A simple model for synchronous firing of biological oscillators based on peskins model of the cardiac pacemaker mathematical aspects of heart physiology, courant institute of mathematical sciences, new york university, new york, 1975, pp. Breathing, pumping blood, chewing, and galloping are examples of rhythmic patterns of motion. By far the best understood biological oscillator is the circadian clock. In multicellular organisms, circadian oscillators are organized into multitissue systems which function as biological clocks that regulate the activities of the organism in relation to environmental cycles and provide an internal temporal framework. Examples where biological data show the presence of pairs of coupled oscillators are given in table 1. They are used to control every aspect of cell physiology, from signalling, motility and development to growth, division and death. This often contrasts with the lowdimensional dynamics. Biological oscillators drive essential physiological and developmental processes in all forms of life, from bacteria through vertebrates. For example if th of the output signal is fed back to be in phase with the input at a particular frequency, and the gain of the amplifier without feedback is 30 times or more, oscillation will take place. Networks of coupled oscillators william bechtel department of philosophy and center for chronobiology university of california, san diego adele a. For instance, excessive neural synchronization is thought to contribute to the motor symptoms including tremor and rigidity associated with parkinsons disease 24, 5, 19, loss of synchronization is thought to contribute.
For example, compared with natural biological oscillators, such as circadian oscillators 3840, the repres. One of the most spectacu lar examples of this kind of coupling can be seen along the tidal rivers ofma laysia, thailand and ew guinea. Macroscopic models and phase resetting of coupled biological. In each case, the scientific background is explained at an elemen. Macroscopic models for networks of coupled biological. Oscillations are abundant from hormonal oscillations with periods of days and months, to genetic fluctuations in the range of hours circadian clock, embryonic oscillators, and metabolic and biochemical oscillations in the order of minutes glycolytic oscillations and seconds calciumdynamics oscillations are central to biology across different temporal and spatial. Biological oscillators can be classified according to the topology of the positive and negativefeedback loops in the underlying regulatory mechanism. These biological oscillators span a wide range of periods and molecular forms, including neural spikes 1 ms10 s, cell cycles 10 min24 hr, somitogenesis 25 min for zebrafish and 2 hr for mice, and circadian clock 24 hr, etc. Crystal oscillators and applications a mechanical or electronic device that works on the principles of oscillation is an oscillator. Oscillatory behaviour is a systemslevel property of the interactions of genes, proteins and metabolites in the cell.
In 2000, elowitz and leibler, in a landmark study in synthetic biology, constructed the first genetic oscillator in escherichia coli. Generally, they can be designed using operational amplifier, resistor, and capacitor. Biological oscillators are not only complicated, but. Moreover, by presenting an algorithm and employing it into various examples, we. Abstract from cyanobacteria to human, sustained oscillations coordinate important biological functions. For example, the cell cycle pathway in kegg figure 1a contains hundreds of molecules. Design principles of biological oscillators through. Oct 30, 2008 biological oscillators can be classified according to the topology of the positive and negativefeedback loops in the underlying regulatory mechanism. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually. Many biological oscillators are stable against noise and perturbation e. Tuned oscillator circuits tuned oscillators use a parallel lc resonant circuit lc tank to provide the oscillations.
Pdf design principles of biochemical oscillators researchgate. A number of gene regulatory network examples with different kinetics and levels of detail are included in the s1 appendix. We consider specific examples of oscillatory processes and discuss four general. Early examples include the acidic bromate oxidation of. Biological oscillators can be classified according to the topology of the. Spontaneous synchronization of coupled oscillator systems. Analytical bounds on the critical coupling strength in a. More recently, oscillations involved in the segmentation of vertebrates 51 and oscillations of the tumor suppressor p53 52. Let g denote the inverse function f which exists since f is monotonic.
For example, a recent journal of experimental biology. Oscillators respond to stimuli at some times in their cycle and may not respond at others. Hernansaizballesteros1, luca cardelli2,3 and attila csikasznagy1,4 abstract background. The following examples show masking by a stimulus that does not entrain the circadian clock, masking in the.
Boolean computation using selfsustaining nonlinear. One of the most spectacular examples of this kind of coupling can be seen along the tidal rivers of ma laysia, thailand and new guinea. Switchlike and oscillatory dynamical systems are widely observed in biology. Hartley the resonant circuit is a tapped inductor or two inductors and one capacitor. The study of synchronization of coupled biological oscillators is fundamental to many areas of biology including neuroscience, cardiac dynamics, and circadian rhythms. May 24, 2005 oscillations are found throughout the physical and biological worlds. For most of the cases in table 1, the coupling between biological oscillators is made through communication via signaling messengers such as hormones and neurotransmitters fig. One of our main concerns is understanding how synchrony is achieved in locally interacting populations of oscillators, where synchrony means that oscillators have the same frequency and phase. Synchronization of globally coupled nonlinear oscillators. Tuned oscillators radio frequency oscillators 17 tuned oscillator is a circuit that generates a radio frequency output by using lc tuned resonant circuit.
Biological oscillators are amenable to qualitative analysis even before they have been described exhaustively in quantitative terms. Colpitts the resonant circuit is an inductor and two capacitors. Biological oscillators can be stoppedtopological study of a. Some examples of biological synchrony occur between organisms. Since logic values are encoded in phase, or time shift, switching between them does not, in principle, involve energy expenditure. Biological waves for single species model and multiplespecies model. The milestone here was to consider biological oscillators as phase oscillators, neglecting the amplitude. In this paper, a general approach for studying rings of coupled biological oscillators is presented. Feedback and oscillators tlt8016 basic analog circuits 20052006 2 9. Resetting central and peripheral circadian oscillators in. The oscillators, which provide an output having a sine wave form, are called sinusoidal or harmonic oscillators. We argue that transient resetting is a possible mechanism for the synchronization in many biological organisms, which might also be further used in medical therapy of rhythmic disorders. Biological and biochemical oscillators 1st edition. Oscillations are abundant from hormonal oscillations with periods of days and months, to genetic fluctuations in the range of hours circadian clock, embryonic oscillators, and metabolic and biochemical oscillations in the order of.
Findings from studying essential biological and synthetic oscillators have been applied in the development of effective drugs for clockrelated diseases 145,146 and other medical application. Coates 200720 frequency control in rf oscillators several different types of frequency control networks are used in high frequency sine wave oscillators. Chpater x how to build a biological oscillator oscillations are. Epstein department of chemistry, brandeis university, waltham, massachusetts 022549110. It is not a comprehensive description of all known biological oscillators, since this would require a much bigger volume as well as a different. Biological and biochemical oscillators compiles papers on biochemical and biological oscillators from a theoretical and experimental standpoint. We define a subclass of timed automata, called oscillator timed automata, suitable to model biological oscillators. Arguably, biological oscillations are a fundamental property of living systems. Introduction oscillators can be found in virtually every area of science and technology. Familiar examples of oscillation include a swinging pendulum and alternating current.
The final programme and poster listing, bus schedule and onsite handout with logistical information are now available for download symposium overview. This book discusses the oscillatory behavior, excitability, and propagation phenomena on membranes and membranelike interfaces. Oscillators can also be driven if the stimulus is strong or if the oscillator is. To investigate the organization of a mammalian circadian system, we constructed a transgenic rat line in which. Biological oscillators can be classified according to the topology of the positive and negative feedback loops in the underlying regulatory mechanism.
Examples on the synchronization of neural and circadian oscillators are presented to verify our hypothesis. The term vibration is precisely used to describe mechanical oscillation. Because of high frequencies, small inductance can be used for the radio frequency of oscillation. We shall only do the elementary analysis, for example, the linearized stability anal. Design principles of biochemical oscillators nature. Storti department of mechanical engineering university of washington seattle, washington 98195 usa july 11, 2000 abstract limit cycle oscillators arise in a wide variety of mechanical, electrical.
Oscillation is the repetitive variation, typically in time, of some measure about a central value often a point of equilibrium or between two or more different states. There are still many opening questions in biological oscillators, the understanding of which will be of both academic and clinical interest. Restrepo3 1department of electrical, computer, and energy engineering, university of colorado, boulder, colorado 80309, usa. Spontaneous synchronization of coupled oscillator systems with frequency adaptation dane taylor,1, edward ott,2 and juan g. The relationship between the model and real communities of biological oscillators is discussed. Systems and synthetic biology approaches in understanding. For readers interested in a thorough and detailed description of biological oscillators, the classical. Aside from these biological examples, there are manmade systems that exhibit the same kind of behavior. Here we explore design principles of biological oscillators from a. Circuit being 1 at some frequencies, resulting in oscillation.
Crystal oscillators these oscillators use quartz crystals and are used to generate highly stabilized output signal with frequencies up to 10 mhz. The experiment of phase shifts resulting from discrete perturbation of stable biological rhythms was developed by perkel and coworkers perkel et al. These pioneering studies illustrate that we have acquired enough biological understanding to begin programming cellular dynamics in a rational way. Incoherent inputs enhance the robustness of biological. Forward and reverse analysis irene oteromuras, julio r. Vii biological oscillators during class we consider the following two coupled differential equations. Circadian rhythms, heart beats, and brain waves are all examples of biological rhythms formed through the aggregation of the rhythmic contributions of thousands of cellular oscillations. Phase locking of biological oscillators to sinusoidal inputs 1 has been observed in a we do not consider the synchronization of biological oscillators to periodic pulsed inputs. Design principles of biological oscillators through optimization.
Qualitative analysis can identify the elements essential for generating the oscillations and can enhance our understanding of underlying oscillator mechanisms. In fact, mathematical models and computational approaches have already helped to build synthetic oscillators 58 we will refer here to this design problem as forward analysis. Properties and principles of entrainment exemplified by the neurosporacircadian clock till roenneberg, zdravko dragovic, and martha merrow centre for chronobiology, institute of medical psychology, medical faculty, university of munich, goethestrasse 31, d80336 munich, germany. Modeling, analysis, and control of biological oscillators rug. A simple model for phase locking of biological oscillators leon glass and michael c. It is a circuit that produces a repetitive waveform on its output with only dc supply as input. Mathematical models of these systems may involve hundreds of variables in thousands of individual cells resulting in an extremely highdimensional description of the system. A design principle underlying the synchronization of. Coates 200720 calculating a theoretical value for k involves some quite complex math, due to the number of factors affecting the mutual coupling and the process is often reduced to deciding either there is little mutual coupling, such that less than half of the magnetic flux produce by one. The practical applications of oscillators include computers, clocks, watches, radios etc. Formal approaches to understanding biological oscillators. Their interactions can result in a systematic process of synchronization called entrainment, which is distinct from a simple stimulusresponse pattern.
In each topics, we shall derive the biological models, then we do the nondimensional analysis to reduce the model to a simple model with fewer parameters. Indeed, synchrony is the most famil iar mode of organization for coupled oscillators. The electronic oscillators may be broadly classified into the following two categories. The piezo oscillator is an example of a crystal oscillator. Boolean computation using selfsustaining nonlinear oscillators. The associated analysis is independent of the mathematical details of the oscillators intrinsic. Many physiological behaviours of cells are repeated periodically in time, such as hormone secretion, second messenger signalling, celldivision cycles and circadian rhythms. Such oscillators can provide output at frequencies ranging from 20 hz to ghz. Tunedinput and tunedoutput oscillator tunedoutput tunedinput feedback coupling ci rf. Their mathematical analysis introduces the main features of the dynamic properties of biological oscillators and the mathematical techniques necessary for their investigation. We investigate the simplest biological switch that is composed of a single molecule that can be autocatalytically converted. Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states.
This thesis concerns the derivation and analysis of macroscopic mathematical models for coupled biological oscillators. In other words, oscillator can be defined as the periodic fluctuations between two things based on changes in energy. Such oscillators are phase shift and weinbridge oscillators. A mathematical model is presented for phase locking of a biological oscillator to a sinusoidal stimulus. The beststudied examples of genetic oscillators are circadian clocks and cell cycle oscillators. Synchronization of networked oscillators is a fascinating phenomenon with abundant examples in the biological sciences. Mackey department of physiology, mcgill university, 3655 drummond street, montreal, quebec, h3g 1y6, canada summary. Note that the signals are denoted as xi, xf, xo, and so on.
In this case, the interaction between two oscillators that are moving in synchrony is minimal. The more steep these regulation functions for example the higher their hill coefficient the stronger the feedback. Biochemical oscillations occur in many contexts metabolism, signaling, development, etc. Modelling biological oscillations limit circle oscillation. Theme coupled oscillators provide a useful paradigm for the study of collective behavior of large complex systems a wonderful world to be in full of interesting mathematical challenges and novel applications physics, chemistry, biology, economics. This approach, which is grouptheoretic in nature, is based on the finding that symmetric ring networks of coupled nonlinear oscillators possess generic patterns of phaselocked oscillations. Single molecules can operate as primitive biological sensors. Tyson abstract cellular rhythms are generated by complex interactions among genes, proteins and metabolites. With the help of several examples of oscillators from various physical domains, we illustrate the techniques involved, and also demonstrate the effectiveness and limitations of describing functions for oscillator analysis.
A simple model for phase locking of biological oscillators. Following these studies, the quantitative approaches have been applied to the discovery and characterization of many more oscillators. To illustrate how such translations can be implemented, three biological oscillators are described schematically. A numerical investigation of phaselocked and chaotic. Positive feedback amplifiers oscillators lc and crystal. Modeling the resonant release of synaptic transmitter by hair cells as an example of biological oscillators with cooperative steps. A grouptheoretic approach to rings of coupled biological. Synchronization of pulsecoupled biological oscillators.