Time from Semiosis: E-series Time for Living Systems

Inter-Subjective Punctuation

We know that “tick marks” can be set simultaneously by more than one living subject inter-subjectively. “Inter-subjective” refers to the processes taking place among living organisms or among parts of a system, which can also be phrased as “inter-agential” or simply “interactive.” Inter-subjective agents are here called the second-person negotiators.

Imagine two percussionists jointly performing, or two kittens being playful with each other. Both achieve their collective action – music or play – by mutually coordinating their physical movements and timing of actions. Neither comes to form itself as an organized whole without coordination. The coordination (i.e., inter-subjective punctuation) is time alignment formed and maintained interactively in the local setting. Inter-subjective punctuation as an alignment of time roughly corresponds to synchronization.

The second-person negotiators such as the percussionists and kittens mutually approach synchronization by making communicative moves to each other. The negotiation permits each participant to mutually attend to the punctuations made by its partner. Without assuming the completed result (i.e., objective time), the negotiators follow and act upon each other’s movement to jointly mold of their temporality. The difference between the third-person observer and the second-person negotiators is substantial. Despite the privilege to declare time objectively, the third-person observer has no room or duration of temporality in which mutual interference and disturbance among the local participants are allowed to prevail, even temporarily.

Thus, another type of punctuation is a candidate for a different type of time in addition to subjective and objective time. We call the inter-subjective or inter-agential method of punctuating for synchronization “E-series time” (Nomura 2010; Nomura et al. 2015; Nomura and Matsuno 2016a, b). E-series time is the consequence of local acts of synchronization of an interactive nature and is accessible to the second-person negotiators but not to the third-person observer.

The second-person negotiators and the third-person observer differ sharply in their views of the present time. While the present time is an invariant point in the present tense for the third-person observer (in the objective time), it is a negotiable temporal zone of “now” for the second-person negotiators (in E-series time). The moment of “now” enables local participants to experience and then revise those mutual interferences and disturbances. Revising the interferences and disturbances can thus guarantee updates to acts of punctuation.

Synchronicity as Time

How then can we relate synchronicity to time? My watch, for example, is roughly synchronized with yours, as well as with the one at the Greenwich Observatory. We also have a long history of counting 24 h based on the Earth’s rotation, synchronizing our time with physical occurrence. Today, our objective time is synchronized with an electronic transition frequency of a cesium atomic clock, which we might call global synchrony. On the other hand, our subjective time is synchronized with our own sense of the past, present, and future. The experienced events may be dotted on our tense scale, whose congruence is an essential part of our sanity. Thus, both the objective and subjective times can be seen as sign activities of synchronization.

How then is the inter-subjective time (of the E-series) related to synchronization? Think of a pair of good dancers whose steps make their performance smooth and closely coordinated. Each step is a punctuation of his/her own dance, as well as a message to the partner about how he/she is going to move. Each step as a punctuation is a boundary between what has occurred and what is going to occur next. What is required for the two to be in place is mutual adjustment of time in order to make up a unified whole that is constantly in its own making.

Human interactions are filled with synchronization. Our conversation, too, presupposes such coordinated actions through intricate mutual maneuvering among speakers: taking turns in utterance, nodding, or the exchange of other nonverbal cues (Sacks et al. 1974). Conversation requires incessant co-adjustment of timing as if dancing. Such co-adjustment is accessible exclusively in second-person negotiations.

Whether it is dance or conversation, both require local management of time apart from the objective time. Metaphorically speaking, dancing or conversation is considered to be a clock. The underlying question is how to make a larger clock from the interferences between two smaller clocks. The time adopted here is jointly generated by local synchronization, not by the global synchrony of wristwatches.

In biology, many organisms have built-in clocks (e.g., circadian clocks) based on the working of clock genes, producing automatic oscillations of approximately 24 h (circadian rhythm). In mammals, a minute region in the brain called the suprachiasmatic nucleus (SCN) resets internal clocks scattered throughout the body according to light signals from the sun. The resetting of a great number of internal clocks indicates rough synchronization within the single organism.

A-Series Time Code

The key factor of the A-series time code is tense: a sense of duration or an unbroken succession of events, which is equivalent to one’s past, present, and future. The A-series corresponds to the subjective time, assuming a single agent having access to its own memory and anticipation. When such flow of time is sensed by the first-person agency, time appears to him/her in the A-series. A-series time code is not interactive but intra-agential.

B-Series Time Code

B-series time code is tense-less -- there is no indication of the past, present, and future. It only shows the relations of earlier/later or before/after to be grasped in the third-person panoramic view, which corresponds to objective time. When punctuated sequences of events are seen from the perspective of earlier/later relations in this panoramic view, time appears to the third-person observer to be in the B-series. B-series time code is unidirectional and does not assume our participation. Ordinary clocks are such an example.

Note that the genesis of the earlier/later relation is basically subsumed under the tense code: the past, present, and future. When someone walks on the street, the footing of before/after is similar to a living organism differentiating the definiteness in retrospect from the indefiniteness in prospect. Thus, such before/after relations are a part of A-series time, since we can observe tense there in the rudimentary sense. This was the point McTaggart (1908) himself realized; that is, it is self-contradictory to admit definite tenses as a matter of principle on one hand and to say the B-series is derivable from the tense-based A-series on the other. Although McTaggart’s philosophical argument suggests the unreality of time, our study comes to reshuffle the basis of time from its a priori linear progression to semiotic activities.

C-series Time Code

C-series time code, being a static array, indicates neither tense nor earlier/later relations. The punctuations (i.e., tick marks) displayed by clock dials, calendars, timetables, musical scores, and the like themselves are static pictures. A clock’s hands show a simple circular motion. Calendars are composed of equally spaced squares, and timetables are simply a list of numbers. Such time-related compositions – lists, sequences, and patterns – belong to the C-series time code. C-series time code does not assume change – it is “time before time” or simply “pictured time.”

A metronome does not necessarily measure time but can simply be a clicking device. It depends on the interpreter. A metronome itself as a gadget is neither in the B-series nor C-series. If a metronome is seen as an external clock to tell correct time intervals, it appears to be in B-series toward the observer. Of course, it remains in the C-series if viewed simply as a tempo-changing toy.

E-series Time Code

E-series time refers to inter-agential or interactive time.

Cellular Circadian Clocks in Plants

The circadian clock is an endogenous timing device based on self-sustained daily rhythms. The rhythms are generated by gene circuits comprised of feedback loops (Pokhilko et al. 2012). Employing a bioluminescent reporter system (AtCCA1::LUC+) using a particle bombardment method, bioluminescent rhythms –endogenous circadian rhythms – are observed in intact duckweed (Lemna gibba) cells (Muranaka and Oyama 2016). Each luminesced cell displays the timing of its luminescence peak (i.e., punctuation) reflecting the inner “voices” of clock genes as the first-person agency (see Fig. 2). Each cell times its gene expressions, generating rhythms that assume a short-spanned tense.

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We thus propose that the feedback loop of the gene circuit can be roughly considered a C-series time code. Fig. 2 shows the organism’s design, which is illustrated by the researcher as a synchronic picture. However, the plant must interpret this to use it diachronically. If not used, the static picture remains as is, as shown in Fig. 2. However, if it is utilized (by a meaning-making organism), the status changes from a static array to an actual chart for behavior, that is, a “scenario” (Hoffmeyer 1996). Regarding meaning-making organisms, C-series time code functions as a “pre-scenario” or a “pre-story” of time, out of which an organism brings its own meanings.

In this way, the sequence of gene expression is “semi-prescribed” in the form of a C-series time code. Each cell reads the chart inscribed in the time code, generating its own rhythms in the A-series, which possess tense. However, the result recorded by scientists, which is the actual sequence of gene expression, gets transformed into the B-series, in which the order of its activation has been fixed.

Under constant light conditions, the rhythm of a single duckweed cell is meaningful only for that particular cell. Each cellular rhythm oscillates with its own period (ranging from 18 h to 28 h) without being affected by neighboring cells. Under light/dark conditions, however, the state of cellular clocks changes remarkably (see Fig. 3). The rhythms of duckweed cells synchronize (or are entrained) to light/dark cycles, and their periods are approximately 24 h (Muranaka and Oyama 2016).

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Furthermore, the cells are found to interact with their neighboring cells. The cells mutually observe the rhythms of others in the vicinity, creating spatial patterns for those sharing similar timing of punctuation (i.e., peak times). Thus, the time code used is that of the E-series.

Kai Protein Oscillators in Cyanobacteria

An example of a circadian clock can also be found in cyanobacteria (Synechococcus elongatus PCC 7942). In the case of duckweeds, circadian rhythms are the result of a gene circuit. In cyanobacteria, in addition to the gene expression of kai clock genes occurring through transcription-translation, circadian rhythms are produced by Kai proteins themselves, which are the products of kai genes.

The three genes generating circadian rhythms are kaiA, kaiB, and kaiC (Ishiura et al. 1998). Circadian clocks in cyanobacteria were experimentally identified when KaiA, KaiB, and KaiC were mixed together with adenosine triphosphate (ATP) in vitro, and the phosphorylation and dephosphorylation cycle of KaiC proteins showed clear circadian oscillations (Nakajima et al. 2005; Tomita et al. 2005).

KaiC is the central molecule among these three proteins that constitute the circadian clock. When ATP is provided, KaiC forms a hexamer that engages in auto-phosphorylation and auto-dephosphorylation activities (Nakajima et al. 2005; Nishiwaki et al. 2007; Rust et al. 2007). KaiA and KaiB interact with the KaiC hexamer, and each alters the level of phosphorylation – the former helps facilitate auto-phosphorylation, and the latter inhibits the effects of KaiA (Iwasaki et al. 2002; Williams et al. 2002; Kitayama et al. 2003; Xu et al. 2003).

When the circadian oscillation of Kai proteins is experimentally reconstituted, circadian rhythms are observed in each process of regulation: (1) auto-phosphorylation and auto-dephosphorylation activities (Nakajima et al. 2005; Nishiwaki et al. 2007; Rust et al. 2007), (2) conformational changes of the KaiC hexamer (Chang et al. 2011; Murayama et al. 2011; Chang et al. 2012), (3) interactions between Kai proteins and complex formation (Kageyama et al. 2006; Akiyama et al. 2008; Qin et al. 2010; Tseng et al. 2014; Snijder et al. 2017; Tseng et al. 2017), and (4) KaiC’s ATP hydrolysis activities (Terauchi et al. 2007; Abe et al. 2015).

The researcher takes samples from the reaction mixture of Kai proteins to examine the above four biochemical processes using several methods and records the changes in each process at scheduled intervals. Time emerges when the continually depicted patterns are punctuated. Objective time of this kind, in which only the earlier-later relationship is discernible, lies in the B-series.

Circadian rhythms of Kai proteins come from four biochemical reactions, which are made possible by the conformation of the KaiC hexamer. Here, we may say that time is mapped out in the structural arrangement of the hexamer since the structural arrangement itself is the circadian time schedule. This time schedule is read by the organism and provides meaning, although the time schedule remains in the C-series before being read. The agency recognizing and reading the C-series text in the context of reconstitution may be intra-molecular KaiC as a subunit and inter-molecular KaiC as a hexamer, as well as KaiA and KaiB.

The four biochemical processes described are mutually dependent and require each other for the creation of rhythms in the circadian Kai protein clock. It is currently hypothesized that KaiC works as a pacemaker by regulating the amount of energy accumulated in KaiC molecules through ATP hydrolysis activity (Terauchi et al. 2007; Ito-Miwa et al. 2016). If so, KaiC as a pacemaker should be able to capture time with tense—the immediate past, present, and immediate future—by observing its own energy level. The energy accumulated inside KaiC through ATP hydrolysis activity should provide markers of the present tense in relation to its past and future, corresponding to A-series time.

With KaiC’s intra-molecular communication within the subunit and its inter-molecular communication in the hexamer, both of which support the four biochemical operations, the resulting periodicity of approximately 24 h is the product of meta-regulation, that is, interaction (or communication) among the four biochemical operations.

The four biochemical processes are not independent; therefore, the experimenter cannot measure the rhythms of each process by disregarding the activities of the other three. Circadian rhythms have a certain degree of freedom, some shorter or some longer than 24 h. That is, a certain amount of freedom is permitted, since the rhythms are the outcome of interaction or negotiation between the parts (i.e., the second-person negotiators). Because the circadian rhythms are regulated by the interaction of these four biochemical processes, local timing produced through synchronization of the four systemic parts may correspond to E-series time.

The Citric Acid Cycle

The oxidative citric acid cycle is ubiquitous in the biological world (Buchanan et al. 2000). It is a reaction cycle that synthesizes ATP, in which hydrogen is extracted by the carbon flow circulating through the system, transforming in the direction of citrate to isocitrate, to α-ketoglutarate, to succinate, to fumarate, to malate, to oxaloacetate, and back to citrate via the confluence of acetyl CoA, a co-enzyme (see Fig. 4).

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The transformational chain can be considered a design drawing. Thus, Fig. 4 has legitimately been read as C-series time code by the biochemist, the external observer. However, if the participating molecules are taken to assume the semiotic capacity of measuring or being measured by the nearby molecules (Matsuno 2012), it then logically follows that the molecules read a part of the C-series time code, a “pre-scenario,” as indispensable members of the system.

Measurement here corresponds to reading of the code, the “pre-scenario,” through which the molecules select their next step, since measurement is taken to be synonymous with an instance of synthetic chemical reaction (Matsuno 2017). Such measurement is indefinitely repetitive. Like changing partners one after another in certain ethnic dances, detecting the completed molecule partner stipulates the following reaction to come, which may indicate the repeated punctuation of the progressive tense by the perfect tense.

Each molecule takes in the necessary elements for transformation from the outside while leaving the derivative products behind. A molecule balancing both ends of the incoming and outgoing flows indicates time alignment, namely, synchronization between the two material flows occurring at their intersection. Adjusting time at the exchange of material elements indicates the local synchronization of E-series time. From the point of view of each individual molecule as a semiotic agent (Tønnessen 2015); however, the citric acid cycle of the C-series appears filled with tense markers of the A-series to be read out.

We should remind ourselves that each citric acid cycle is “the one and only,” that is, each system is unique. The uniqueness is twofold: it resides not only in the cycle itself but also in the relationship each molecule has with others, as well as with the cycle as a whole. This point is vital. Otherwise, the transformation may simply become mechanistic instead of semiotic.

Accordingly, the citric acid cycle as a goal-directed agent orchestrates different processes (i.e., punctuations) around the system, transforming them into time codes. When such a reaction cycle is seen from the first-person perspective, time appears in the A-series, alternating the incumbent tense to reshuffle the constituent elements. The citric acid cycle is thus capable of generating and integrating both its own foresight and hindsight through self-governing activity. That is, each molecule in the cycle is both going to be part of the reaction cycle to others (the future) and already under the influence of the reaction cycle formed by others (the past), as figuratively referred to in Uexküll’s Umwelt tunnel (Tønnessen 2014). It is the generation and integration of different tenses at the present moment of “now.” These are the perspectives from the A-series. In contrast, the fixed record of observation abstracted by the external observer as a result remains in the B-series.

On the other hand, timekeeping critical to a reaction cycle is found in the coordination between the sequential transformation of each upstream reactant into the one immediately downstream and the concurrent presence of all the participating reactants. Key to the timekeeping endeavor specific to a reaction cycle of any kind is co-adjustment of the time by multi-participants, despite inevitable conflicts, inconsistencies or incompatibilities between being sequential and being simultaneous.

The reactants view others encountered nearby as the second-person negotiators. Who then may be the timekeeper? It would be goal-directed multi-agencies interacting in constant efforts to maintain local synchronization of the E-series, which may correspond at least partially to Gregory Bateson’s concept of ecology of mind (1972, pp. 454–471). Biological clocks adapted to circadian rhythms may be no exception in maintaining goal-directed multi-agencies. All clocks seem to take advantage of reaction cycles in one way or another.