# Examination of Intermolecular Forces Influencing Headspace Analysis of Biological Samples
## 1 Introduction  
Complex living organisms, such as humans and animals, consist of billions of cells generating a wide variety of metabolites, from macromolecules (e.g., proteins) to small molecules (e.g., acids and ketones) as products of countless chemical reactions [1, 2]. A small portion of these small metabolites are volatile in nature. The study of volatile metabolites, while encompassing all living systems, has particularly focused on human metabolites, as it can enhance our understanding of biological processes within the human body in real time [3, 4]. Volatile metabolites emitted from the human body are complex mixtures influenced by both endogenous and exogenous factors. While the exact origin of these volatile metabolites has yet to be fully understood, several pathways contribute to their production. They arise from both normal and abnormal metabolic processes occurring within the body [5, 6, 7, 8], and are emitted in various forms, including skin emanations, urine, saliva, feces, and blood [9, 10]. Volatile metabolites comprise a chemically diverse group of small organic compounds, generally with a molecular weight in the range of 50-200 Daltons. They exhibit significant vapor pressure under ambient conditions, contributing to distinctive odors [11]. If studies using trained animal biosensors (e.g., dogs) are any indication [12; 13; 14], volatile metabolites can serve as chemical indicators for assessing human health status in a non-invasive manner [15; 16; 17]. While various technologies are employed to detect volatile metabolites, GC-MS is the most commonly used. Headspace sampling with SPME is highly effective for the qualitative or quantitative analysis of volatile compounds, offering minimal extraction steps and reducing column contamination from sample sources [18]. SPME, invented in the early nineties, enables the solventless extraction of volatile analytes from a wide range of matrices [19; 20]. It functions as a three-phase system, involving two key equilibria: (1) equilibrium between the sample and its headspace, and (2) equilibrium between the headspace and the fiber. Because of these independent equilibria, the ratio of any two metabolites in the sample may not be accurately represented on the SPME sorbent, as determined by the activity coefficients of the two compounds [21]. These deviations may arise from intermolecular forces and the interaction between the analyte and the solvent, or other solute molecules. The first interaction can be estimated from the octanol-water partition coefficient (K\({}_{\text{ow}}\)) which describes the hydrophilic or lipophilic nature of the compound [22]. For instance, the equilibrium of very lipophilic metabolites in blood will favor the sample over the headspace due to its increased solubility in the lipid-rich sample [23; 24]. Reactions with other solute molecules in the sample represent another factor influencing the first equilibrium. Chief among these in blood is the adsorption of small molecules to proteins present in the sample [25]. Human serum albumin (HSA), the most abundant binding protein in blood, is known to bind with a variety of substances, including fatty acids, bilirubin, drugs, and many other low-molecular-weight molecules [26; 27]. As a result, the amounts measured by headspace analysis reflect only the unbound portion of these molecules, not the total amounts present in samples. Biomarker discovery remains challenging due to this complex matrix effect [28]. In this study, we aimed to understand how interactions between volatile metabolites and components of the sample matrix affect detection and quantitation in headspace. Several volatile compounds in different sample media were investigated. Metabolite compounds selected in this study represent common small metabolites in biosamples. Lipid and serum solutions were used to simulate common biological sample conditions in biomarker discovery research. They were chosen in order to provide a range of equilibria between headspace and sample.