Neural engineering

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Neural_engineering

Neural engineering (also known as neuroengineering) is a discipline within biomedical engineering that uses engineering techniques to understand, repair, replace, or enhance neural systems. Neural engineers are uniquely qualified to solve design problems at the interface of living neural tissue and non-living constructs.

Overview

The field of neural engineering draws on the fields of computational neuroscience, experimental neuroscience, neurology, electrical engineering and signal processing of living neural tissue, and encompasses elements from robotics, cybernetics, computer engineering, neural tissue engineering, materials science, and nanotechnology.

Prominent goals in the field include restoration and augmentation of human function via direct interactions between the nervous system and artificial devices.

Much current research is focused on understanding the coding and processing of information in the sensory and motor systems, quantifying how this processing is altered in the pathological state, and how it can be manipulated through interactions with artificial devices including brain–computer interfaces and neuroprosthetics.

Other research concentrates more on investigation by experimentation, including the use of neural implants connected with external technology.

Neurohydrodynamics is a division of neural engineering that focuses on hydrodynamics of the neurological system.

History

The origins of neural engineering begins with Italian physicist and biologist Luigi Galvani. Galvani along with pioneers like Emil du Bois-Reymond discovered that electrical signals in nerves and muscles control movement, which marks the first understanding of the brain's electrical nature. As neural engineering is a relatively new field, information and research relating to it is comparatively limited, although this is changing rapidly. The first journals specifically devoted to neural engineering, The Journal of Neural Engineering and The Journal of NeuroEngineering and Rehabilitation both emerged in 2004. International conferences on neural engineering have been held by the IEEE since 2003, from 29 April until 2 May 2009 in Antalya, Turkey 4th Conference on Neural Engineering, the 5th International IEEE EMBS Conference on Neural Engineering in April/May 2011 in Cancún, Mexico, and the 6th conference in San Diego, California in November 2013. The 7th conference was held in April 2015 in Montpellier. The 8th conference was held in May 2017 in Shanghai.

Fundamentals

The fundamentals behind neuroengineering involve the relationship of neurons, neural networks, and nervous system functions to quantifiable models to aid the development of devices that could interpret and control signals and produce purposeful responses.

Neuroscience

Messages that the body uses to influence thoughts, senses, movements, and survival are directed by nerve impulses transmitted across brain tissue and to the rest of the body. Neurons are the basic functional unit of the nervous system and are highly specialized cells that are capable of sending these signals that operate high and low level functions needed for survival and quality of life. Neurons have special electro-chemical properties that allow them to process information and then transmit that information to other cells. Neuronal activity is dependent upon neural membrane potential and the changes that occur along and across it. A constant voltage, known as the membrane potential, is normally maintained by certain concentrations of specific ions across neuronal membranes. Disruptions or variations in this voltage create an imbalance, or polarization, across the membrane. Depolarization of the membrane past its threshold potential generates an action potential, which is the main source of signal transmission, known as neurotransmission of the nervous system. An action potential results in a cascade of ion flux down and across an axonal membrane, creating an effective voltage spike train or "electrical signal" which can transmit further electrical changes in other cells. Signals can be generated by electrical, chemical, magnetic, optical, and other forms of stimuli that influence the flow of charges, and thus voltage levels across neural membranes.

Engineering

Engineers employ quantitative tools that can be used for understanding and interacting with complex neural systems. Methods of studying and generating chemical, electrical, magnetic, and optical signals responsible for extracellular field potentials and synaptic transmission in neural tissue aid researchers in the modulation of neural system activity. To understand properties of neural system activity, engineers use signal processing techniques and computational modeling. To process these signals, neural engineers must translate the voltages across neural membranes into corresponding code, a process known as neural coding. Neural coding studies on how the brain encodes simple commands in the form of central pattern generators (CPGs), movement vectors, the cerebellar internal model, and somatotopic maps to understand movement and sensory phenomena. Decoding of these signals in the realm of neuroscience is the process by which neurons understand the voltages that have been transmitted to them. Transformations involve the mechanisms that signals of a certain form get interpreted and then translated into another form. Engineers look to mathematically model these transformations. There are a variety of methods being used to record these voltage signals. These can be intracellular or extracellular. Extracellular methods involve single-unit recordings, extracellular field potentials, and amperometry; more recently, multielectrode arrays have been used to record and mimic signals.

Scope

Neuromechanics

Neuromechanics is the coupling of neurobiology, biomechanics, sensation and perception, and robotics. Researchers are using advanced techniques and models to study the mechanical properties of neural tissues and their effects on the tissues' ability to withstand and generate force and movements as well as their vulnerability to traumatic loading. This area of research focuses on translating the transformations of information among the neuromuscular and skeletal systems to develop functions and governing rules relating to operation and organization of these systems. Neuromechanics can be simulated by connecting computational models of neural circuits to models of animal bodies situated in virtual physical worlds. Experimental analysis of biomechanics including the kinematics and dynamics of movements, the process and patterns of motor and sensory feedback during movement processes, and the circuit and synaptic organization of the brain responsible for motor control are all currently being researched to understand the complexity of animal movement. Dr. Michelle LaPlaca's lab at Georgia Institute of Technology is involved in the study of mechanical stretch of cell cultures, shear deformation of planar cell cultures, and shear deformation of 3D cell containing matrices. Understanding of these processes is followed by development of functioning models capable of characterizing these systems under closed loop conditions with specially defined parameters. The study of neuromechanics is aimed at improving treatments for physiological health problems which includes optimization of prostheses design, restoration of movement post injury, and design and control of mobile robots. By studying structures in 3D hydrogels, researchers can identify new models of nerve cell mechanoproperties. For example, LaPlaca et al. developed a new model showing that strain may play a role in cell culture.

Neuromodulation

Neuromodulation aims to treat disease or injury by employing medical device technologies that would enhance or suppress activity of the nervous system with the delivery of pharmaceutical agents, electrical signals, or other forms of energy stimulus to re-establish balance in impaired regions of the brain. Researchers in this field face the challenge of linking advances in understanding neural signals to advancements in technologies delivering and analyzing these signals with increased sensitivity, biocompatibility, and viability in closed loops schemes in the brain such that new treatments and clinical applications can be created to treat those with neural damage of various kinds. Neuromodulator devices can correct nervous system dysfunction related to Parkinson's disease, dystonia, tremor, Tourette's, chronic pain, OCD, severe depression, and eventually epilepsy. Neuromodulation is appealing as treatment for varying defects because it focuses in on treating highly specific regions of the brain only, contrasting that of systemic treatments that can have side effects on the body. Neuromodulator stimulators such as microelectrode arrays can stimulate and record brain function and with further improvements are meant to become adjustable and responsive delivery devices for drugs and other stimuli.

Neural regrowth and repair

Neural engineering and rehabilitation applies neuroscience and engineering to investigating peripheral and central nervous system function and to finding clinical solutions to problems created by brain damage or malfunction. Engineering applied to neuroregeneration focuses on engineering devices and materials that facilitate the growth of neurons for specific applications such as the regeneration of peripheral nerve injury, the regeneration of the spinal cord tissue for spinal cord injury, and the regeneration of retinal tissue. Genetic engineering and tissue engineering are areas developing scaffolds for spinal cord to regrow across thus helping neurological problems.

Research and applications

Research focused on neural engineering utilizes devices to study how the nervous system functions and malfunctions.

Neural imaging

Neuroimaging techniques are used to investigate the activity of neural networks, as well as the structure and function of the brain. Neuroimaging technologies include functional magnetic resonance imaging (fMRI), magnetic resonance imaging (MRI), positron emission tomography (PET) and computed axial tomography (CAT) scans. Functional neuroimaging studies are interested in which areas of the brain perform specific tasks. fMRI measures hemodynamic activity that is closely linked to neural activity. It is used to map metabolic responses in specific regions of the brain to a given task or stimulus. PET, CT scanners, and electroencephalography (EEG) are currently being improved and used for similar purposes.

Neural networks

Scientists can use experimental observations of neuronal systems and theoretical and computational models of these systems to create Neural networks with the hopes of modeling neural systems in as realistic a manner as possible. Neural networks can be used for analyses to help design further neurotechnological devices. Specifically, researchers handle analytical or finite element modeling to determine nervous system control of movements and apply these techniques to help patients with brain injuries or disorders. Artificial neural networks can be built from theoretical and computational models and implemented on computers from theoretically devices equations or experimental results of observed behavior of neuronal systems. Models might represent ion concentration dynamics, channel kinetics, synaptic transmission, single neuron computation, oxygen metabolism, or application of dynamic system theory. Liquid-based template assembly was used to engineer 3D neural networks from neuron-seeded microcarrier beads.

Neural interfaces

Neural interfaces are a major element used for studying neural systems and enhancing or replacing neuronal function with engineered devices. Engineers are challenged with developing electrodes that can selectively record from associated electronic circuits to collect information about the nervous system activity and to stimulate specified regions of neural tissue to restore function or sensation of that tissue (Cullen et al. 2011). The materials used for these devices must match the mechanical properties of neural tissue in which they are placed and the damage must be assessed. Neural interfacing involves temporary regeneration of biomaterial scaffolds or chronic electrodes and must manage the body's response to foreign materials. Microelectrode arrays are recent advances that can be used to study neural networks (Cullen & Pfister 2011). Optical neural interfaces involve optical recordings and optogenetics, making certain brain cells sensitive to light in order to modulate their activity. Fiber optics can be implanted in the brain to stimulate or silence targeted neurons using light, as well as record photon activity—a proxy of neural activity— instead of using electrodes. Two-photon excitation microscopy can study living neuronal networks and the communicatory events among neurons.

Brain–computer interfaces

Brain–computer interfaces seek to directly communicate with human nervous system to monitor and stimulate neural circuits as well as diagnose and treat intrinsic neurological dysfunction. Deep brain stimulation is a significant advance in this field that is especially effective in treating movement disorders such as Parkinson's disease with high frequency stimulation of neural tissue to suppress tremors (Lega et al. 2011).

Microsystems

Neural microsystems can be developed to interpret and deliver electrical, chemical, magnetic, and optical signals to neural tissue. They can detect variations in membrane potential and measure electrical properties such as spike population, amplitude, or rate by using electrodes, or by assessment of chemical concentrations, fluorescence light intensity, or magnetic field potential. The goal of these systems is to deliver signals that would influence neuronal tissue potential and thus stimulate the brain tissue to evoke a desired response.

Microelectrode arrays

Microelectrode arrays are specific tools used to detect the sharp changes in voltage in the extracellular environments that occur from propagation of an action potential down an axon. Dr. Mark Allen and Dr. LaPlaca have microfabricated 3D electrodes out of cytocompatible materials such as SU-8 and SLA polymers which have led to the development of in vitro and in vivo microelectrode systems with the characteristics of high compliance and flexibility to minimize tissue disruption.

Neural prostheses

Neuroprosthetics are devices capable of supplementing or replacing missing functions of the nervous system by stimulating the nervous system and recording its activity. Electrodes that measure firing of nerves can integrate with prosthetic devices and signal them to perform the function intended by the transmitted signal. Sensory prostheses use artificial sensors to replace neural input that might be missing from biological sources. Engineers researching these devices are charged with providing a chronic, safe, artificial interface with neuronal tissue. Perhaps the most successful of these sensory prostheses is the cochlear implant which has restored hearing abilities to the deaf. Visual prosthesis for restoring visual capabilities of blind persons is still in more elementary stages of development. Motor prosthetics are devices involved with electrical stimulation of biological neural muscular system that can substitute for control mechanisms of the brain or spinal cord. Smart prostheses can be designed to replace missing limbs controlled by neural signals by transplanting nerves from the stump of an amputee to muscles. Sensory prosthetics provide sensory feedback by transforming mechanical stimuli from the periphery into encoded information accessible by the nervous system. Electrodes placed on the skin can interpret signals and then control the prosthetic limb. These prosthetics have been very successful. Functional electrical stimulation (FES) is a system aimed at restoring motor processes such as standing, walking, and hand grasp.

Neurorobotics

Neurorobotics is the study of how neural systems can be embodied and movements emulated in mechanical machines. Neurorobots are typically used to study motor control and locomotion, learning and memory selection, and value systems and action selection. By studying neurorobots in real-world environments, they are more easily observed and assessed to describe heuristics of robot function in terms of its embedded neural systems and the reactions of these systems to its environment. For instance, making use of a computational model of epilectic spike-wave dynamics, it has been already proven the effectiveness of a method to simulate seizure abatement through a pseudospectral protocol. The computational model emulates the brain connectivity by using a magnetic imaging resonance from a patient with idiopathic generalized epilepsy. The method was able to generate stimuli able to lessen the seizures.

Neural tissue regeneration

Neural tissue regeneration, or neuroregeneration looks to restore function to those neurons that have been damaged in small injuries and larger injuries like those caused by traumatic brain injury. Functional restoration of damaged nerves involves re-establishment of a continuous pathway for regenerating axons to the site of innervation. Researchers like Dr. LaPlaca at Georgia Institute of Technology are looking to help find treatment for repair and regeneration after traumatic brain injury and spinal cord injuries by applying tissue engineering strategies. Dr. LaPlaca is looking into methods combining neural stem cells with an extracellular matrix protein based scaffold for minimally invasive delivery into the irregular shaped lesions that form after a traumatic insult. By studying the neural stem cells in vitro and exploring alternative cell sources, engineering novel biopolymers that could be utilized in a scaffold, and investigating cell or tissue engineered construct transplants in vivo in models of traumatic brain and spinal cord injury, Dr. LaPlaca's lab aims to identify optimal strategies for nerve regeneration post injury.

Current approaches to clinical treatment

End to end surgical suture of damaged nerve ends can repair small gaps with autologous nerve grafts. For larger injuries, an autologous nerve graft that has been harvested from another site in the body might be used, though this process is time-consuming, costly and requires two surgeries. Clinical treatment for CNS is minimally available and focuses mostly on reducing collateral damage caused by bone fragments near the site of injury or inflammation. After swelling surrounding injury lessens, patients undergo rehabilitation so that remaining nerves can be trained to compensate for the lack of nerve function in injured nerves. No treatment currently exists to restore nerve function of CNS nerves that have been damaged.

Engineering strategies for repair

Engineering strategies for the repair of spinal cord injury are focused on creating a friendly environment for nerve regeneration. Only Peripheral PNS nerve damage has been clinically possible so far, but advances in research of genetic techniques and biomaterials demonstrate the potential for SC nerves to regenerate in permissible environments.

Grafts

Advantages of autologous tissue grafts are that they come from natural materials which have a high likelihood of biocompatibility while providing structural support to nerves that encourage cell adhesion and migration.^[13] Nonautologous tissue, acellular grafts, and extracellular matrix based materials are all options that may also provide ideal scaffolding for nerve regeneration. Some come from allogenic or xenogenic tissues that must be combined with immunosuppressants. while others include small intestinal submucosa and amniotic tissue grafts.Synthetic materials are attractive options because their physical and chemical properties can typically be controlled. A challenge that remains with synthetic materials is biocompatibility. Methylcellulose-based constructs have been shown to be a biocompatible option serving this purpose. AxoGen uses a cell graft technology AVANCE to mimic a human nerve. It has been shown to achieve meaningful recovery in 87 percent of patients with peripheral nerve injuries.

Nerve guidance channels

Nerve guidance channels, Nerve guidance conduit are innovative strategies focusing on larger defects that provide a conduit for sprouting axons directing growth and reducing growth inhibition from scar tissue. Nerve guidance channels must be readily formed into a conduit with the desired dimensions, sterilizable, tear resistant, and easy to handle and suture. Ideally they would degrade over time with nerve regeneration, be pliable, semipermeable, maintain their shape, and have a smooth inner wall that mimics that of a real nerve.

Biomolecular therapies

Highly controlled delivery systems are needed to promote neural regeneration. Neurotrophic factors can influence development, survival, outgrowth, and branching. Neurotrophins include nerve growth factor (NGF), brain derived neurotrophic factor (BDNF), neurotrophin-3 (NT-3) and neurotrophin-4/5 (NT-4/5). Other factors are ciliary neurotrophic factor (CNTF), glial cell line-derived growth factor (GDNF) and acidic and basic fibroblast growth factor (aFGF, bFGF) that promote a range of neural responses. Fibronectin has also been shown to support nerve regeneration following TBI in rats. Other therapies are looking into regeneration of nerves by upregulating regeneration associated genes (RAGs), neuronal cytoskeletal components, and antiapoptosis factors. RAGs include GAP-43 and Cap-23, adhesion molecules such as L1 family, NCAM, and N-cadherin. There is also the potential for blocking inhibitory biomolecules in the CNS due to glial scarring. Some currently being studied are treatments with chondroitinase ABC and blocking NgR, ADP-ribose.

Delivery techniques

Delivery devices must be biocompatible and stable in vivo. Some examples include osmotic pumps, silicone reservoirs, polymer matrices, and microspheres. Gene therapy techniques have also been studied to provide long-term production of growth factors and could be delivered with viral or non-viral vectors such as lipoplexes. Cells are also effective delivery vehicles for ECM components, neurotrophic factors and cell adhesion molecules. Olfactory ensheathing cells (OECs) and stem cells as well as genetically modified cells have been used as transplants to support nerve regeneration.

Advanced therapies

Advanced therapies combine complex guidance channels and multiple stimuli that focus on internal structures that mimic the nerve architecture containing internal matrices of longitudinally aligned fibers or channels. Fabrication of these structures can use a number of technologies: magnetic polymer fiber alignment, injection molding, phase separation, solid free-form fabrication, and ink jet polymer printing.

Neural enhancement

Augmentation of human neural systems, or human enhancement using engineering techniques is another possible application of neuroengineering. Deep brain stimulation has already been shown to enhance memory recall as noted by patients currently using this treatment for neurological disorders. Brain stimulation techniques are postulated to be able to sculpt emotions and personalities as well as enhance motivation, reduce inhibitions, etc. as requested by the individual. Ethical issues with this sort of human augmentation are a new set of questions that neural engineers have to grapple with as these studies develop.

Neurophysics

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Neurophysics

Neurophysics (or neurobiophysics) is the branch of biophysics dealing with the development and use of physical methods to gain information about the nervous system. Neurophysics is an interdisciplinary science using physics and combining it with other neurosciences to better understand neural processes. The methods used include the techniques of experimental biophysics and other physical measurements such as EEG mostly to study electrical, mechanical or fluidic properties, as well as theoretical and computational approaches. The term "neurophysics" is a portmanteau of "neuron" and "physics".

Among other examples, the theorisation of ectopic action potentials in neurons using a Kramers-Moyal expansion and the description of physical phenomena measured during an EEG using a dipole approximation use neurophysics to better understand neural activity.

Another quite distinct theoretical approach considers neurons as having Ising model energies of interaction and explores the physical consequences of this for various Cayley tree topologies and large neural networks. In 1981, the exact solution for the closed Cayley tree (with loops) was derived by Peter Barth for an arbitrary branching ratio and found to exhibit an unusual phase transition behavior in its local-apex and long-range site-site correlations, suggesting that the emergence of structurally-determined and connectivity-influenced cooperative phenomena may play a significant role in large neural networks.

Recording techniques

Old techniques to record brain activity using physical phenomena are already widespread in research and medicine. Electroencephalography (EEG) uses electrophysiology to measure electrical activity within the brain. This technique, with which Hans Berger first recorded brain electrical activity on a human in 1924, is non-invasive and uses electrodes placed on the scalp of the patient to record brain activity. Based on the same principle, electrocorticography (ECoG) requires a craniotomy to record electrical activity directly on the cerebral cortex.

In the recent decades, physicists have come up with technologies and devices to image the brain and its activity. The Functional Magnetic Resonance Imaging (fMRI) technique, discovered by Seiji Ogawa in 1990, reveals blood flow changes inside the brain. Based on the existing medical imaging technique Magnetic Resonance Imaging (MRI) and on the link between the neural activity and the cerebral blood flow, this tool enables scientists to study brain activities when they are triggered by a controlled stimulation. Another technique, the Two Photons Microscopy (2P), invented by Winfried Denk (for which he has been awarded the Brain Prize in 2015), John H. Strickler and Watt W. Webb in 1990 at Cornell University, uses fluorescent proteins and dyes to image brain cells. This technique combines the two-photon absorption, first theorized by Maria Goeppert-Mayer in 1931, with lasers. Today, this technique is widely used in research and often coupled with genetic engineering to study the behavior of a specific type of neuron.

Theories of consciousness

Consciousness is still an unknown mechanism and theorists have yet to come up with physical hypotheses explaining its mechanisms. Some theories rely on the idea that consciousness could be explained by the disturbances in the cerebral electromagnetic field generated by the action potentials triggered during brain activity. These theories are called electromagnetic theories of consciousness. Another group of hypotheses suggest that consciousness cannot be explained by classical dynamics but with quantum mechanics and its phenomena. These hypotheses are grouped into the idea of quantum mind and were first introduced by Eugene Wigner.

Neurophysics institutes

• The Theoretical Neurophysics Laboratory, University of Bremen
• Department of Neurophysics, Max-Planck Institute
• Center of Functionally Integrative Neuroscience, Neurophysics group, Aarhus University
• W. M. Keck Center for Neurophysics, UCLA
• Neurophysics Program, Georgia State University
• Neurophysics at the Institute of Neurology, University College of London
• Neurophysics at Radboud University, Radboud University, Nijmegen, Netherlands

Awards

Among the list of prizes that reward neurophysicists for their contribution to neurology and related fields, the most notable one is the Brain Prize, whose last laureates are Adrian Bird and Huda Zoghbi for "their groundbreaking work to map and understand epigenetic regulation of the brain and for identifying the gene that causes Rett syndrome". The other most relevant prizes that can be awarded to a neurophysicist are: the NAS Award in the Neurosciences, the Kavli Prize and to some extent the Nobel Prize in Physiology or Medicine. It can be noted that a Nobel Prize was awarded to scientists that developed techniques which contributed widely to a better understanding of the nervous system, such as Neher and Sakmann in 1991 for the patch clamp, and also to Lauterbur and Mansfield for their work on Magnetic resonance imaging (MRI) in 2003.

Biophysics

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Biophysic

Kinesin uses protein domain dynamics on nanoscales to "walk" along a microtubule.

Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. Biophysical research shares significant overlap with biochemistry, molecular biology, physical chemistry, physiology, nanotechnology, bioengineering, computational biology, biomechanics, developmental biology and systems biology.

The term biophysics was originally introduced by Karl Pearson in 1892. The term biophysics is also regularly used in academia to indicate the study of the physical quantities (e.g. electric current, temperature, stress, entropy) in biological systems. Other biological sciences also perform research on the biophysical properties of living organisms including molecular biology, cell biology, chemical biology, and biochemistry.

Overview

Molecular biophysics typically addresses biological questions similar to those in biochemistry and molecular biology, seeking to find the physical underpinnings of biomolecular phenomena. Scientists in this field conduct research concerned with understanding the interactions between the various systems of a cell, including the interactions between DNA, RNA and protein biosynthesis, as well as how these interactions are regulated. A great variety of techniques are used to answer these questions.

A ribosome is a biological machine that utilizes protein dynamics

Fluorescent imaging techniques, as well as electron microscopy, x-ray crystallography, NMR spectroscopy, atomic force microscopy (AFM) and small-angle scattering (SAS) both with X-rays and neutrons (SAXS/SANS) are often used to visualize structures of biological significance. Protein dynamics can be observed by neutron spin echo spectroscopy. Conformational change in structure can be measured using techniques such as dual polarisation interferometry, circular dichroism, SAXS and SANS. Direct manipulation of molecules using optical tweezers or AFM, can also be used to monitor biological events where forces and distances are at the nanoscale. Molecular biophysicists often consider complex biological events as systems of interacting entities which can be understood e.g. through statistical mechanics, thermodynamics and chemical kinetics. By drawing knowledge and experimental techniques from a wide variety of disciplines, biophysicists are often able to directly observe, model or even manipulate the structures and interactions of individual molecules or complexes of molecules.

In addition to traditional (i.e. molecular and cellular) biophysical topics like structural biology or enzyme kinetics, modern biophysics encompasses an extraordinarily broad range of research, from bioelectronics to quantum biology involving both experimental and theoretical tools. It is becoming increasingly common for biophysicists to apply the models and experimental techniques derived from physics, as well as mathematics and statistics, to larger systems such as tissues, organs, populations and ecosystems. Biophysical models are used extensively in the study of electrical conduction in single neurons, as well as neural circuit analysis in both tissue and whole brain.

Medical physics, a branch of biophysics, is any application of physics to medicine or healthcare, ranging from radiology to microscopy and nanomedicine. For example, physicist Richard Feynman theorized about the future of nanomedicine. He wrote about the idea of a medical use for biological machines (see nanomachines). Feynman and Albert Hibbs suggested that certain repair machines might one day be reduced in size to the point that it would be possible to (as Feynman put it) "swallow the doctor". The idea was discussed in Feynman's 1959 essay There's Plenty of Room at the Bottom.

History

The studies of Luigi Galvani (1737–1798) laid groundwork for the later field of biophysics. Some of the earlier studies in biophysics were conducted in the 1840s by a group known as the Berlin school of physiologists. Among its members were pioneers such as Hermann von Helmholtz, Ernst Heinrich Weber, Carl F. W. Ludwig, and Johannes Peter Müller.

William T. Bovie (1882–1958) is credited as a leader of the field's further development in the mid-20th century. He was a leader in developing electrosurgery.

The popularity of the field rose when the book What Is Life? by Erwin Schrödinger was published. Since 1957, biophysicists have organized themselves into the Biophysical Society which now has about 9,000 members over the world.

Some authors such as Robert Rosen criticize biophysics on the ground that the biophysical method does not take into account the specificity of biological phenomena.

Focus as a subfield

While some colleges and universities have dedicated departments of biophysics, usually at the graduate level, many do not have university-level biophysics departments, instead having groups in related departments such as biochemistry, cell biology, chemistry, computer science, engineering, mathematics, medicine, molecular biology, neuroscience, pharmacology, physics, and physiology. Depending on the strengths of a department at a university differing emphasis will be given to fields of biophysics. What follows is a list of examples of how each department applies its efforts toward the study of biophysics. This list is hardly all inclusive. Nor does each subject of study belong exclusively to any particular department. Each academic institution makes its own rules and there is much overlap between departments.

• Biology and molecular biology – Gene regulation, single protein dynamics, bioenergetics, patch clamping, biomechanics, virophysics.
• Structural biology – Ångstrom-resolution structures of proteins, nucleic acids, lipids, carbohydrates, and complexes thereof.
• Biochemistry and chemistry – biomolecular structure, siRNA, nucleic acid structure, structure-activity relationships.
• Computer science – Neural networks, biomolecular and drug databases.
• Computational chemistry – molecular dynamics simulation, molecular docking, quantum chemistry
• Bioinformatics – sequence alignment, structural alignment, protein structure prediction
• Mathematics – graph/network theory, population modeling, dynamical systems, phylogenetics.
• Medicine – biophysical research that emphasizes medicine. Medical biophysics is a field closely related to physiology. It explains various aspects and systems of the body from a physical and mathematical perspective. Examples are fluid dynamics of blood flow, gas physics of respiration, radiation in diagnostics/treatment and much more. Biophysics is taught as a preclinical subject in many medical schools, mainly in Europe.
• Neuroscience – studying neural networks experimentally (brain slicing) as well as theoretically (computer models), membrane permittivity.
• Pharmacology and physiology – channelomics, electrophysiology, biomolecular interactions, cellular membranes, polyketides.
• Physics – negentropy, stochastic processes, and the development of new physical techniques and instrumentation as well as their application.
• Quantum biology – The field of quantum biology applies quantum mechanics to biological objects and problems. Decohered isomers to yield time-dependent base substitutions. These studies imply applications in quantum computing.
• Agronomy and agriculture

Many biophysical techniques are unique to this field. Research efforts in biophysics are often initiated by scientists who were biologists, chemists or physicists by training.

Evolutionary ecology

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Evolutionary_ecology

A phylogenetic tree of living things

Evolutionary ecology lies at the intersection of ecology and evolutionary biology. It approaches the study of ecology in a way that explicitly considers the evolutionary histories of species and the interactions between them. Conversely, it can be seen as an approach to the study of evolution that incorporates an understanding of the interactions between the species under consideration. The main subfields of evolutionary ecology are life history evolution, sociobiology (the evolution of social behavior), the evolution of interspecific interactions (e.g. cooperation, predator–prey interactions, parasitism, mutualism) and the evolution of biodiversity and of ecological communities.

Evolutionary ecology mostly considers two things: how interactions (both among species and between species and their physical environment) shape species through selection and adaptation, and the consequences of the resulting evolutionary change.

Evolutionary models

A large part of evolutionary ecology is about utilising models and finding empirical data as proof. Examples include the Lack clutch size model devised by David Lack and his study of Darwin's finches on the Galapagos Islands. Lack's study of Darwin's finches was important in analyzing the role of different ecological factors in speciation. Lack suggested that differences in species were adaptive and produced by natural selection, based on the assertion by G.F. Gause that two species cannot occupy the same niche.

Richard Levins introduced his model of the specialization of species in 1968, which investigated how habitat specialization evolved within heterogeneous environments using the fitness sets an organism or species possesses. This model developed the concept of spatial scales in specific environments, defining fine-grained spatial scales and coarse-grained spatial scales. The implications of this model include a rapid increase in environmental ecologists' understanding of how spatial scales impact species diversity in a certain environment.

Another model is Law and Diekmann's 1996 models on mutualism, which is defined as a relationship between two organisms that benefits both individuals. Law and Diekmann developed a framework called adaptive dynamics, which assumes that changes in plant or animal populations in response to a disturbance or lack thereof occurs at a faster rate than mutations occur. It is aimed to simplify other models addressing the relationships within communities.

Tangled nature model

The tangled nature model provides different methods for demonstrating and predicting trends in evolutionary ecology. The model analyzes an individual prone to mutation within a population as well as other factors such as extinction rate. The model was developed by Simon Laird, Daniel Lawson, and Henrik Jeldtoft Jensen of the Imperial College London in 2002. The purpose of the model is to create a simple and logical ecological model based on observation. The model is designed such that ecological effects can be accounted for when determining form, and fitness of a population.

Ecological genetics

Main article: Ecological genetics

Ecological genetics tie into evolutionary ecology through the study of how traits evolve in natural populations. Ecologists are concerned with how the environment and timeframe leads to genes becoming dominant. Organisms must continually adapt in order to survive in natural habitats. Genes define which organisms survive and which will die out. When organisms develop different genetic variations, even though they stem from the same species, it is known as polymorphism. Organisms that pass on beneficial genes continue to evolve their species to have an advantage inside of their niche.

Evolutionary ecologists

Julia Margaret Cameron's portrait of Darwin

Charles Darwin

The basis of the central principles of evolutionary ecology can be attributed to Charles Darwin (1809–1882), specifically in referencing his theory of natural selection and population dynamics, which discusses how populations of a species change over time. According to Ernst Mayr, professor of zoology at Harvard University, Darwin's most distinct contributions to evolutionary biology and ecology are as follows: "The first is the non-constancy of species, or the modern conception of evolution itself. The second is the notion of branching evolution, implying the common descent of all species of living things on earth from a single unique origin." Additionally, "Darwin further noted that evolution must be gradual, with no major breaks or discontinuities. Finally, he reasoned that the mechanism of evolution was natural selection."

George Evelyn Hutchinson

George Evelyn Hutchinson's (1903–1991) contributions to the field of ecology spanned over 60 years, in which he had significant influence in systems ecology, radiation ecology, limnology, and entomology. Described as the "father of modern ecology"  by Stephen Jay Gould, Hutchinson was one of the first scientists to link the subjects of ecology and mathematics. According to Hutchinson, he constructed "mathematical models of populations, the changing proportions of individuals of various ages, birthrate, the ecological niche, and population interaction in this technical introduction to population ecology." He also had a vast interest in limnology, due to his belief that lakes could be studied as a microcosm that provides insight into system behavior. Hutchinson is also known for his work Circular Causal Systems in Ecology, in which he states that "groups of organisms may be acted upon by their environment, and they may react upon it. If a set of properties in either system changes in such a way that the action of the first system on the second changes, this may cause changes in properties of the second system which alter the mode of action of the second system on the first."

Robert MacArthur

Robert MacArthur (1930–1972) is best known in the field of Evolutionary Ecology for his work The Theory of Island Biogeography, in which he and his co-author propose "that the number of species on any island reflects a balance between the rate at which new species colonize it and the rate at which populations of established species become extinct."

Eric Pianka

According to the University of Texas, Eric Pianka's (1939–2022) work in evolutionary ecology includes foraging strategies, reproductive tactics, competition and niche theory, community structure and organization, species diversity, and understanding rarity. Pianka is also known for his interest in lizards to study ecological occurrences, as he claimed they were "often abundant, making them relatively easy to locate, observe, and capture."

Michael Rosenzweig

Michael L. Rosenzweig (1941–present) created and popularized Reconciliation ecology, which began with his theory that designated nature preserves would not be enough land to conserve the biodiversity of Earth, as humans have used so much land that they have negatively impacted biogeochemical cycles and had other ecological impacts that have negatively affected species compositions.

Other notable evolutionary ecologists

• R. A. Fisher (1890–1962), whose 1930 fundamental theorem of natural selection recognised the power of rigorous application of the theory of natural selection to population biology.
• David Lack (1910–1973), a follower of Charles Darwin, worked to merge the fields of evolutionary biology and ecology, focusing mainly on birds and evolution.
• Thierry Lodé (1956–present), a French ecologist whose work focused on how sexual conflict in populations of species impacts evolution.

Research

Michael Rosenzweig's idea of reconciliation ecology was developed based on existing research, which was conducted on the principle first suggested by Alexander von Humboldt stating that larger areas of land will have increased species diversity as compared to smaller areas. This research focused on species-area relationships (SPARs) and the different scales on which they exist, ranging from sample-area to interprovincial SPARs. Steady-state dynamics in diversity gave rise to these SPARs, which are now used to measure the reduction of species diversity on Earth. In response to this decline in diversity, Rosenzweig's reconciliation ecology was born.

Evolutionary ecology has been studied using symbiotic relationships between organisms to determine the evolutionary forces by which such relationships develop. In symbiotic relationships, the symbiont must confer some advantage to its host in order to persist and continue to be evolutionarily viable. Research has been conducted using aphids and the symbiotic bacteria with which they coevolve. These bacteria are most frequently conserved from generation to generation, displaying high levels of vertical transmission. Results have shown that these symbiotic bacteria ultimately confer some resistance to parasites to their host aphids, which both increases the fitness of the aphids and lead to symbiont-mediated coevolution between the species.

Color variation in cichlid fish

The effects of evolutionary ecology and its consequences can be seen in the case of color variation among African cichlid fish. With over 2,000 species, cichlid fishes are very species-rich and capable of complex social interactions. Polychromatism, the variation of color patterns within a population, occurs within cichlid fishes due to environmental adaptations and to increase chances of sexual reproduction.

Quantum evolution

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Quantum_evolution

Quantum evolution is a component of George Gaylord Simpson's multi-tempoed theory of evolution proposed to explain the rapid emergence of higher taxonomic groups in the fossil record. According to Simpson, evolutionary rates differ from group to group and even among closely related lineages. These different rates of evolutionary change were designated by Simpson as bradytelic (slow tempo), horotelic (medium tempo), and tachytelic (rapid tempo).

Quantum evolution differed from these styles of change in that it involved a drastic shift in the adaptive zones of certain classes of animals. The word "quantum" therefore refers to an "all-or-none reaction", where transitional forms are particularly unstable, and thereby perish rapidly and completely. Although quantum evolution may happen at any taxonomic level, it plays a much larger role in "the origin taxonomic units of relatively high rank, such as families, orders, and classes."

Quantum evolution in plants

Usage of the phrase "quantum evolution" in plants was apparently first articulated by Verne Grant in 1963 (pp. 458-459). He cited an earlier 1958 paper by Harlan Lewis and Peter H. Raven, wherein Grant asserted that Lewis and Raven gave a "parallel" definition of quantum evolution as defined by Simpson. Lewis and Raven postulated that species in the Genus Clarkia had a mode of speciation that resulted

...as a consequence of a rapid reorganization of the chromosomes due to the presence, at some time, of a genotype conducive to extensive chromosome breakage. A similar mode of origin by rapid reorganization of the chromosomes is suggested for the derivation of other species of Clarkia. In all of these examples the derivative populations grow adjacent to the parental species, which they resemble closely in morphology, but from which they are reproductively isolated because of multiple structural differences in their chromosomes. The spatial relationship of each parental species and its derivative suggests that differentiation has been recent. The repeated occurrence of the same pattern of differentiation in Clarkia suggests that a rapid reorganization of chromosomes has been an important mode of evolution in the genus. This rapid reorganization of the chromosomes is comparable to the systemic mutations proposed by Goldschmidt as a mechanism of macroevolution. In Clarkia, we have not observed marked changes in physiology and pattern of development that could be described as macroevolution. Reorganization of the genomes may, however, set the stage for subsequent evolution along a very different course from that of the ancestral populations

Harlan Lewis refined this concept in a 1962 paper where he coined the term "Catastrophic Speciation" to describe this mode of speciation, since he theorized that the reductions in population size and consequent inbreeding that led to chromosomal rearrangements occurred in small populations that were subject to severe drought.

Leslie D. Gottlieb in his 2003 summary of the subject in plants stated

we can define quantum speciation as the budding off of a new and very different daughter species from a semi-isolated peripheral population of the ancestral species in a cross-fertilizing organism...as compared with geographical speciation, which is a gradual and conservative process, quantum speciation is rapid and radical in its phenotypic or genotypic effects or both.

Gottlieb did not believe that sympatric speciation required disruptive selection to form a reproductive isolating barrier, as defined by Grant, and in fact Gottlieb stated that requiring disruptive selection was "unnecessarily restrictive" in identifying cases of sympatric speciation. In this 2003 paper Gottlieb summarized instances of quantum evolution in the plant species Clarkia, Layia, and Stephanomeria.

Mechanisms

According to Simpson (1944), quantum evolution resulted from Sewall Wright's model of random genetic drift. Simpson believed that major evolutionary transitions would arise when small populations, that were isolated and limited from gene flow, would fixate upon unusual gene combinations. This "inadaptive phase" (caused by genetic drift) would then (by natural selection) drive a deme population from one stable adaptive peak to another on the adaptive fitness landscape. However, in his Major Features of Evolution (1953) Simpson wrote that this mechanism was still controversial:

"whether prospective adaptation as prelude to quantum evolution arises adaptively or inadaptively. It was concluded above that it usually arises adaptively . . . . The precise role of, say, genetic drift in this process thus is largely speculative at present. It may have an essential part or none. It surely is not involved in all cases of quantum evolution, but there is a strong possibility that it is often involved. If or when it is involved, it is an initiating mechanism. Drift can only rarely, and only for lower categories, have completed the transition to a new adaptive zone."

This preference for adaptive over inadaptive forces led Stephen Jay Gould to call attention to the "hardening of the Modern Synthesis", a trend in the 1950s where adaptationism took precedence over the pluralism of mechanisms common in the 1930s and 40s.

Simpson considered quantum evolution his crowning achievement, being "perhaps the most important outcome of [my] investigation, but also the most controversial and hypothetical."

Mathematical and theoretical biology

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Mathematical_and_theoretical_biology

Yellow chamomile head showing the Fibonacci numbers in spirals consisting of 21 (blue) and 13 (aqua). Such arrangements have been noticed since the Middle Ages and can be used to make mathematical models of a wide variety of plants.

Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to test scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.

Mathematical biology aims at the mathematical representation and modeling of biological processes, using techniques and tools of applied mathematics. It can be useful in both theoretical and practical research. Describing systems in a quantitative manner means their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter. This requires precise mathematical models.

Because of the complexity of the living systems, theoretical biology employs several fields of mathematics, and has contributed to the development of new techniques.

History

Early history

Mathematics has been used in biology as early as the 13th century, when Fibonacci used the famous Fibonacci series to describe a growing population of rabbits. In the 18th century, Daniel Bernoulli applied mathematics to describe the effect of smallpox on the human population. Thomas Malthus' 1789 essay on the growth of the human population was based on the concept of exponential growth. Pierre François Verhulst formulated the logistic growth model in 1836.

Fritz Müller described the evolutionary benefits of what is now called Müllerian mimicry in 1879, in an account notable for being the first use of a mathematical argument in evolutionary ecology to show how powerful the effect of natural selection would be, unless one includes Malthus's discussion of the effects of population growth that influenced Charles Darwin: Malthus argued that growth would be exponential (he uses the word "geometric") while resources (the environment's carrying capacity) could only grow arithmetically.

The term "theoretical biology" was first used as a monograph title by Johannes Reinke in 1901, and soon after by Jakob von Uexküll in 1920. One founding text is considered to be On Growth and Form (1917) by D'Arcy Thompson, and other early pioneers include Ronald Fisher, Hans Leo Przibram, Vito Volterra, Nicolas Rashevsky and Conrad Hal Waddington.

Recent growth

Interest in the field has grown rapidly from the 1960s onwards. Some reasons for this include:

• The rapid growth of data-rich information sets, due to the genomics revolution, which are difficult to understand without the use of analytical tools
• Recent development of mathematical tools such as chaos theory to help understand complex, non-linear mechanisms in biology
• An increase in computing power, which facilitates calculations and simulations not previously possible
• An increasing interest in in silico experimentation due to ethical considerations, risk, unreliability and other complications involved in human and animal research

Areas of research

Several areas of specialized research in mathematical and theoretical biology as well as external links to related projects in various universities are concisely presented in the following subsections, including also a large number of appropriate validating references from a list of several thousands of published authors contributing to this field. Many of the included examples are characterised by highly complex, nonlinear, and supercomplex mechanisms, as it is being increasingly recognised that the result of such interactions may only be understood through a combination of mathematical, logical, physical/chemical, molecular and computational models.

Abstract relational biology

Abstract relational biology (ARB) is concerned with the study of general, relational models of complex biological systems, usually abstracting out specific morphological, or anatomical, structures. Some of the simplest models in ARB are the Metabolic-Replication, or (M,R)--systems introduced by Robert Rosen in 1957–1958 as abstract, relational models of cellular and organismal organization.

Other approaches include the notion of autopoiesis developed by Maturana and Varela, Kauffman's Work-Constraints cycles, and more recently the notion of closure of constraints.

Algebraic biology

Algebraic biology (also known as symbolic systems biology) applies the algebraic methods of symbolic computation to the study of biological problems, especially in genomics, proteomics, analysis of molecular structures and study of genes.

Complex systems biology

An elaboration of systems biology to understand the more complex life processes was developed since 1970 in connection with molecular set theory, relational biology and algebraic biology.

Computer models and automata theory

A monograph on this topic summarizes an extensive amount of published research in this area up to 1986, including subsections in the following areas: computer modeling in biology and medicine, arterial system models, neuron models, biochemical and oscillation networks, quantum automata, quantum computers in molecular biology and genetics, cancer modelling, neural nets, genetic networks, abstract categories in relational biology, metabolic-replication systems, category theory applications in biology and medicine, automata theory, cellular automata, tessellation models and complete self-reproduction, chaotic systems in organisms, relational biology and organismic theories.

Modeling cell and molecular biology

This area has received a boost due to the growing importance of molecular biology.

• Mechanics of biological tissues
• Theoretical enzymology and enzyme kinetics
• Cancer modelling and simulation
• Modelling the movement of interacting cell populations
• Mathematical modelling of scar tissue formation
• Mathematical modelling of intracellular dynamics
• Mathematical modelling of the cell cycle
• Mathematical modelling of apoptosis

Modelling physiological systems

• Modelling of arterial disease
• Multi-scale modelling of the heart
• Modelling electrical properties of muscle interactions, as in bidomain and monodomain models

Computational neuroscience

Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is the theoretical study of the nervous system.

Evolutionary biology

Ecology and evolutionary biology have traditionally been the dominant fields of mathematical biology.

Evolutionary biology has been the subject of extensive mathematical theorizing. The traditional approach in this area, which includes complications from genetics, is population genetics. Most population geneticists consider the appearance of new alleles by mutation, the appearance of new genotypes by recombination, and changes in the frequencies of existing alleles and genotypes at a small number of gene loci. When infinitesimal effects at a large number of gene loci are considered, together with the assumption of linkage equilibrium or quasi-linkage equilibrium, one derives quantitative genetics. Ronald Fisher made fundamental advances in statistics, such as analysis of variance, via his work on quantitative genetics. Another important branch of population genetics that led to the extensive development of coalescent theory is phylogenetics. Phylogenetics is an area that deals with the reconstruction and analysis of phylogenetic (evolutionary) trees and networks based on inherited characteristics Traditional population genetic models deal with alleles and genotypes, and are frequently stochastic.

Many population genetics models assume that population sizes are constant. Variable population sizes, often in the absence of genetic variation, are treated by the field of population dynamics. Work in this area dates back to the 19th century, and even as far as 1798 when Thomas Malthus formulated the first principle of population dynamics, which later became known as the Malthusian growth model. The Lotka–Volterra predator-prey equations are another famous example. Population dynamics overlap with another active area of research in mathematical biology: mathematical epidemiology, the study of infectious disease affecting populations. Various models of the spread of infections have been proposed and analyzed, and provide important results that may be applied to health policy decisions.

In evolutionary game theory, developed first by John Maynard Smith and George R. Price, selection acts directly on inherited phenotypes, without genetic complications. This approach has been mathematically refined to produce the field of adaptive dynamics.

Mathematical biophysics

The earlier stages of mathematical biology were dominated by mathematical biophysics, described as the application of mathematics in biophysics, often involving specific physical/mathematical models of biosystems and their components or compartments.

The following is a list of mathematical descriptions and their assumptions.

Deterministic processes (dynamical systems)

A fixed mapping between an initial state and a final state. Starting from an initial condition and moving forward in time, a deterministic process always generates the same trajectory, and no two trajectories cross in state space.

• Difference equations/Maps – discrete time, continuous state space.
• Ordinary differential equations – continuous time, continuous state space, no spatial derivatives. See also: Numerical ordinary differential equations.
• Partial differential equations – continuous time, continuous state space, spatial derivatives. See also: Numerical partial differential equations.
• Logical deterministic cellular automata – discrete time, discrete state space. See also: Cellular automaton.

Stochastic processes (random dynamical systems)

A random mapping between an initial state and a final state, making the state of the system a random variable with a corresponding probability distribution.

• Non-Markovian processes – generalized master equation – continuous time with memory of past events, discrete state space, waiting times of events (or transitions between states) discretely occur.
• Jump Markov process – master equation – continuous time with no memory of past events, discrete state space, waiting times between events discretely occur and are exponentially distributed. See also: Monte Carlo method for numerical simulation methods, specifically dynamic Monte Carlo method and Gillespie algorithm.
• Continuous Markov process – stochastic differential equations or a Fokker–Planck equation – continuous time, continuous state space, events occur continuously according to a random Wiener process.

Spatial modelling

One classic work in this area is Alan Turing's paper on morphogenesis entitled The Chemical Basis of Morphogenesis, published in 1952 in the Philosophical Transactions of the Royal Society.

• Travelling waves in a wound-healing assay
• Swarming behaviour
• A mechanochemical theory of morphogenesis
• Biological pattern formation
• Spatial distribution modeling using plot samples
• Turing patterns

Mathematical methods

A model of a biological system is converted into a system of equations, although the word 'model' is often used synonymously with the system of corresponding equations. The solution of the equations, by either analytical or numerical means, describes how the biological system behaves either over time or at equilibrium. There are many different types of equations and the type of behavior that can occur is dependent on both the model and the equations used. The model often makes assumptions about the system. The equations may also make assumptions about the nature of what may occur.

Molecular set theory

Molecular set theory (MST) is a mathematical formulation of the wide-sense chemical kinetics of biomolecular reactions in terms of sets of molecules and their chemical transformations represented by set-theoretical mappings between molecular sets. It was introduced by Anthony Bartholomay, and its applications were developed in mathematical biology and especially in mathematical medicine. In a more general sense, MST is the theory of molecular categories defined as categories of molecular sets and their chemical transformations represented as set-theoretical mappings of molecular sets. The theory has also contributed to biostatistics and the formulation of clinical biochemistry problems in mathematical formulations of pathological, biochemical changes of interest to Physiology, Clinical Biochemistry and Medicine.

Organizational biology

Theoretical approaches to biological organization aim to understand the interdependence between the parts of organisms. They emphasize the circularities that these interdependences lead to. Theoretical biologists developed several concepts to formalize this idea.

For example, abstract relational biology (ARB) is concerned with the study of general, relational models of complex biological systems, usually abstracting out specific morphological, or anatomical, structures. Some of the simplest models in ARB are the Metabolic-Replication, or (M,R)--systems introduced by Robert Rosen in 1957–1958 as abstract, relational models of cellular and organismal organization.

Model example: the cell cycle

Main article: Cellular model

The eukaryotic cell cycle is very complex and has been the subject of intense study, since its misregulation leads to cancers. It is possibly a good example of a mathematical model as it deals with simple calculus but gives valid results. Two research groups  have produced several models of the cell cycle simulating several organisms. They have recently produced a generic eukaryotic cell cycle model that can represent a particular eukaryote depending on the values of the parameters, demonstrating that the idiosyncrasies of the individual cell cycles are due to different protein concentrations and affinities, while the underlying mechanisms are conserved (Csikasz-Nagy et al., 2006).

By means of a system of ordinary differential equations these models show the change in time (dynamical system) of the protein inside a single typical cell; this type of model is called a deterministic process (whereas a model describing a statistical distribution of protein concentrations in a population of cells is called a stochastic process).

To obtain these equations an iterative series of steps must be done: first the several models and observations are combined to form a consensus diagram and the appropriate kinetic laws are chosen to write the differential equations, such as rate kinetics for stoichiometric reactions, Michaelis-Menten kinetics for enzyme substrate reactions and Goldbeter–Koshland kinetics for ultrasensitive transcription factors, afterwards the parameters of the equations (rate constants, enzyme efficiency coefficients and Michaelis constants) must be fitted to match observations; when they cannot be fitted the kinetic equation is revised and when that is not possible the wiring diagram is modified. The parameters are fitted and validated using observations of both wild type and mutants, such as protein half-life and cell size.

To fit the parameters, the differential equations must be studied. This can be done either by simulation or by analysis. In a simulation, given a starting vector (list of the values of the variables), the progression of the system is calculated by solving the equations at each time-frame in small increments.

In analysis, the properties of the equations are used to investigate the behavior of the system depending on the values of the parameters and variables. A system of differential equations can be represented as a vector field, where each vector described the change (in concentration of two or more protein) determining where and how fast the trajectory (simulation) is heading. Vector fields can have several special points: a stable point, called a sink, that attracts in all directions (forcing the concentrations to be at a certain value), an unstable point, either a source or a saddle point, which repels (forcing the concentrations to change away from a certain value), and a limit cycle, a closed trajectory towards which several trajectories spiral towards (making the concentrations oscillate).

A better representation, which handles the large number of variables and parameters, is a bifurcation diagram using bifurcation theory. The presence of these special steady-state points at certain values of a parameter (e.g. mass) is represented by a point and once the parameter passes a certain value, a qualitative change occurs, called a bifurcation, in which the nature of the space changes, with profound consequences for the protein concentrations: the cell cycle has phases (partially corresponding to G1 and G2) in which mass, via a stable point, controls cyclin levels, and phases (S and M phases) in which the concentrations change independently, but once the phase has changed at a bifurcation event (Cell cycle checkpoint), the system cannot go back to the previous levels since at the current mass the vector field is profoundly different and the mass cannot be reversed back through the bifurcation event, making a checkpoint irreversible. In particular the S and M checkpoints are regulated by means of special bifurcations called a Hopf bifurcation and an infinite period bifurcation.