br Conflict of interest br Acknowledgements This work
Conflict of interest
Acknowledgements This work was supported by the Basic Science Research Program through the National Research Foundation (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1076117) and also by the Priority Research Centers Program through the NRF funded by the Ministry of Education (2012R1A6A1029029).
Introduction There is by now varied empirical evidence that enzyme action is accompanied by conformational dynamics of the enzyme–substrate complex, see Závodszky and Hajdí (2013), Nagel et al. (2011), and Eisenmesser et al. (2002). If several conformations are involved in catalysis a natural question is then whether each instance of the formation of the complex occurs in a fixed conformation that varies from instance to instance, or whether each instance is a quantum superposition of various conformations. In the latter case the complex is a small Schrödinger cat state. The set of states of various instances can be described by a density matrix either by states in fixed conformations or by states in superposition of conformations. We shall focus mainly on pure state to exhibit the underlying individual phenomena. The use of mixed states in quantum biology is common but needs a more nuanced treatment than what has usually been done. We return to this point later. Since all interactions will entangle some separated initial states, such cat states are expected to be ubiquitous. The question that remains is whether such superpositions play any role in catalysis. We must point out that even though we were led to this question by the established presence of conformation dynamics, which suggest a possibility of quantum superpositions, we are not directly considering the contributions of such dynamics (considered as classical motion) to catalysis. In fact, what these contribution might be is still debated. What we are asking is whether several conformations acting at once in a quantum superposition can affect catalysis. Dynamics in such a situation would not consist of classical motion and would have to be described by multipartite quantum evolution. An important consideration in the case of cat states is the effect of interactions with Eribulin mesylate outside of the complex, the so-called environment. These interactions will modify the initial cat state, and one possibility is that it can “decohere” to a one fixed conformation or other, but other processes are possible. Even under decoherence, given the time scales involved, the cat state may still offer quantum advantages to the catalytic process. It is generally argued that decoherence acts so quickly that no such quantum advantage can be had. Though estimates of decoherence rates generally uphold this view, we feel that such a conclusion may be premature. The cellular environment is fairly complex, heterogeneous, crowded and compartmentalized, presenting a quantum channel whose characteristics have not been well established. By now there is a large literature (too numerous to list) on environmental influences of a much more varied character than inhibiting certain quantum effects that would be present otherwise, but in fact acting to create, maintain, or facilitate them. A case in point is given by Burgarth et al. (2014) who show that “…even local noise can lead to an exponentially complex dynamics.” See also Mohseni et al. (2008) and Allegra et al. (2016) for an example in photosynthesis. Another possibility of long-lived quantum coherence in biological system is proposed by Vattay et al. (2014). Environmentally induced processes are ubiquitous in the cell, and could be considered a resource. If, as has now been argued in the literature, they can have enhancing effects on molecular processes, then natural selection could well provide an evolutionary pathway to their effective use. Cellular crowding is a major feature of living cells whose effect on cellular processes is still very poorly understood. Recent results show that one cannot reliably infer in vivo situations from in vitro results even with simulated crowding. For instance Smith et al. (2016) state “Our results contradict predictions from accepted theories of macromolecular crowding and show that cosolutes commonly used to mimic the cellular interior do not yield physiologically relevant information.” Crowding can have opposite effects depending on a given situation. As shown by Wilcox et al. (2016), crowding can either enhance or suppress enzyme activity depending on the substrate. We feel that reliable conclusions about environmental effect can only be obtained by in vivo experimental evidence or realistic in silico studies. Any decoherence related conjectures at this time would not have a secure basis and we have not considered them. For a recent, if not the first, realistic computer simulation of molecular crowding see Yu et al. (2016).