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The present chapter contains a brief introduction to membranes in living cells. This chapter describes the composition and functions of cell membranes and the functions of some of the organelles present in eukariotic cells. The presentation of biochemical and biological concepts provided in this book is quite simplified. It is directed to computer scientists, not biologists. This chapter's aim is to give sufficient background for the understanding of the biological processes and phenomena which inspired the considered models of membrane systems.

The Soma model simulates the origin of the resting potential in nerve cells. Because this model demonstrates steady-state conditions, or slow changes in the steady state, the membrane capacitance is ignored. In addition, there are no voltage- or time-dependent membrane conductances in this model. The equilibrium (Nernst) potentials for sodium, potassium, calcium, and chloride ions are calculated from the relevant ionic concentrations. The relationship between temperature and equilibrium potentials can be explored by altering the simulated temperature. This model also includes an electrogenic pump, which generates a net outflow of positive ions and therefore acts to hyperpolarize the membrane.

The Soma model illustrates the origins of the membrane potential based on the parallel conductance model, with the capacitor not included in the simulation. In addition, none of the membrane conductances are voltage dependent. This chapter describes the equations underlying the resting potential, based on the fundamental Nernst equation, which gives the relationship between ionic concentrations and electrical potential.

This chapter gives a very brief introduction to computability emphasising concepts playing an important role here. The chapter describes how in the 1920s the interest of Alan Turing in describing in mathematical terms the activity of computers, clerks performing computations, led to the definition of an abstract device called a Turing machine, to the start the study of computability and to the enunciation of the Church-Turing thesis. In a similar way the chapter indicates how in 2000 the internal organization of eukariotic cells inspired Gheorghe Păun to define membrane systems, also called P systems, where ‘P’ stands for ‘Păun’. Moreover, the chapter explains some of the advantages offered by membrane computing, the field of research using membrane systems to define computability models in order to study computation and computational complexity issues and to model processes of biology, linguistics, economics, etc., with respect to more classical approaches.

The complexity of behavior of single neurons derives from a number a factors: they have complicated shapes; voltage-dependent conductances have intricate properties, and the conductances are distributed across the membrane with non-uniform densities; and synaptic conductances operate on many different time scales. Furthermore, each type of neuron has its own repertoire of shape, channel distribution, synaptic receptors, and firing properties.

This chapter discusses several often-neglected areas of respirometry infrastructure. These include the correct selection of scrubber chemicals for removing water vapor and/or carbon dioxide from airstreams, without undesirable interactions; chemical-free scrubbing techniques such as selective membranes and thermal condensing systems; selecting tubing; evaluating the different tubing chemistries in light of the intended application; selecting appropriate tubing diameters; selecting tubing connectors; maintaining connector gender conventions, and other related topics.

This chapter discusses defects in transmembrane proteins. Topics covered include the endosomal/lysosomal v-ATPase, Niemann–Pick C disease, Batten disease, Salla disease, Danon disease, cystinosis, and mucolipidosis type IV. A theme beginning to emerge from studies of transmembrane proteins is the apparent complexity of their regulation and function(s). Disease pathogenesis is not caused simply by abnormal accumulation of metabolites. A fact that is often overlooked is that these proteins exhibit a symport or antiport activity in order to power transport. The importance of this activity and the consequences of disrupting it have not been addressed. However, these activities almost certainly balance and regulate the activity of the v-ATPase to maintain the delicate electrochemical gradient across the endosomal/lysosomal membranes.

This chapter describes transport processes in membrane systems. The emphasis is made on stationary processes, although some examples of the solution of the transport equations in transient conditions are also worked out. Homogeneous and porous membranes, both neutral and charged, are considered. The transport through neutral porous membranes under applied concentration gradients, electric current, and pressure gradient is described. The use of mass balances to analyse the changes in the bathing solution concentration receives particular attention. Donnan equilibria and the description of the electrical double layer at the membrane¦external solution interfaces are then presented. Transport through homogeneous charged membranes is thoroughly explained. The solution of the transport equations in multi-ionic systems is worked out in detail and applied to the study of classical topics, such as the bi-ionic potential and uphill transport. The influence of the diffusion boundary layers on the membrane permselectivity is analysed. Finally, transport through charged porous membranes is described from a very practical point of view. The space charge model is briefly explained.

This chapter explores the capacitative properties of biological membranes and provides ways to measure the membrane capacitance in striated muscle. The capacitance of a bilayer is inversely related to the chain length of its constituent hydrocarbons, and the latter is in turn proportional to bilayer thickness. The nature of the polar head groups does not greatly affect membrane capacitance. Skeletal muscle membranes form a network of 50-nm diameter branching tubules penetrating into the fibre whose lumina are continuous with extracellular fluid. Such a system would intrinsically have particular capacitative properties. Using the Laplace transform, a square-root relationship between membrane impedance properties and the input parameters is found. The ‘lumped’ four-component model offers the simplest available electrical description of striated muscle membrane geometry. In contrast, distributed models represent the transverse tubules as a cable system that allows radial voltage differences. Lattice models have proven useful in both the interpretation of the measurements of linear capacitances and the localization of non-linear charge to different regions of membrane. The chapter also discusses voltage-clamp methods for studying the dielectric properties of skeletal muscle. Each voltage-clamp method has characteristic advantages and limitations. The most appropriate equivalent circuit to represent the transverse tubular system remains incompletely resolved. The cable properties of tubular membrane necessitate an operational definition of measured effective capacitance arising from an application of the properties of the Laplace transform to a general circuit network. The studies suggest that, at least through the frequency range over which charge movements have been measured, the effective capacitance accurately reflects the properties of the actual electrical elements of surface or tubular membrane, given appropriate bathing solutions and voltage-clamp geometry.

This chapter provides simple kinetic treatments of intramembrane charge properties with a view to realistically characterizing underlying mechanisms, beginning with simple linear descriptions of the time course of capacity currents to provide limiting schemes as a basis for subsequent discussion. Simple linear models, or their direct variants, do not account for even major features of the membrane currents. Nevertheless, these models provide a useful starting point for further analysis. The chapter then introduces more complex, if somewhat speculative, descriptions that may form the basis for further investigation of voltage-regulated physiological processes. The basic rate equations are elaborated by higher-order terms. The formalisms implicit in this treatment can be adapted to a simple two-level model in which the intervening energy barrier would fall successively with ON charge transfer, so enhancing further charge movement. An analytic treatment of membrane dielectric behaviour is applied to the transient responses of striated muscle membrane obtained by small applied voltage steps. This is achieved through an extension of Fourier's integral theorem to discrete time series of infinite period. The frequency resolution obtained made it possible to attribute simple dielectric loss peaks and straightforward arc loci to the q _ß system. The Hodgkin-Huxley scheme is described and its limitations highlighted. Charge movements reflect configurational changes in integral membrane proteins exposed to the transmembrane electric field. Accordingly, a more general kinetic analysis is needed to examine their dielectric properties as a function of frequency at different potentials. The real part of such complex dielectric spectra would normally decline monotonically from a zero frequency value corresponding to the maximum available capacitative charge.

A specific kind of chemical reaction, biochemical reactions involving catalysts, inspired the model of membrane systems, called P systems with catalysts, are considered in this chapter. Some of these devices do not have several of the features shared by the majority of the models of membrane systems. For instance, the environment, a compartment with symbols present in an unbounded amount, is not present. Often also the underlying topological structure is absent, that is, it ‘collapses’ to just one compartment (so, no passage of symbols between compartments). The resulting membrane systems are then multiset rewriting systems.

This chapter considers P systems with active membranes, a model of membrane systems able to modify their underlying structure while computing: membranes, and related compartments, can be created or dissolved. This chapter describes how some biological process and phenomena have been of inspiration for the description of models of membrane systems that in turn allowed the definition of new computational complexity classes. The chapter presents results concerning the computational complexity of the resulting abstract systems.

Thanks to the pioneering experiments of the Italian physician Luigi Galvani, it has long been understood that electricity plays a vital role in the functioning of the nervous system. That these electrical signals are intrinsic to animal tissues was demonstrated by the German electrophysiologist du Bois Reymond, who showed that cells have a “resting” potential, the constant voltage across the cell membrane in the absence of stimulation. This chapter describes the Nernst equation, which predicts the strength of electrical potentials that arise from ionic concentrations differences across membranes. The fundamental role of the Nernst equation for electrophysiology is presented in relationship to the parallel conductance model for the cell membrane potential. Basic equations for resting potential, including the role of the electrogenic membrane ion pump, are presented.

Symmetry is key in solving many scientific and engineering problems. Drawing on examples from chemical engineering, this chapter illustrates how recognizing fractal scaling and other invariant patterns that envelop multiple scales is an excellent way to bridge multi-scale gaps. Such invariants are frequently observed in biological systems, which are only able to function thanks to the conservation of microscopic properties up to macroscopic scales in a scale-free way. Similarly, by imposing such invariant distributions in engineering designs, the advantages of microscopic (micro- or nanoscale) designs are preserved for macro-scale applications, while considerably reducing complexity and increasing efficiency. This holistic view helps to simplify multi-scale problems, and is proposed as a useful supplement to atomistic, bottom-up approaches.

Fast synaptic transmission is crucial for real-time functioning of the brain. All the receptor molecules that mediate fast transmission events are also ligand-gated ion channels, i.e., they are ion channels that undergo allosteric structural changes on binding a particular neurotransmitter molecule, resulting in the opening of the channel, the entry of selected ions into the neuron and subsequent signalling events. Their primary function is to receive signal input at postsynaptic membranes, where some also play central roles in synaptic plasticity. However, they are also found in postsynaptic membranes outside synapses, and in presynaptic terminals, where they are involved in the control of transmitter release. This chapter presents an overview of current knowledge of the molecular biology of these receptors.

The aqueous environments both inside and surrounding animal cells profoundly affect the structure and function of molecules and membranes. Solutes dissolved in water are surrounded by a shell of water molecules. The polarity of the water molecules in the shell is determined by the solute's ionic charge. The structure of proteins is profoundly affected by the activity of the water in which they reside, and by the types and quantities of ions present. The interactions of lipids with water are dominated by hydrophobic interactions. These interactions dictate the structure of membranes, and influence the locations and functions of proteins associated with membranes. The lipid bi-layer acts as a powerful barrier to trans-membrane movements. Proteins sited within the membrane can therefore play important roles as channels and transport moieties.

This chapter presents an autobiography of Shigetada Nakanishi. Nakanishi's early studies elucidated the characteristic precursor architectures of various neuropeptides and vasoactive peptides by introducing recombinant DNA technology. Subsequently, he established a novel functional cloning strategy for membrane receptors and ion channels by combining electrophysiology and Xenopus oocyte expression. He determined the molecular structure and elucidated the regulatory mechanisms of several peptide receptors as well as several G protein-coupled metabotropic-type and NMDA-type glutamate receptors. His early years, career, and achievements are discussed.