Sharp, localized phase transitions in single neuronal cells

Phase-State-Dependent Silica Nanoparticle Uptake of Giant Unilamellar Vesicles

We quantify endocytosis-like nanoparticle (NP) uptake of model membranes as a function of temperature and, therefore, phase state. As model membranes, we use giant unilamellar vesicles (GUV) consisting of 1,2-dipentadecanoyl-sn-glycero-3-phosphocholine (15:0 PC). Time-series micrographs of the vesicle shrinkage show uptake rates that are a highly nonlinear function of temperature. A global maximum appears close to the main structural phase transition at T = Tm + 3 K = 37 °C and a minor peak at the pretransition T = Tp = 22 °C. The quality of linear fits to the shrinkage, and thus uptake kinetics, reveals a deviation from the linear trend at the vesicle shrinkage peaks. Taking values for the bending modulus as a function of temperature from literature and Helfrich's model allows us to draw qualitative conclusions on the membrane tension and the adhesion of the NP to the membrane as a function of temperature. These findings provide valuable insights into the dynamic interplay between temperature, membrane phase transitions, and NP uptake, shedding light on the complex behavior of biological membranes.

Nonlinear Growth Dynamics of Neuronal Cells Cultured on Directional Surfaces

During the development of the nervous system, neuronal cells extend axons and dendrites that form complex neuronal networks, which are essential for transmitting and processing information. Understanding the physical processes that underlie the formation of neuronal networks is essential for gaining a deeper insight into higher-order brain functions such as sensory processing, learning, and memory. In the process of creating networks, axons travel towards other recipient neurons, directed by a combination of internal and external cues that include genetic instructions, biochemical signals, as well as external mechanical and geometrical stimuli. Although there have been significant recent advances, the basic principles governing axonal growth, collective dynamics, and the development of neuronal networks remain poorly understood. In this paper, we present a detailed analysis of nonlinear dynamics for axonal growth on surfaces with periodic geometrical patterns. We show that axonal growth on these surfaces is described by nonlinear Langevin equations with speed-dependent deterministic terms and gaussian stochastic noise. This theoretical model yields a comprehensive description of axonal growth at both intermediate and long time scales (tens of hours after cell plating), and predicts key dynamical parameters, such as speed and angular correlation functions, axonal mean squared lengths, and diffusion (cell motility) coefficients. We use this model to perform simulations of axonal trajectories on the growth surfaces, in turn demonstrating very good agreement between simulated growth and the experimental results. These results provide important insights into the current understanding of the dynamical behavior of neurons, the self-wiring of the nervous system, as well as for designing innovative biomimetic neural network models.

Thinking about the action potential: the nerve signal as a window to the physical principles guiding neuronal excitability

Ever since the work of Edgar Adrian, the neuronal action potential has been considered as an electric signal, modeled and interpreted using concepts and theories lent from electronic engineering. Accordingly, the electric action potential, as the prime manifestation of neuronal excitability, serving processing and reliable "long distance" communication of the information contained in the signal, was defined as a non-linear, self-propagating, regenerative, wave of electrical activity that travels along the surface of nerve cells. Thus, in the ground-breaking theory and mathematical model of Hodgkin and Huxley (HH), linking Nernst's treatment of the electrochemistry of semi-permeable membranes to the physical laws of electricity and Kelvin's cable theory, the electrical characteristics of the action potential are presented as the result of the depolarization-induced, voltage- and time-dependent opening and closure of ion channels in the membrane allowing the passive flow of charge, particularly in the form of Na+ and K+ -ions, into and out of the neuronal cytoplasm along the respective electrochemical ion gradient. In the model, which treats the membrane as a capacitor and ion channels as resistors, these changes in ionic conductance across the membrane cause a sudden and transient alteration of the transmembrane potential, i.e., the action potential, which is then carried forward and spreads over long(er) distances by means of both active and passive conduction dependent on local current flow by diffusion of Na+ ion in the neuronal cytoplasm. However, although highly successful in predicting and explaining many of the electric characteristics of the action potential, the HH model, nevertheless cannot accommodate the various non-electrical physical manifestations (mechanical, thermal and optical changes) that accompany action potential propagation, and for which there is ample experimental evidence. As such, the electrical conception of neuronal excitability appears to be incomplete and alternatives, aiming to improve, extend or even replace it, have been sought for. Commonly misunderstood as to their basic premises and the physical principles they are built on, and mistakenly perceived as a threat to the generally acknowledged explanatory power of the "classical" HH framework, these attempts to present a more complete picture of neuronal physiology, have met with fierce opposition from mainstream neuroscience and, as a consequence, currently remain underdeveloped and insufficiently tested. Here we present our perspective that this may be an unfortunate state of affairs as these different biophysics-informed approaches to incorporate also non-electrical signs of the action potential into the modeling and explanation of the nerve signal, in our view, are well suited to foster a new, more complete and better integrated understanding of the (multi)physical nature of neuronal excitability and signal transport and, hence, of neuronal function. In doing so, we will emphasize attempts to derive the different physical manifestations of the action potential from one common, macroscopic thermodynamics-based, framework treating the multiphysics of the nerve signal as the inevitable result of the collective material, i.e., physico-chemical, properties of the lipid bilayer neuronal membrane (in particular, the axolemma) and/or the so-called ectoplasm or membrane skeleton consisting of cytoskeletal protein polymers, in particular, actin fibrils. Potential consequences for our view of action potential physiology and role in neuronal function are identified and discussed.

Characterizing Oscillatory and Excitability Regimes in a Protein-Free Lipid Membrane

Observations of electric potential oscillations in artificial lipid bilayers near the order-disorder transition indicate the existence of a stable limit cycle and, therefore, the possibility of producing excitable signals close to the bifurcation. We present a theoretical investigation of membrane oscillatory and excitability regimes induced by an increase in ion permeability at the order-disorder transition. The model accounts for the coupled effects of state-dependent permeability, membrane charge density, and hydrogen ion adsorption. A bifurcation diagram shows a transition between fixed-point and limit cycle solutions, enabling both oscillatory and excitability responses at different values of the acid association parameter. Oscillations are identified in terms of the membrane state, electric potential difference, and ion concentration near the membrane. The emerging voltage and time scales agree with measurements. Excitability is demonstrated by applying an external electric current stimulus, and the emerging signals display a threshold response and the appearance of repetitive signals upon using a long-lasting stimulus. The approach highlights the important role of the order-disorder transition, enabling membrane excitability in the absence of specialized proteins.

Tuning Targeted Liposome Avidity to Cells via Lipid Phase Separation

The addition of both cell-targeting moieties and polyethylene glycol (PEG) to nanoparticle (NP) drug delivery systems is a standard approach to improve the biodistribution, specificity, and uptake of therapeutic cargo. The spatial presentation of these molecules affects avidity of the NP to target cells in part through an interplay between the local ligand concentration and the steric hindrance imposed by PEG molecules. Here, we show that lipid phase separation in nanoparticles can modulate liposome avidity by changing the proximity of PEG and targeting protein molecules on a nanoparticle surface. Using lipid-anchored nickel-nitrilotriacetic acid (Ni-NTA) as a model ligand, we demonstrate that the attachment of lipid anchored Ni-NTA and PEG molecules to distinct lipid domains in nanoparticles can enhance liposome binding to cancer cells by increasing ligand clustering and reducing steric hindrance. We then use this technique to enhance the binding of RGD-modified liposomes, which can bind to integrins overexpressed on many cancer cells. These results demonstrate the potential of lipid phase separation to modulate the spatial presentation of targeting and shielding molecules on lipid nanocarriers, offering a powerful tool to enhance the efficacy of NP drug delivery systems.

The excitable fluid mosaic

The Fluid Mosaic Model by Singer & Nicolson proposes that biological membranes consist of a fluid lipid layer into which integral proteins are embedded. The lipid membrane acts as a two-dimensional liquid in which the proteins can diffuse and interact. Until today, this view seems very reasonable and is the predominant picture in the literature. However, there exist broad melting transitions in biomembranes some 10-20 degrees below physiological temperatures that reach up to body temperature. Since they are found below body temperature, Singer & Nicolson did not pay any further attention to the melting process. But this is a valid view only as long as nothing happens. The transition temperature can be influenced by membrane tension, pH, ionic strength and other variables. Therefore, it is not generally correct that the physiological temperature is above this transition. The control over the membrane state by changing the intensive variables renders the membrane as a whole excitable. One expects phase behavior and domain formation that leads to protein sorting and changes in membrane function. Thus, the lipids become an active ingredient of the biological membrane. The melting transition affects the elastic constants of the membrane. This allows for the generation of propagating pulses in nerves and the formation of ion-channel-like pores in the lipid membranes. Here we show that on top of the fluid mosaic concept there exists a wealth of excitable phenomena that go beyond the original picture of Singer & Nicolson.¹.

Evidence for a transition in the cortical membranes of Paramecium

Ever since the pioneering studies in the 1960s and 70s, the importance of order transitions for cell membrane functions has remained a matter of debate. Recently, it has been proposed that the nonlinear stimulus-response curve of excitable cells, which manifests in all-or-none pulses (action potentials (AP)), is due to a transition in the cell membrane. Indeed, evidence for transitions has accumulated in plant cells and neurons, but studies with other excitable cells are expedient in order to show if this finding is of a general nature. Herein, we investigated intact, motile specimens of the "swimming neuron" Paramecium. The cellular membranes were labelled with the solvatochromic fluorophores LAURDAN or Di-4-ANEPPDHQ. Subsequently, a cell was trapped in a microfluidic channel and investigated by fluorescence spectroscopy. The generalized polarization (GP) of the fluorescence emission from cell cortical membranes (probably plasma and alveolar membranes) was extracted by an edge-finding algorithm. The thermo-optical state diagram, i.e. the dependence of GP on temperature, exhibited clear indications for a reversible transition. This transition had a width of ~10-15 °C and a midpoint that was located ~4 °C below the growth temperature. The state diagrams with LAURDAN and Di-4-ANEPPDHQ had widely identical characteristics. These results suggested that the cortical membranes of Paramecium reside in an order transition regime under physiological growth conditions. Based on these findings, membrane potential fluctuations, spontaneous depolarizing spikes, and thermal excitation of Paramecium was interpreted.

The thermodynamic soliton theory of the nervous impulse and possible medical implications

The textbook picture of nerve activity is that of a propagating voltage pulse driven by electrical currents through ion channel proteins, which are gated by changes in voltage, temperature, pressure or by drugs. All function is directly attributed to single molecules. We show that this leaves out many important thermodynamic couplings between different variables. A more recent alternative picture for the nerve pulse is of thermodynamic nature. It considers the nerve pulse as a soliton, i.e., a macroscopic excited region with properties that are influenced by thermodynamic variables including voltage, temperature, pressure and chemical potentials of membrane components. All thermodynamic variables are strictly coupled. We discuss the consequences for medical treatment in a view where one can compensate a maladjustment of one variable by adjusting another variable. For instance, one can explain why anesthesia can be counteracted by hydrostatic pressure and decrease in pH, suggest reasons why lithium over-dose may lead to tremor, and how tremor is related to alcohol intoxication. Lithium action as well as the effect of ethanol and the anesthetic ketamine in bipolar patients may fall in similar thermodynamic patterns. Such couplings remain obscure in a purely molecular picture. Other fields of application are the response of nerve activity to muscle stretching and the possibility of neural stimulation by ultrasound.