Volume-Energy Correlations in the Slow Degrees of Freedom of Computer-Simulated Phospholipid Membranes

Abstract

Constant-pressure molecular-dynamics simulations of phospholipid membranes in the fluid Lα phase reveal strong correlations between equilibrium fluctuations of volume and energy on the nanosecond time-scale. The existence of strong volume-energy correlations was previously deduced indirectly by Heimburg from experiments focusing on the phase transition between the Lα and the L β phases. The correlations, which are reported here for three different membranes (DMPC, DMPS-Na, and DMPSH), have volume-energy correlation coefficients ranging from 0.81 to 0.89. The DMPC membrane was studied at two temperatures showing that the correlation coefficient increases as the phase transition is approached.Biological membranes are essential parts of living cells. They not only act as passive barriers between outside and inside, but also play an active role in various biological mechanisms. The major constituent of biological membranes are phospholipids. Pure phospholipid membranes often serve as a models for the more complex biological membranes. Close to physiological temperatures membranes undergo a transition from the high-temperature fluid L α phase (often referred to as the "biologically relevant phase") to a low-temperature ordered gel phase L β . In the melting regime response functions such as heat capacity, volume-expansion coefficient, and area-expansion coefficient increase dramatically. Also, the characteristic time for the collective degrees of freedom increases and becomes longer than milliseconds. Some time ago Heimburg found that the slow, dominating parts of heat capacity and volume-expansion coefficient of DMPC as a function of temperature can be superimposed close to the melting temperature T m [1] (see also Refs. 2 and 3). Thus the response functions are related in such a way that a single function describes the temperature dependence of both.The fluctuation-dissipation (FD) theorem connects (linear) response functions to equilibrium fluctuations. The isobaric heat capacity c p can be calculated from enthalpy fluctuations as follows:2 ), where . . . is an average in the constant temperature and pressure ensemble and ∆ is deviation from the average value. Similarly, volume fluctuations are connected to the isothermal volume compressibility by the expression κ T = (∆V ) 2 /(V k B T ). If the response functions were described by a single parameter, fluctuations are also described by a single parameter [1,4] and the microstates were connected via the relation ∆H i = γ vol ∆V i . At constant pressure this relation applies if and only if ∆E i = γ vol ∆V i (where E is energy), which is the relation investigated below. This situation is referred to as a that of a single-parameter description [4]. A single-parameter description applies to a good approximation for several models of van der Waals bonded liquids as well as for experimental super-critical argon [5].Unfortunately, molecular-dynamics simulations are not possible for investigating "single parameter"-ness of membranes close to T m , because the relaxation ti...

Correlated Volume−Energy Fluctuations of Phospholipid Membranes: A Simulation Study

“…The correlation strengths are calculated for a range of time scales. We show that V − U fluctuations correlate strongly, but only on long time scales [32]. We also investigate how well membrane area as well as chain orderparameter fluctuations correlate with V and U fluctuations; such correlations are generally weak.…”

Hidden Scale Invariance in Condensed Matter

“…25,28−31 For constant-volume fluctuations the c(r/σ) term contributes little to the W and U fluctuations because if a particle is moved, some of its nearest-neighbor distances decrease and some increase, with the result that their sum is almost unchanged. 25 This explains the strong WU correlations for LJ-type systems but not why strong correlations are observed also in more complex systems like the Lewis−Wahnstrom ortho-terphenyl (OTP) model (three rigidly connected LJ spheres with a 75°b ond angle 32,33 ), the rigid-bond flexible LJ-chain model, 34 a seven-atom toluene model, 23 the slow degrees of freedom of an all-atom biomembrane model, 35,36 etc. This paper, however, focuses on the consequences of strong WU correlations, not their origin for which a general theory does not yet exist.…”

“…This explains the strong WU correlations for LJ-type systems but not why strong correlations are observed also in more complex systems like the Lewis–Wahnström ortho -terphenyl (OTP) model (three rigidly connected LJ spheres with a 75° bond angle , ), the rigid-bond flexible LJ-chain model, a seven-atom toluene model, the slow degrees of freedom of an all-atom biomembrane model, , etc. This paper, however, focuses on the consequences of strong WU correlations, not their origin for which a general theory does not yet exist.…”