Introduces some simple reaction-diffusion equations to describe pattern formation in bacterial cells and biofilms including anomalous wave fronts, Turing patterns and the French flag model.

Considers how to track cells and molecules. Introduces tracking algorithms and statistical tools to analyse the resultant data.

Introduces models for biofilms including agent-based models, Vicsek models and cellular automata.

Describes a range of physical techniques that can be applied to bacterial biophysics including sample culture, flow cytometry, microscopy, photonics, NMR, mass spectrometry and electrophoresis.

Introduces the physical action of antibiotics and antiseptics including penetration through biofilms, persister cells, surface activity, physical sterilization and antibiofilm molecules.

Considers diffusion and statistical models for bacterial motility from the perspective of anomalous transport.

Gives a brief review of systems biology and synthetic biology with populations of bacteria.

The standard two-step scheme for modeling extracellular signals is to first compute the neural membrane currents using multicompartment neuron models (step 1) and next use the volume-conductor theory to compute the extracellular potential resulting from these membrane currents (step 2). We here give a brief introduction to the multicompartment modeling of neurons in step 1. The formalism presented, which has become the gold standard within the field, combines a Hodgkin-Huxley-type description of membrane mechanisms with the cable theory description of the membrane potential in dendrites and axons.

Readers who do not have strong schooling in physics can consult this book chapter for an introduction to key concepts such as ion fluxes, electric fields, electric potentials, and electric currents as well as for definitions of the ohmic, electrodiffusive, and capacitive currents that govern the electrodynamics of brain tissue. Building on the biophysical principles and approximations introduced here, we explain how the electric potential surrounding neurons can be computed based on the principles of current conservation and electroneutrality, and wegive a brief overview of modeling schemes designed to perform such computations on computers. Towards the end of the chapter, we show how the standard theory for computing extracellular potentials relates to Maxwell’s equations and list the approximations that we typically make when we apply these equations in a complex medium like brain tissue.

The standard two-step scheme for modeling extracellular signals is to first compute the neural membrane currents using multicompartment neuron models (step 1) and next use volume-conductor theory to compute the extracellular potential resulting from these membrane currents (step 2). In this chapter, we introduce ways to implement this scheme in computer simulations based on designated software such as LFPy, the NEURON simulator, or the Arbor simulator. We also introduce various methods for reducing the computational cost of simulating the extracellular potentials of large networks of neurons as well as introduce heuristic approximate signal prediction methods.

When a neuron fires an action potential, it causes a rapid fluctuation in the extracellular potential. This fluctuation is referred to as a spike and is normally “visible” only close to the neuron it originates from. Spikes are typically studied experimentally by high-pass filtering the extracellular potential. Here, we use computer simulations and approximate analytical formulas of spikes to explore how the amplitude and shape of spikes depend on various factors such as (i) the morphology of the neuron, (ii) the presence of active ion channels in the neuron’s dendrites, (iii) the part of the neuron (soma vs. dendrite) where the spike is recorded, (iv) the distance from the neuron the spike is recorded, and (v) the location in the neuron that the action potential is initiated. We also briefly discuss how the presence of the electrode can affect spike recordings as well as how to analyze data containing overlapping spikes from several neurons simultaneously.

The diffusion of ions in the extracellular space of the brain is normally assumed to have negligible effects on extracellular potentials. However, during periods of intense neural activity or in pathological conditions such as spreading depression, concentration gradients in brain tissue can become quite pronounced, and the effects of diffusion on electric potentials cannot be a priori neglected. We here present the theory for computing diffusion potentials, and we evaluate whether diffusion potentials can become “visible” within the frequency range considered in standard LFP recordings.