrix represents the transition from (e_<2^>^) , j increasing from 1 to 2 n , to its next integrated state represented by a column vector (e_<2^>^) . Specifically, the left most column of the transition matrix represents the transition from (e_<2^>^<1>) to its next integrated state, and the right most column in the matrix represents the transition from (e_<2^>^<2^>) to its next integrated state. Therefore, there are a total of 2 n outgoing arrows in the time transition diagram and a node may have multiple incoming arrows but has only one outgoing arrow.

            Reachability of a node in the time transition diagram means the corresponding integrated state can be reached from any initial integrated state in finite time. If each node in the time transition diagram is reachable, the Boolean network is reachable.

            Finding 1

            A Boolean network with n nodes (n>1) is reachable if and only if the signal flow goes through each node in the time transition diagram by one direction, indicating that each node has one outgoing arrow and one incoming arrow.

            There are some specific properties for the transition matrix of a reachable Boolean network: 1) There is only one 1 in each column and each row, suggesting an integrate state can only be reached by one other integrated state 2) Every diagonal elements is zero. It means that the j th column is not (e_<2^>^) . This property excludes self transition of one integrated state. 3) If the j th column is (e_<2^>^) , then the k th column is not (e_<2^>^) , n≥2, which excludes transition between two integrated states. However, this property is not true for a 1-node reachable Boolean network. The transition matrix of 1-node reachable boolean network satisfies that the 1 st column is (^<2>>) while the 2 nd column is (^<1>>) .

            Here, an example of a 3-node Boolean network is presented in Fig. 1 to show how the reachability is determined and all 8 integrated states representing possible status of the 3 nodes in the Boolean network are listed in Table 2. Based on these integrated states listed in Table 2 and time transition diagram in Fig. 1, whatever changes we make to the nodes through knock out of a node (value 0) nor dosage injection to a node (value 1), the network can not reach the integrated state (^<1>>) (node 1 is 0, node 2 is 1, and node 3 is 1), (^<2>>) (node 1 is 1, node 2 is 1, and node 3 is 0), (^<6>>) (node 1 is 0, node 2 is 1, and node 3 is 0). If we force the initial status of the system to be these three states, the network will deviate from these states and never come back. This result can provide a guideline for experiment design to examine down stream effect for a giving pathway with known Boolean network. For the network shown in Fig. 1, when (^<1>>) , or (^<2>>) , or (^<6>>) is a desired state we would like the network to go, a more complicated control strategy should be introduced in stead of just modify status of one node of a group of nodes.

            Determination of the reachability of a three-node Boolean network with given Boolean functions. Based on the logical operations (a) for this network, the corresponding time transition matrix (b) and the time transition diagram (c) can be obtained by semi-tensor product. A signal flow among five integrated states (^<3>> o ^<5>> o ^<7>> o ^<8>> o ^<4>> o ^<3>>) is formed as a circle. According to Finding 1, it means that all these five integrated states are reachable, which are highlighted in red, while the other three states (^<1>>) , (^<2>>) and (^<6>>) are not reachable, which are highlighted in blue

            Reachable 2-node Boolean network with logical operations. We examined all 2-node Boolean networks with combinations of 16 logical operations as shown in Table 1. We found that there were only six simplest forms of reachable 2-node Boolean networks. These six Boolean networks were shown in Fig. 2 with their corresponding time transition diagrams and transition matrices.

            The six simplest 2-node reachable Boolean networks with their logic operations. The left column shows simplest reachable Boolean functions of two variables, the middle column represents the state transition matrix, and the right column illustrates the time transition diagram among four integrated states of two variables. The four integrated states of all six Boolean networks are all reachable

            Interestingly, these six simplest networks show highly coupled property, which can be divided into three groups. In each group, if state x 1 is swapped with x 2 in one of the coupled networks, it exactly becomes the other network. Therefore, for any given 2-node Boolean network dynamics with logical operations, it will be straightforward to know that it is reachable or not when it reduces to its simplest form. In addition, this provided a baseline to check reachability and controllability of a Boolean network with more nodes.

            Feedback control design for N-node lower-triangle Boolean networks Starting from the known 6 forms of 2-node reachable Boolean networks, their extensions to N-node Boolean networks can be derived based on the property of transition matrix. Further, for the extended N-node Boolean network with control input added to the nth node directly, the feedback control input can be designed to implement the reachability of the N-node Boolean network.

            Finding 2

            For a given N-node lower-triangle Boolean network dynamic with control input located at the nth node, if the first N-1 Boolean network dynamic is a reachable (N-1)-node Boolean dynamics, a feedback control can be designed, which is extracted from the N th logical function of extended N-node reachable Boolean dynamics from the (N-1)-node reachable Boolean dynamics.

            Given one of the 6 reachable 2-node boolean networks in Fig. 2, we can extend the network with extra nodes once the added boolean functions guarantee the time transition diagram satisfy the condition in our 1st finding. For an extended N-node reachable Boolean network, if we divide its (2 n ×2 n transition matrix L N into sub-blocks, and define 0-block as a square matrix with all zero elements, and 1-block as square matrix with non-zero element, the structure of the transition matrix L N in terms of the sub-blocks will mimic the transition matrix for boolean networks with less nodes.

            Specifically, if 1-block in transition matrix of 2-node network appears at row i and column j, then for a 3-node network extended from 2-node network, the two 1-blocks only appear at row 2i−1 and column 2j−1, row 2i and column 2j or at row 2i−1 and column 2j, row 2i and column 2j−1 respectively. An example of how to design the feedback control input of the 3-node Boolean network is shown below, which extends from 2-node reachable Boolean network. And the relationship between transition matrices was shown in Fig. 3. Further, the Boolean function for the 3rd node can be treated as control input u as shown below,

            The pipeline of extended 3-node reachable Boolean network from 2-node reachable Boolean network. If transition matrix L 3(2 3 ×2 3 ) of 3-node Boolean network system, is divided into 4×4 blocks, then the new transition matrix represented by the 4×4 matrix is exactly the same as transition matrix L 2 of fundamental 2-node Boolean network dynamic. a The transition matrix of a 2-node reachable network (b) Time transition diagram of 2-node network (c) Each 1-block is extended to two 1-blocks (d) The transition matrix of extended 3-node extended reachable network (e) Corresponding time transition diagram of extended 3-node extended network

            where u is the control input of the lower-triangle dynamic, which will be designed later.

            For the 2-node reachable Boolean network represented by

            we illustrate the inter relationship between the transition matrices and time transition diagram. Based on one possible transition matrix that guarantees the reachability of each integrated state, the boolean operation matrix M can be obtained and the corresponding boolean function for the 3rd node is determined. With the possible transition matrix shown in Fig. 3, the corresponding Boolean function is listed as

            Then, the feedback control input u is designed as

            Analysis of reachability for P53 pathway

            The p53 pathway responds to intrinc and extrinsic stress signals that can disrupt the fidelity of DNA replication, genome stability, cell cycle progression, and cell division. The pathway contains complicated feedback regulatory mechanisms and many experimental results have been accumulated to illustrate the regulations. In the major switch of p53 pathways as shown in Fig. 4, there are four state nodes are denoted as x 1, x 2, x 3 and x 4, which present as ‘ATM’, ‘p53’, ‘Wip1’, ‘Mdm2’, respectively [16]. The relationship between integrated states and its corresponding Boolean values of four genes is shown in Table 3 below.

            The major switch of p53 pathway. The major interactions for p53 pathway, were presented among four nodes: ‘ATM’, ‘p53’, ‘Wip1’, ‘Mdm2’ respectively. The red line means the inhibition impact while the black linestands for the promotion impact

            The Boolean network representation of 4 genes is

            The corresponding time transition diagram is shown in Fig. 5. From the time transition diagram, there exists a cycle including (^<8>, e_<16>^<4>, e_<16>^<2>, e_<16>^<10>, e_<16>^<13>, e_<16>^<15>>) , suggesting a stable pulse generated by P53 pathway switches. Based on Table 3, each integrated state corresponds the specific values of four states. In Fig. 5, the high expression level of a gene presents Boolean value ‘1’ while low expression level means Boolean value ‘0’.

            The time transition diagram of sixteen integrated states of 4 nodes in p53 pathway. The solid lines present the time path. As time goes on, any initial integrated state will reach a signal flow including six integrated states (e_<16>^<8> o e_<16>^<4> o e_<16>^<2> o e_<16>^<10> o e_<16>^<13> o e_<16>^<15> o e_<16>^<8>) . This phenomena induces that the states change periodically after a period of time

            Additionally, this stable pulse can be reached by different initial integrated states. One of the time course, which includes the main loop, is presented in Fig. 6 based on our simulation. The network exhibits the one-phase or two-phase dynamic, which depends on the initial states. If the initial is one of (e_<16>^<8>, e_<16>^<4>, e_<16>^<2>, e_<16>^<10>, e_<16>^<13>, e_<16>^<15>) , there exists only one-phase pulse, i.e. steady state pulse, which is a periodical pulse. If the initial states are others integrated states, there exists the two-phase pulse (transient pulse and steady state pulse), where the first phase is depends on the time distance between any state belongs to the periodical circle and the initial states and it ends at reaching any one state in the (e_<16>^<8> o e_<16>^<4> o e_<16>^<2> o e_<16>^<10> o e_<16>^<13> o e_<16>^<15> o e_<16>^<8>) circle. The second phase is characterized by the periodical circle.

            The pulses of p53 pathway. Expression levels of four genes in the major switch of P53 pathway lead to pulse diagram. The high expression level of a gene presents Boolean value ‘1’ while low expression level means Boolean value ‘0’. Expression levels of each node also lead to a specific integrated state in the time transition diagram. The four different pulse lines, which are ATM (black solid line), p53 (blue solid line), Wip1 (green solid line), Mdm2 (red solid line), show cyclic changes after 10 sec

            To verify that our predictions on P53 pathway progression, we examined the experimental results published on P53 pathways. The published results confirmed that 1) P53 pathway has a stable pattern pulses generation [17], and 2) there exists two-phase transition in P53 pathways [18].


            Overview

            Summary

            A survey of how engineering techniques from control and systems theory can be used to help biologists understand the behavior of cellular systems.

            Issues of regulation and control are central to the study of biological and biochemical systems. Thus it is not surprising that the tools of feedback control theory—engineering techniques developed to design and analyze self-regulating systems—have proven useful in the study of these biological mechanisms. Such interdisciplinary work requires knowledge of the results, tools and techniques of another discipline, as well as an understanding of the culture of an unfamiliar research community. This volume attempts to bridge the gap between disciplines by presenting applications of systems and control theory to cell biology that range from surveys of established material to descriptions of new developments in the field. The first chapter offers a primer on concepts from dynamical systems and control theory, which allows the life scientist with no background in control theory to understand the concepts presented in the rest of the book. Following the introduction of ordinary differential equation-based modeling in the first chapter, the second and third chapters discuss alternative modeling frameworks. The remaining chapters sample a variety of applications, considering such topics as quantitative measures of dynamic behavior, modularity, stoichiometry, robust control techniques, and network identification.

            Contributors David Angeli, Declan G. Bates, Eric Bullinger, Peter S. Chang, Domitilla Del Vecchio, Francis J. Doyle III, Hana El-Samad, Dirk Fey, Rolf Findeisen, Simone Frey, Jorge Gonçalves, Pablo A. Iglesias, Brian P. Ingalls, Elling W. Jacobsen, Mustafa Khammash, Jongrae Kim, Eric Klavins, Eric C. Kwei, Thomas Millat, Jason E. Shoemaker, Eduardo D. Sontag, Stephanie R. Taylor, David Thorsley, Camilla Trané, Sean Warnick, Olaf Wolkenhauer

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            Editors

            Pablo A. Iglesias

            Brian P. Ingalls

            Reviews

            [A]n important contribution to systems biology. This volume will be very useful to researchers in bioinformatics, mathematics, as well as biology as it addresses a highly interdisciplinary area.

            The Quarterly Review of Biology

            Endorsements

            Historically, control theory has its roots in the analysis and understanding of physical and technological systems. However, in recent times it has revealed its wider potential as a tool for describing the complex dynamical behavior of living things. This valuable book is therefore timely, since it places control theory where it belongs—at the heart of our search for the principles by which living systems operate.

            Science Foundation Ireland Research Professor of Systems Biology, Hamilton Institute, National University of Ireland

            A landmark in bringing rigor and relevance to theory for systems biology.

            Professor of Control and Dynamical Systems and Electrical Engineering, Caltech


            About the Contributors

            Editors

            Nicholas M. Holden is Professor of Biosystems Engineering and Head of Teaching and Learning in the School of Biosystems and Food Engineering at University College Dublin, where he has worked for the last 25 years. His research is focused on the environmental impact and sustainability of agriculture, and food systems. He teaches life cycle assessment, precision agriculture, and green technology project modules and is the Programme Director of the BAgrSc Agricultural Systems Technology programme. He has been an ASABE member for over 20 years.

            Mary Leigh Wolfe is Professor in the Department of Biological Systems Engineering (BSE) at Virginia Tech. After serving on the faculty at Texas A&M University for over six years, she moved to Virginia Tech in 1992. Recently, she served as head of the BSE department for over eight years. Her research and teaching has focused on hydrologic modeling, nonpoint source (NPS) pollution control strategies, and decision support tools for NPS pollution control and watershed management. She has also conducted research related to engineering education. She is a Fellow, past president, and life member of ASABE.

            Jactone A. Ogejo is an Associate Professor in the Department of Biological Systems Engineering (BSE) at Virginia Tech. His research and extension programs focus on improving the management and use of bioresidues from production agriculture and food processing. His work encompasses recovering value-added products from bioresidues, agricultural air quality, and, more importantly, advancing knowledge to increase the acceptance and adoption of technology for manure management on animal production farms. He has been an ASABE member since 1992.

            Enda J. Cummins is a Professor and Head of Research, Innovation and Impact in the School of Biosystems and Food Engineering at University College Dublin. His main research area is food safety, risk assessment, and predictive modelling, with a particular focus on implications for human health and environmental contamination. He teaches quantitative risk assessment, food physics, and research and teaching methods. He is Programme Director for the Masters of Engineering Science in Food Engineering at UCD. He has been an ASABE member since 2002.


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