NOTE-1492: Bechtel & Abrahamsen — dynamic mechanistic explanation

Contribution

It names and illustrates “dynamic mechanistic explanation”: mechanistic decomposition into parts and operations, joined to quantitative modelling of how the organized operations unfold in time. It extracts six contributions such models make from the circadian literature of 1990–2007. It then sets cognitive modelling beside them. Cognitive models make the same kinds of contribution but rest on no independent identification of parts, so their evidential standing is weaker in a definite way.

Key insight

The same equations can be a description of a mechanism or a conjecture about one. Which they are depends on whether their variables were tied to parts and operations found by other means before the model was written. When they were, model experiments explore that mechanism’s dynamics. When they were not, fit to behaviour shows only that some mechanism of the posited kind could produce it. “Empirical evidence can rule out specific models, but usually cannot decide between competing architectures” (p. 332).

Assumptions

• Mechanism, as the authors define it (p. 323): “A mechanism is a structure performing a function in virtue of its component parts, component operations, and their organization. The orchestrated functioning of the mechanism, manifested in patterns of change over time in properties of its parts and operations, is responsible for one or more phenomena.” The second sentence is the 2010 addition.
• Models are ordinary differential equations in time. Variables are chosen properties of parts or operations, and some quantities are parameters. “a property initially treated as a parameter may, as the model is further explored, become a variable” (p. 323).
• Independent identification of parts is possible for circadian clocks and, so far, mostly not for cognition (p. 329). The argument depends on the contrast, not on any claim that cognitive parts cannot be found.

Key results

The six contributions, each with its circadian exemplar.

• C1, sufficiency (pp. 324–325). “A model can demonstrate that a mechanism, whose parts, operations, and organization have been at least partially identified, is able to exhibit the phenomenon of interest.” The exemplar is Goldbeter (1995). Its five kinetic equations for per-mRNA and PER, with cytoplasmic mRNA dM/dt = v_s K_Iⁿ/(K_Iⁿ + P_Nⁿ) − v_m M/(K_m + M), give limit-cycle oscillations only in a parameter range. A degradation parameter v_d sets periods from 19.3 to 64 h. Mental simulation cannot find that range. The paper calls this, after Craver (2007), a “how possibly” explanation (p. 325). Footnote 2 (p. 324) gives a history: Griffith (1968) showed that negative feedback through one gene product gives undamped oscillation only for a Hill coefficient n > 9. Later models escaped this by adding nonlinearity elsewhere, in degradation.
• C2, parameter exploration (p. 325). Leloup and Goldbeter (1998), ten equations with TIM, simulate light by doubling TIM’s degradation rate. This reproduces phase advances and delays, and in some ranges birhythmicity and chaos. Model experiments “do not show that the mechanism in fact could produce these effects”. They show that “if particular parameter values and mode of organization were realized in the actual system, the effects should correspond”.
• C3, which parts belong (p. 326). “A model can indicate which parts and operations of a system that have been identified empirically are essential for producing the phenomenon of interest, and therefore should count as components of the responsible mechanism.” Smolen et al. (2001) fixed the concentration of CLOCK in a reduced model, and oscillation continued, robust to the other parameters. They concluded that the positive CLOCK loop “was not critical”, and that the rhythm comes from the PER/TIM negative loops. Simplified models make it easier to see “which are components of the system but not of the responsible mechanism for that particular phenomenon”. The same clamp in vivo would need a buffer, so it “is much easier to accomplish in a model”.
• C4, disorder (p. 327). Altering the phosphorylation parameters of PER in Leloup and Goldbeter’s mammalian model mimics advanced and delayed sleep phase syndromes. This was later matched by point mutations at the CKIδ/ε sites in families with ASPS.
• C5, coupling (p. 327). “A model can reveal conditions under which independent mechanisms, each with its own internally determined dynamical (oscillatory) behavior, can be coupled so as to exhibit coordinated collective behavior.”
  • Gonze et al. (2005): a mean-field VIP term with coupling 0 leaves periods scattered, and with coupling 0.5 the oscillators synchronize. In the two-oscillator analysis, single neurons’ oscillations may damp without VIP.
  • To et al. (2007): about 40% of model cells can sustain oscillation alone. Without VIP about 60% become arrhythmic and the rest desynchronize, matching Aton et al. (2005).
• C6, restoring relations (p. 328). “A model provides a means of exploring the space of possibilities for altering and restoring relations between multiple mechanisms.”
  • The question it serves: peripheral oscillators were long thought “slaves” to the SCN, damping without its input. Newer evidence was that they keep oscillating but lose synchrony, so the SCN is “a conductor … than … a ringmaster” (Davidson et al. 2004).
  • Leise and Siegelmann (2006) use two-variable oscillators, dX/dt = r_X/(1 + Y²) − q_X X and dY/dt = r_Y X²(t − τ_lag) − q_Y Y, “whose biochemical interpretation they left unspecified”. With these they model core, shell and periphery, with coupling by thresholds.
  • Under a simulated six-hour advance, damped peripheral oscillators regain their phase relation quickly. Self-sustained ones take longer, need strong coupling, and sometimes resynchronize by delaying fifteen hours rather than advancing six.
  • The paper’s reading: modelling both kinds “can reveal the empirical signatures that each may leave … and so guide empirical attempts to answer this question”.
• The cognitive comparisons (pp. 329–332).
  • Rumelhart and McClelland’s past-tense network (C1) led to a debate with Pinker and Prince. Without constraint from parts it was “irresolvable”: “The relevant models are underdetermined” (p. 330).
  • McClelland et al. (1995) illustrate C3. They modelled no hippocampus, supplying “only the interleaved output it was presumed to send to neocortex”. Stopping that training stands for a hippocampal lesion and gives graded retrograde amnesia (p. 331).
  • Hinton and Shallice’s lesioned attractor network illustrates C4: deep dyslexia’s mixed errors (p. 331).
  • van Leeuwen’s coupled logistic-map lattice illustrates C5–C6: alternating groupings of a dot grid (pp. 331–332).
  • Each is, “At best”, a suggestion of “how and why the actual mechanism behaves this way, if it in fact employs” the model’s organization (p. 332).
• Describing against mirroring (p. 329, n. 5). A circadian model is not itself a clock, because its variables track properties of parts rather than performing their operations. Cognitive models are often taken to think because their operations are posited to be the mind’s.

Claims

id	claim	strength	support
C1	Models of an empirically identified mechanism can show it suffices for the phenomenon, and in which parameter ranges	strong	Goldbeter 1995 and successors (pp. 324–325)
C2	Clamping a variable in such a model can show that an identified part is not needed for the phenomenon, and so is not a component of the responsible mechanism	moderate	one case, Smolen et al. 2001 (p. 326); valid only as far as the model is faithful
C3	Whether peripheral clocks are self-sustained or driven damped oscillators was open in 2010, and the two leave different modelled signatures under phase shifts	moderate as a report; the signatures are model outputs, not data	Davidson et al. 2004; Leise & Siegelmann 2006 (p. 328)
C4	Cognitive models are de novo proposals checked by fit, so fit usually cannot decide between architectures	moderate	the past-tense debate (p. 330) and four further cases; an argument from examples
C5	Modelling anchored in empirically identified parts is the path for cognitive science to follow	weak, a recommendation	conclusion (p. 332)

Concepts

• Dynamic mechanistic explanation: mechanistic decomposition plus a computational model of the real-time dynamics of the identified parts and operations (pp. 322–323).
• Anchoring: tying a model’s variables and parameters to properties of identified parts and operations (p. 323).
• Responsible mechanism: the subset of a system’s components needed for a given phenomenon. It is relative to that phenomenon, so a part can be a component of the system and not of the responsible mechanism (p. 326).
• De novo model: a model that posits a mechanism to account for behaviour, with no independent evidence for its parts (abstract, p. 321).

Connections

It builds on Bechtel and Abrahamsen 2005’s account of mechanism, here extended to dynamics, and anticipates their “Complex biological mechanisms: cyclic, oscillatory, and autonomous” (then in press). It cites Craver 2007 (LIT-832) for “how possibly”. The C3 test is a model-based version of the interlevel experiments in Craver and Bechtel (LIT-1928): an ideal intervention on a part, which the model makes cheap. It does not engage the dynamicist challenge to mechanism (van Gelder, Kelso). Its Beer and van Leeuwen examples show dynamical tools used within a mechanistic project.

Limitations

• Six exemplars, one field each, chosen to illustrate rather than to test. Nothing measures how often grounded models in fact outperform de novo ones.
• C3 is only as good as the model. Smolen et al.’s clamp shows that CLOCK oscillation is not needed in a reduced model that merged PER and TIM and replaced transport by a delay. The paper does not say whether later experiments confirmed this. Its own general caution under C2 applies: equations “may even misrepresent or leave out critical components”.
• Grounding is treated as all or nothing between the two fields. Beer’s model is “less hypothetical” (p. 330), but no scale of anchoring is offered.
• Same dynamics from different mechanisms is not discussed as such. The paper’s distinction implies it: de novo models can match behaviour and still differ in architecture. But it does not state when two anchored models with different parts give the same dynamics, or how that would be detected.

Open questions

• Did isolation experiments settle whether peripheral clocks are self-sustained? The paper treats it as open. The answer bears on THEORY-1292.
• Are Leise and Siegelmann’s signatures (recovery time, a fifteen-hour delay instead of a six-hour advance) seen in tissue? Then a perturbation of state alone would tell the two arrangements apart, because they are not dynamically equivalent.

Bearing on the record’s own argument

• CASE-189 and CASE-190 are de novo, how-possibly models in this paper’s sense. Their variables, “constraint capacities”, a connector q, a copying catalyst, are posited to exhibit maintenance. They are not properties of parts found by experiment, which the cases themselves say (“Which terms are internal is stipulated”, CASE-189). So they can make contributions C1 and C2: an organization of this kind can be maintained, is lost at a fold, and so on. They also make C3 and C5 inside the model: the knockouts and the coupling. What they cannot do, on this paper’s account, is show that any actual system is organized that way. That needs anchoring. The record already says this in its own terms. This paper gives it a name and a precedent.
• CLAIM-522: the dynamics underdetermine the mechanism, and grounding is the remedy. CLAIM-522’s pair has identical equations, so no model of the dynamics alone can choose between them. This paper’s answer is the one CLAIM-522 gives: identify the parts and intervene on them. Two cases in the paper have CLAIM-522’s structure. Same structure, not shown same mechanism:
  • McClelland et al. (p. 331). The hippocampus is not modelled. Its output is supplied from outside the model as a training schedule. Stopping the schedule “corresponds to” a hippocampal lesion. Within the model nothing distinguishes a training signal produced by an internal part from one supplied by the modeller. Whether the hippocampus is a component of the memory mechanism is settled by anatomy and lesion, outside the model, just as CLAIM-522’s boundary is declared.
  • The peripheral clocks (p. 328). “Slave” against “conductor” is exactly the question where an oscillation is maintained: by the peripheral cell itself, or by its drive from the SCN. The direct test, by definition of the two kinds, is to remove the drive, which is the intervention CLAIM-522 names. The paper does not say what the evidence it reports was.
  • The modelled phase-shift signatures show the limit of CLAIM-522’s ideal case. A driven damped oscillator is not dynamically equivalent to a self-sustained one, so a perturbation of state can separate them. CLAIM-522 holds where the outside supplier reproduces the production law exactly, and a damped oscillator plus its drive does not.
  • That is THEORY-1292, which bears on QUESTION-086’s search for an intervention short of removal.
• CLAIM-519: the cognitive half of this paper is CLAIM-519 at the level of practice. CLAIM-519 says competent behaviour does not establish an internal world model, and that establishing a mechanism needs evidence that discriminates implementations. This paper says the same of cognitive models in general: fit is “indirect evidence” (p. 330), and architectures stay underdetermined. Footnote 5’s contrast between describing and mirroring bears on CLAIM-519’s two readings of “contains a model”. A model that tracks variables of a mechanism is not thereby a component that performs the operations.
• CLAIM-515: its “realized” question needs anchored evidence. CLAIM-515’s third question, which mechanisms realize a capability, is the question this paper says cognitive modelling cannot answer by fit. Its fourth question, maintenance, is the one circadian models of damage and recovery (C4, C6) approach.
• CLAIM-521: a contrast, not a counterexample. CLAIM-521’s dissociation needs “no feedback from the coupled units to the maintaining core”. In To et al.’s SCN model the coupling signal (VIP) is itself what sustains oscillation in about 60% of the cells (p. 327). There, losing the coupling loses the maintenance, so coupling strength would not stay high up to a fold of maintenance. The record’s dissociation is a property of one-way architectures. Same structure, not shown same mechanism.
• Clamping is the ideal intervention on a part that a construction makes free. In CASE-189, CASE-190 and the record’s knockouts, removing a production pathway is C3 in this paper’s sense. It decides whether that pathway is a component of the mechanism responsible for maintenance, relative to the phenomenon and the model (THEORY-1289). Which pathways count as inside is not decided by the clamp. That is CLAIM-530’s point.