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(UCM) to understand motor behavior”

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Brief History of the Uncontrolled Manifold Hypothesis and Its Role in Motor Control

MARK L. LATASH1

1 Department of Kinesiology, The Pennsylvania State University, University Park, PA, USA

Correspondence to: Mark L. Latash

Department of Kinesiology, Rec.Hall-267, The Pennsylvania State University, University Park, PA 16802, USA

tel: (814) 863-5374

email: mll11@psu.edu

https://doi.org/10.20338/bjmb.v18i1.433

HIGHLIGHTS

• The concept of uncontrolled manifold is readily

compatible with the principle of abundance

• The UCM concept can be applied to different effectors

from a muscle to the whole body

• The UCM concept offers insightful applications to

movement disorders

• This concept requires generalization to spaces of

neural control variables

ABBREVIATIONS

ASAs Anticipatory synergy adjustments

ASASS Steady-State ASA

ASATR Transient ASA

C- Coactivation command

E1 Elemental variable 1

E2 Elemental variable 2

Fx Effector producing force

J Jacobian matrix

k Apparent stiffness

ME Motor equivalent

ORT Orthogonal

PD Parkinson’s disease

R- Reciprocal command

RC Reference Coordinates

UCM Uncontrolled manifold

VF Virtual finger

VUCM Inter-trial variance components along the

UCM

VORT Inter-trial variance components along the

ORT

X Spatial coordinate

∆V Synergy index

PUBLICATION DATA

Received 18 07 2024

Accepted 09 09 2024

Published 31 10 2024

BACKGROUND: The apparent problem of motor redundancy was replaced by the principle of

abundance and turned into a theoretical framework and associated toolbox for exploration of

performance-stabilizing synergies.

AIM and METHOD: We review briefly the development of the main methods within the UCM

framework and some of the main findings, both basic and clinical. The UCM framework is

naturally merged with the theory of hierarchical movement control with spatial referent

coordinates.

RESULTS: The UCM framework has established itself as a productive framework for the

analysis of movement control, in particular as related to stability of salient performance

variables. It led to the discovery of novel phenomena such as trade-offs within hierarchical

systems, anticipatory synergy adjustments, synergies within systems of different complexity

from single muscles to the whole body. It has also led to promising results offering sensitive

biomarkers to various neurological disorders. Recent experiments suggest the existence of

three main levels of organization of performance-stabilizing synergies tentatively associated

with cortical, subcortical, and spinal circuitry.

CONCLUSION: Currently, this approach is in its adulthood. Further progress may be

expected in focusing on spaces of neural control variables, developing the method for analysis

across species, and expanding the range and depth of clinical studies.

KEYWORDS: Abundance | Stability | Synergy | Referent coordinate | Hierarchy

“To the memory of John P. Scholz – A friend, a gentleman, and a scientist”

LIFE BEFORE UCM

It is hard to believe that a quarter of a century has passed since the seminal publication by John Scholz and Gregor Schöner in

1999 1 inaugurating the uncontrolled manifold (UCM) hypothesis. The origins of this hypothesis can be traced back to the classical study

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of Nikolai Bernstein 2 of professional blacksmiths who performed their labor movement – hitting the chisel with the hammer – multiple

times. Bernstein quantified the trajectories of the tip of the hammer and of individual arm joints and claimed that the former showed the

smallest inter-trial variability. Since, clearly, the brain could only send signals to muscles crossing the joints, not to the hammer, the result

implied that the joints compensated for each other errors (deviations from the mean trajectories) across trials to keep the hammer

trajectory relatively consistent. In 1994, we discussed with Gregor Schöner how Bernstein could compare variability of the tip of the

hammer measured in spatial Euclidian coordinates with variability in the joint space measured in angular units. Clearly, some kind of

mapping between these two spaces was necessary to reach the main Bernstein conclusion. The necessity of such mapping was explicitly

formulated by Gregor Schöner in a paper published in 1995 3.

The general idea of error compensation among effectors had been expressed in several studies preceding the introduction of

the UCM concept. Such studies involved either external perturbations applied to one or a few of the effectors or self-generated actions

perturbing the salient task-specific variable, or simply repetitive movements without any explicit perturbations. They explored a range of

actions including speech 4, precision grip 5, multi-joint pointing 6, and multi-finger accurate force production 7. All the mentioned studies

have shown that task-specific performance variables could show relatively small deviations in the presence of relatively large changes in

the contributions of elements (digits, joints, articulators, etc.).

For many years, general theoretical conceptualization of the phenomena of error compensation has been elusive. One of the

problems can be traced back to another important contribution by Bernstein, his formulation of the problem of motor redundancy. In any

action, multiple elements are involved at different levels of analysis (joints, digits, muscles, articulators, etc.), producing a large number of

elemental variables, more than the number of task constraints. In any given realization, a specific combination of the elemental variables

is observed. How does the brain select those specific combinations from the infinite number of solutions? Bernstein viewed this as a

central problem of motor control and saw the solution in the elimination of redundant degrees-of-freedom 8 (see also 9). This view

dominated the field for decades leading to the development and application of the concept of optimization to voluntary movements

(reviewed in 10-12).

At closer examination, the problem of motor redundancy seems to be ill-formulated (reviewed in 13-15). It is not inherent to the

neural control of movement but reflects specific levels of analysis selected by individual researchers. For example, the problem of

pressing with a finger and producing a certain force level is non-redundant at the finger level (in contrast, for example, to the same task

performed while pressing with four fingers). The same problem is redundant at the level of muscle involvement. Another example: Muscle

co-contraction has been viewed as a means of alleviating the problem of motor redundancy at the joint configuration level by “freezing”

joints (cf. 16), while it obviously leads to making this problem worse at the level of muscle activation. Assuming that this problem is

inherent to brain processes involved in the neural control of movement requires committing to a motor control theory. We will return to

this issue based on the theory of control with spatial referent coordinates (reviewed in 17), a development of the equilibrium-point

hypothesis 18,19.

An alternative view on the apparent excess of elemental variables was suggested as the principle of abundance 13,20. According

to this principle, the numerous elemental variables (at all levels) are not sources of computational problems for the brain but important

parts of mechanisms that allow to provide desired degree of dynamical stability for salient task-specific performance variables. This idea

was implied in the formulation of the UCM hypothesis: No degrees-of-freedom are ever eliminated, they are all used to provide dynamical

stability of performance. Note that both features, addressing the problem of motor redundancy and ensuring dynamical stability of

performance, have been discussed by Bernstein as originating at the same level of movement construction, the Level of Synergies. This

term comes from a Greek word combination meaning “work together”, and it has been used for ages in numerous fields from theology to

motor control. Further, we will use the term synergy to address both aspects, grouping of elements at the selected level of analysis and

covariation of elemental variables contributing to stability of performance (reviewed in 8,15).

THE UCM-BASED TOOLBOX

Formal analysis of synergies, within the UCM framework, starts with defining mapping between the spaces of elemental

variables (those produced by elements at the selected level of analysis) and a potentially important performance variable, which can be

multi-dimensional. In a linear approximation, this has been done using the matrix of partial derivatives of the selected performance

variable with respect to the elemental variables, i.e., the Jacobian matrix (J). It is assumed that the average across repetitive trials value

(time series) of the performance variable represents its desired value (time series), and that deviations from this value are reflections of

its imperfect stability under the action of unpredictable factors, both extrinsic and intrinsic. It is also assumed that the average point (time

series) in the multi-dimensional space of elemental variables represents a preferred solution for the problem of producing the

performance variable. Further, for any given value of the performance variable, a solution subspace (the UCM) is approximated as the

null-space of the J, i.e., a subspace where small deviations of elemental variables have no effect on the performance variable.

Figure 1 illustrates a simple task of producing a desired value of the sum of two elemental variables (E1 and E2). The J matrix

for this task is [1 1], and its null-space is shown as the slanted line corresponding to the equation E1 + E2 = C. An average across multiple

trials solution is shown as the black point. The thin lines show potential fields along the UCM and along the orthogonal to the UCM

subspace (ORT) illustrating that the ORT direction shows higher stability as compared to the UCM.

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Figure 1. A schematic illustration of a task of producing a constant value of the sum of two elemental variables (E1 + E2 = C). The solutions space is shown as the solid

slanted line. An average across multiple trials solutions is shown as the black point. The curved lines show potential fields along the UCM and along the orthogonal to the

UCM subspace (ORT), UCM and ORT. Note that variance along the UCM is larger than along the ORT (VUCM > VORT).

The most commonly used method of analysis has compared inter-trial variance components along the UCM and along ORT,

VUCM and VORT, normalized per dimension in each subspace. It has been assumed that, if the selected performance variable is stabilized

by some neural mechanisms, VUCM is expected to be larger than VORT, i.e., the unavoidable inter-trial variance is channeled into the space

where deviations of elemental variables have no effect on the performance variable. Commonly, the two metrics, VUCM and VORT, have

been combined into a single metric, a synergy index (∆V) reflecting the relative amounts of the two variance components in the total

amount of variance in the space of elemental variables. VUCM has been addressed informally as “good variance” because large amounts

of VUCM both reflect stability of the salient performance variable and allow performing secondary tasks with the same set of elemental

variables without detrimental effects on that salient performance variable.

Another method quantified and compared deviations within UCM and ORT following a brief action or a quick response to an

external perturbation. Deviations within the UCM are motor equivalent (ME) in a sense that they, by definition, lead to no change in the

salient performance variable. In other words, these deviations are wasteful if the task is to change the performance variable quickly and

efficiently, for example with minimal expenditure of metabolic energy – a common currency within the body (cf. 21) and a commonly used

cost function within optimization approaches 11,22,23. A number of studies have shown that quick corrections of actions in response to

unexpected perturbations have very large ME components as compared to the non-ME components, which are required to produce

corrections 24-26. These apparently wasteful components of actions have been interpreted as consequences of much lower stability along

the UCM.

The two pairs of outcome variables, {VUCM; VORT} and {ME; non-ME}, are expected to correlate if the data are sampled from a

single distribution (cf. 27). Such correlations have indeed been shown in experiments 28, although not without exceptions 29, The

exceptions have been interpreted as consequences of intentional corrections by the subjects resulting in sampling from different

distributions. The relative usefulness of the two pairs of metrics remains to be explored in detail. In particular, the number of trials to

reach a criterion of statistical robustness is smaller for {ME; non-ME} as compared to {VUCM; VORT} 30 making quantification of motor

equivalence attractive in clinical studies when participants may not be able to perform multiple trials per conditions to allow estimation of

the variance indices.

APPLICATIONS TO SPACES OF MECHANICAL AND ELECTROPHYSIOLOGICAL VARIABLES

Early studies applied the analysis of variance within the UCM framework to spaces of kinematic 1,31 and kinetic 32,33 elemental

variables. These applications were relatively straightforward since the J matrix could be computed from the configuration of the effector.

There were, however, hidden problems. Drawing conclusion relevant to the neural control of movement based on results of such studies

assumes that, in the absence of a special control process, the data distributions are expected to be spherical. This is far from being

obvious. For example, the presence of biarticular and multi-articular muscles and inter-joint reflexes makes joint rotations coupled. So,

analysis in a joint configuration space may be expected to produce non-spherical data distributions in the absence of any specific

synergies. By chance, such distributions can be elongated along the UCM computed for a performance variable or orthogonal to it

leading to spurious conclusions. How practically important are these factors? In particular, can humans move one joint at a time? There

are no data answering these questions. The situation is even more complicated for analysis in spaces of segmental angles because,

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obviously, moving a single proximal joint alone leads to changes in the segmental angles of all the more distal segments. These built-in

covariations may also lead to spurious conclusions. It is better to avoid analysis in spaces where unavoidable covariation of elemental

variables is produced by peripheral, including biomechanical, factors.

The situation becomes even more complicated in the analysis of multi-digit actions because of the phenomenon of enslaving 34,

which makes digit forces non-independent. Originally, to account for finger enslaving, finger forces were transformed into modes,

hypothetical central variables that could be manipulated by the brain one at a time 32,35. Such analyses implied that enslaving was a

robust phenomenon and, after being defined on a set of tasks, it could be applied to other tasks. Recent studies have shown, however,

that enslaving tends to drift (increase) with time during constant finger force production tasks 36,37. Whether using finger modes should be

preferred as compared to analysis in finger force spaces remains an open issue.

Application of the UCM framework to spaces of electrophysiological variables, such as EMG indices, led to the emergence of

an auxiliary toolbox. It would be naïve to assume that the brain manipulates a set of neural variables directed at individual muscles. So,

the first step in those studies has been defining muscle groups that show parallel changes in the activation levels of individual muscles.

This has been done with the help of various matrix factorization methods, in particular the principal component analysis, which leads to a

set of orthogonal eigenvectors – an advantage for further normalization of the variance indices. Such groups have been addressed with

various terms such as factors, primitives, modes, and synergies. Further, since the mapping between indices of EMG (such as mV or

mVs) and mechanical variables directly relevant to the task is typically unknown, the only practical approach has been to discover the J

matrix using experimental data, commonly with the help of multiple linear regression techniques 38,39. Relatively recently, the UCM-based

analysis has been applied to studies of performance-stabilizing synergies in spaces of firing frequencies of individual motor units within a

muscle and across agonist-antagonist muscle pairs 40 (reviewed in 41). Both features of synergies were demonstrated: Grouping motor

units into a small number of groups (MU-modes) and stabilization of the task-specific performance variable organized in the spaces of

MU-modes, i.e., VUCM > VORT.

APPLICATIONS TO SPACES OF HYPOTHETICAL CONTROL VARIABLES

All the aforementioned studies analyzed inter-trial variance and/or motor equivalence in spaces of peripheral elemental

variables. This has always been a potential weakness of the approach because peripheral mechanical and muscle activation variables

cannot in principle be prescribed by the brain as emphasized by many researchers starting with Bernstein 8. In particular, the discovered

patterns could be consequences of correlated changes in the reflex contributions to muscle activation levels. To extend the method to

spaces of control variables, one had to commit to a theory of motor control, which specifies such variables explicitly. This has been done

within the framework of the theory of control with spatial referent coordinates (RCs, linear or angular; reviewed in 17,42). Within this

framework, the control of any effector can be described with two basic commands, the reciprocal command (R-command) and

coactivation command (C-command). The R-command defines spatial coordinate where the net force by the agonist and antagonist

muscles is zero, i.e., its RC. The C-command defines the range where both agonist and antagonist muscles are active simultaneously.

This is illustrated in Figure 2 for an effector producing force FX along a spatial coordinate X. Note that, at the level of mechanics,

changing the C-command leads to changes in the shape of the resultant FX(X) characteristic or, in a linear approximation, the apparent

stiffness (k) of the effector (cf. 43).

Figure 2. An effector produces force FX along a spatial coordinate X. The thin curves show force-coordinate characteristics for two opposing muscles, agonist (positive

force values) and antagonist (negative force values). They were addressed as “invariant characteristics” in the original publications 18,19. The agonist and antagonist muscle

groups are controlled by setting referent coordinates, RCAG and RCANT. At the level of mechanics, changing the R-command leads to shifts in the RC for the effector.

Changes in the C-command leads, in a linear approximation, to changes in the apparent stiffness (k) of the effector.

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The presence of the two basic commands makes the control of any effector abundant with a possibility of performance-

stabilizing synergies. However, the two commands are not directly measurable, and so far, studies of synergies at the level of control

have been limited to using mechanical proxies of the two commands, the intercept and slope of the FX(X) characteristic. Such studies

have been informative showing performance-stabilizing synergies for different effectors, from single fingers to the whole body 44,45. The

UCM in the {RC; k} space stabilizing force by an effector is typically hyperbolic and does not allow linearization. This has been another

problem preventing researchers from using analysis of inter-trial variance. Instead, hyperbolic regression and randomization methods (cf.

46) have been used to quantify synergies in the {RC; k } space.

The concept of control with spatial RCs can be applied to different effectors, from the whole body to individual muscles and

motor units (reviewed in 14,42). Figure 3 illustrates a hypothetical hierarchy involved in the control of a multi-joint effector. Note that the

dimensionality of control increases from the task level down to the levels of specific effectors, joints, digits, muscles, and motor units.

These few-to-many transformations afford the possibility of organizing synergies stabilizing higher-level control variables by co-varied

involvement of lower-level variables. This can potentially be based on feedback loops from peripheral sensory endings as well as those

within the central nervous system shown by arrows. The scheme in Figure 3 has to be taken with a big grain of salt. It is motivated by the

anatomy of the human body, and some of the levels may be apparent, not real. For example, a study of spino-cerebellar pathways in cats

has shown modulation of those signals not with joint angles, which have dedicated sensors, but with higher-order variables such as “leg

length” and “leg orientation”, which do not have dedicated sensors 47.

Figure 3. A schematic illustration of the control in a hierarchy involved in the control of an effector. Note that the dimensionality o f control (referent coordinates, RC)

increases from the task level down to the levels of specific joints, digits, muscles, and motor units. Back-coupling loops stabilizing behavior from peripheral sensory endings

and within the central nervous system are shown with arrows.

The relations between the theory of control with RCs and the UCM-based concept of synergy are non-trivial. On the one hand,

within the hierarchical scheme in Figure 3, synergies stabilizing performance variables desired by the actor and indirectly encoded in the

low-dimensional task-level RC time functions can be organized using feedback loops both within the central nervous system, from

abundant sets of lower-level RC time functions, and from peripheral sensory endings. On the other hand, what matters for the actor is

stability of salient performance variable, not necessarily its source. So, it is possible that peripheral factors, including anatomical and

biomechanical ones, may drive covariations of elemental variables stabilizing performance with minimal contribution from the neural

control levels. In most cited studies, it has been assumed that action stability is primarily a function of the neural control, i.e., of the RC

hierarchy, but the role of peripheral factors remains relatively underexplored.

The organization of synergic control in a hierarchical system is non-trivial. Indeed, consider only two levels of a hierarchy

(Figure 4). To have a synergy stabilizing performance at the upper level, VUCM has to be relatively large, which requires relatively large

inter-trial variance of the elements. At the lower level, variance of each of the elements is, by definition, VORT. This large VORT requires

very large VUCM to ensure synergic control. This may be problematic, although not impossible. A study of two-hand, multi-finger pressing

tasks showed that, indeed, in such tasks no synergies were seen stabilizing the contribution of each individual hand, while there were

strong synergies at the two-hand level 48. During prehensile tasks performed using the prismatic grip – the thumb opposing the four

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fingers – the control is commonly viewed as hierarchical. At the top level, the task is shared between the thumb and “virtual finger” (VF,

an imagined digit with the force/moment vector equal to the summed vectors of the individual fingers, 49). At the lower level, the VF action

is shared among the four actual fingers. A study of synergies stabilizing force and moment components has shown that some of them

were stabilized at one level only, while others – at both levels 50. Such studies may be useful as windows into the salient control levels,

which may differ from the apparent anatomy-based levels shown in Figure 4.

Figure 4. Consider the task of keeping constant the sum of two effectors (E1 and E2), when the output of each effector is the sum of two lower-level effectors, e11 + e12

and e21 + e22. A synergy stabilizing performance implies large VUCM, which requires large inter-trial variance of the elements, VE1 and VE2. At the lower level, variance of

each of the elements is, by definition, VORT. This creates a problem for arranging synergies at both levels.

ANTICIPATORY CHANGES IN ACTION STABILITY

The UCM-based method of analysis of stability has led to several discoveries. Some of them have already been mentioned.

Here we address a group of phenomena related to anticipation in motor behavior. High stability of salient variables may be functionally

important during steady-state or slow actions. If one wants to change a performance variable quickly, strong synergies stabilizing this

variable become counter-productive. This has been discussed in detail as a stability-agility trade-off (reviewed in 51). Evolutionary success

required controlled stability of action, and a number of studies have shown that humans can adjust action stability independently of other

action characteristics, as seen, for example, in average across trials performance. These phenomena have been addressed as

anticipatory synergy adjustments (ASAs, reviewed in 14,15).

There are two types of ASAs. The first is associated with a drop in the index of performance-stabilizing synergy seen in young

healthy persons 300±100 ms prior to a self-initiated quick action or reaction to a predictable perturbation 52,53. The second type

represents a drop in the synergy index (the normalized difference between VUCM and VORT) during steady-state performance under

conditions that a quick action or a change in the ongoing action may be required at an unpredictable time in future or in only some of the

trials 54-56. These have been labeled as transient ASAs (ASATR) and steady-state ASAs (ASASS), respectively. They are illustrated in

Figure 5 using the earlier example of two elements contributing to a common task. Panel A shows the task of producing a constant output

with a possibility of unexpected changes in the output magnitude followed by a self-initiation quick change in (E1 + E2). Panel B shows

cartoon inter-trial distributions of the data points for a steady-state action in the absence of any changes in performance, during steady-

state when an unexpected target could emerge, and prior to the self-initiated quick change in (E1 + E2). Panel C illustrates the same data

assuming that stability of action reflects depth of a potential field.

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Figure 5. A: The task of producing a constant output of two elements (E1 + E2 = C) with a possibility of unexpected changes in the output magnitude followed by a self-

initiation quick change in (E1 + E2). B: Inter-trial distributions of the data points for a steady-state action in the absence of any changes in performance (the dark ellipse),

when an unexpected target could emerge (the lighter ellipse), and prior to the self-initiated quick action (the very light ellipse). C: An illustration of the same data assuming

that stability of action reflects depth of a potential field, .

ASASS can be seen with the naked eye in some athletic competitions. For example, a tennis player getting ready for a powerful

serve and a goalkeeper preparing for a penalty shot both show visibly increased postural sway reflecting a decrease in postural stability.

This facilitates the initiation of a fast action independently of its direction. Relative invariance of ASATR to action direction has also been

shown experimentally 57.

Theoretically, a drop in the synergy index may be due to an increase in VORT and/or a drop in VUCM; both scenarios have been

documented in the mentioned papers. Recently, sensitivity of both ASATR and ASASS to speed of a future action has been documented 58:

Both types of ASAs become smaller and may even disappear when the planned upcoming action is slower as compared to very fast

actions used in most of the earlier studies. This is potentially an important finding for clinical applications when control participants

typically are able to perform faster actions as compared to groups of patients with impaired neural control of movements. We will return to

clinical applications of ASA indices a bit later.

WHERE DOES THE UCM COME FROM?

While the UCM concept and associated methods of analysis involve computational steps, these computations have not been

assumed to happen within the central nervous system, only in the minds of the researchers. Just like equations in classical physics

involve computations, these are never assumed to reside in the objects to which they apply. From the very beginning, the controlled

stability of actions has been assumed to reflect physical (including physiological) processes within the body. The most developed

accounts for the UCM concept have been developed by the group of Gregor Schöner 59,60, which also incorporate the ideas of control with

spatial RCs. While the mapping between the assumed processes and neurophysiological structures remains speculative, the basic ideas

of back-coupling and the role of feedback circuits within the central nervous system and from peripheral receptors are important for

conceptualization of the UCM.

In particular, an important role of short-latency feedback circuits in ensuring stability of actions has been suggested nearly

twenty years ago 61. Recent studies of intra-muscle synergies corroborate this idea and suggest that intra-spinal and reflex-based circuits

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contribute to movement stability across tasks and effectors (reviewed in 51) in addition to supraspinal synergic mechanisms, which are

more task-specific and sensitive to conditions of movement execution, in particular to the presence of visual feedback on salient

variables. Recent studies of intra-muscle and multi-effector (multi-muscle) synergies have strongly suggested the existence of at least

two classes of performance-stabilizing synergies. Intra-muscle synergies stabilize reflex-induced changes in performance, show no

effects of hemispheric dominance, and are robust independently of the availability of visual feedback 62-64. In contrast, multi-effector

synergies show no stabilization of reflex-based changes in performance, show strong effects of dominance (compatible with the dynamic

dominance hypothesis, 65), and are highly sensitive to visual feedback. For example, turning off the visual feedback on the force produced

by the four fingers of a hand leads to unintentional force drifts (cf. 66,67) accompanied by the disappearance of multi-finger force-stabilizing

synergies with no effects on intra-muscle synergies 64.

It seems feasible that the two classes of synergies reflect different levels of back-coupling hypothesized within the scheme by

Martin and colleagues 60, those targeting spinal levels of control and those updating the RC functions at higher levels. As far as

supraspinal mechanisms of synergies are concerned, a number of studies have shown high sensitivity of synergies to disorders of

subcortical circuitry in such conditions as Parkinson’s disease, multi-system atrophy, and multiple sclerosis (reviewed in 68). In contrast,

effects of cortical stroke have been variable ranging from no effects on synergy indices to weakening of the synergies 69-72 (reviewed in

68,73).

A recent study explored the indices of synergies at three levels during multi-finger accurate force production tasks 74. In addition

to analysis of intra-muscle and multi-finger force-stabilizing synergies, this study quantified the synergies at the {RC; k} level reflecting the

hypothetical R- and C-commands. Force-stabilizing synergies were found at all three levels of analysis. However, no correlations were

found across the synergy indices quantified at the three levels suggesting their independent origins. A hypothetical scheme reflecting

these findings is illustrated in Figure 6. It seems feasible that the {RC; k} synergies are hierarchically the highest, possibly involving pre-

M1 cortical levels, followed by the multi-finger synergies based on subcortical circuitry, and by intra-muscle synergies based on spinal

circuitry. The presence of multiple parallel mechanisms contributing to dynamical stability of movements ensures that no major disruption

happens when one of these mechanisms stops contributing to action for some reason. For example, as mentioned earlier, turning visual

feedback off during accurate force production tasks leads to loss of force stability reflected in its drifts. On the other hand, the drifts are

not erratic but relatively consistent in their patterns and limited in magnitude suggesting that stability is not completely lost but rather

attenuated.

Figure 6. Three hypothetical levels of ensuring stability of action by an effector and the hypothetical neurophysiological substrates. Force by an effector (e.g., a hand) may

be stabilized at the level of R- and C-commands, at the level of sharing it across the fingers (I – index, M – middle, R – ring, and L – little), and at the level of involvement of

the motor unit groups (MU-modes).

SUBCLINICAL AND CLINICAL APPLICATIONS

Many conditions, from natural aging to neurological disorders, are associated with problems related to movement stability.

Examples range from mishandling hand-held objects to ataxic limb movements, and to problems with postural stability. Less obviously,

problems with movement initiation may also be related to impaired control of stability, the most obvious example may be episodes of

freezing in Parkinson’s disease. In this case, however, they are related to impaired ability to attenuate stability of salient performance

variables and make it difficult to initiate properly timed quick changes in the performance variables (see the earlier example of ASAs).

The two aspects of the impaired control of movement stability have been addressed as impaired stability and impaired agility (reviewed in

68).

Indices of stability quantified within the UCM framework show high sensitivity to relatively mild changes in the control of

movements, e.g., those seen under atypical development, under fatigue, with healthy aging, and in populations at high risk for

neurological disorders (reviewed in 15). In particular, persons with Down syndrome show reduced indices of multi-finger synergies during

accurate force production 75, muscle fatigue can lead to increased multi-effector synergy indices and reduced intra-muscle synergies 76,77,

older persons show reduced synergy indices during steady-state tasks and reduced ASAs in preparation to quick actions 78,79, and

professional welders who are predisposed to basal ganglia disorders due to the accumulation of manganese and iron in the brain show

smaller synergy indices 80.

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The high sensitivity of synergy indices to Parkinson’s disease (PD) has been shown in studies, which demonstrated

significantly changed indices of both performance-stabilizing synergies and ASAs in effectors and tasks apparently unaffected by the

disease (according to the clinical examination) 81,82 and in de novo PD patients 83,84. These indices are also differentially sensitive to both

dopamine-replacement treatment and deep brain stimulation in PD 85-87. Overall, even though clinical studies using the UCM-based

methods are still relatively few, they promise important practical impact as behavioral biomarkers at early stages of neurological disorders

and as predictors of both treatment and disease progression, e.g., predicting episodes of freezing in PD 73,88.

It remains mostly unknown if training can lead to improved control of the action stability. So far, various studies have shown that

at early stages of practicing an unusual task, synergies stabilizing performance variables strengthen, primarily due to the drop in VORT,

and at later stages they can weaken, primarily due to a disproportionate drop in VUCM 89-91. In conditions challenging stability, an increase

in VUCM can accompany a drop in VORT 92,93 (cf. 94). This is encouraging given that a number of clinical studies have documented reduced

amounts of VUCM leading to low synergy indices 82,95. So, designing studies to encourage higher VUCM seems a promising strategy.

Unfortunately, so far, transfer of the effects of practice to more functional tasks has been limited (reviewed in 96).

THE FUTURE OF THE UCM

One of the most difficult aspects of understanding and exploring the UCM concept is separating underlying hypotheses from

the associated toolbox. The primary hypothesis is that the central nervous system uses abundant sets of elemental variables to ensure

task-specific dynamical stability of salient performance variables. Secondary hypotheses have emerged based on experimental

explorations of the primary hypothesis. They relate, in particular, to ability of the brain to modulate stability of action depending on plans

and expectations (as reflected in ASAs), changes in the ability to ensure proper stability properties of movements with subclinical (fatigue

and aging) and clinical states, the role of timing and spatial errors in the dynamical stability 97,98, and a few others. So far, the toolbox to

explore these hypotheses has most frequently included the analysis of the structure of inter-trial variance and of motor equivalence.

Clearly, it is unproductive to try to disprove the toolbox, although delineating its limits of application and reliability of the outcome

variables is important. In contrast, trying to disprove specific hypotheses is potentially very valuable and can lead to their refinement or

even falsification and replacement by a different theoretical framework.

As of now, the process account of the UCM-associated stability of movements 60 provides the most useful framework and

guidelines for future analysis. The most obvious gap in our knowledge is related to only speculative links of the assumed processes to

neurophysiological substrate. The current guesses are based primarily on a handful of studies using the UCM-based analysis in patient

populations. Very few studies have applied this method to studies of movement stability in animals (e.g., 99,100). Potentially, animal studies

can provide more direct information on the underlying neurophysiological circuitry given the possibility of performing invasive procedures

and more direct recordings.

One of the challenges in analysis of synergies is shifting from sets of elemental variables at the level of performance (which are

typically selected subjectively, commonly based on the available equipment) to sets of theory-based control variables such as RCs. The

first described attempts have provided promising results but the available tools for recording control variables (s, RCs, R-command, and

C-command) and their changes in real time are currently limited and based on a number of assumptions and simplifications. So far,

mechanical and EMG-based proxies of those variables have been used. Maybe, combining analysis of both mechanical and

electrophysiological variables could lead to progress in this field.

The idea of hierarchical control with RCs (see Figure 4) raises a problem related to the described trade-offs between synergies

at different levels of a hierarchy. Recent studies have suggested the existence of three levels at which synergies are organized, the task

level of the R- and C-commands, the level of sharing the task across effectors (such as limbs and digits), and the level of stabilizing

action of individual muscles 64,74. The presence of multiple circuits stabilizing action is not surprising given the obvious importance of

action stability in the process of evolution. Other levels, e.g., those involved in stabilizing movement in individual joints, may be apparent,

not real, unless single-joint movement represents a salient task component. A related issue is the unintentional drifts in performance that

have been reported during isometric force production tasks (reviewed in 15). So far, studies of such drifts within the UCM-framework have

reported disappearance of synergies at the level of effector involvement, dramatic reduction of synergies at the level of the R- and C-

commands, and no effects on motor unit-based synergies 64,101. These studies have to be reproduced using a variety of tasks. The

differential sensitivity of circuits involved in action stability may be an important factor defining specific features of movement disorders,

but such studies have not been performed yet.

So far, most UCM-based studies have explored indices of the relative amounts of inter-trial variance or displacement within the

UCM and ORT. Less attention has been paid to analysis of data within the UCM (cf. 102), although the importance of reduced VUCM has

been emphasized in several clinical studies 86,95. It seems that excessive stability along the UCM (as reflected in low VUCM), i.e., preferring

stereotypical solutions, is highly important in its effects on stability of everyday movements. A related underexplored issue is the structure

of variance within the UCM. It is possible that some directions within the UCM are stabilized more than others reflecting importance of

other variables in addition to the variables for which the UCM was computed. Note that the UCM-based analysis is always subjective: It

starts with selecting a performance variable that is seen by the researcher as salient for the task. A number of early studies have shown,

however, that the brain can reformulate the task based on its past experience and other criteria and stabilize a variable that has not been

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mentioned in the task formulation 32,33. Maybe combining the UCM-based toolbox with more objective analysis of the structure of

variance, e.g., the principal component analysis, can help discover hidden salient variables.

An aspect of synergic control that has not been explored in detail is the apparent trade-off among three properties of

movements, their stability (as reflected in the structure of variance, VUCM > VORT), optimality (sticking to a criterion that defines average

across trials sharing of the salient variable across elemental variables), and agility (ability to change a salient variable quickly) (reviewed

in 51). Such trade-offs have been invoked, in particular, in studies of ASAs and synergy indices in the dominant and non-dominant

extremities 103,104 and in studies of individual digits of the human hand 105. Can such inherent trade-offs be avoided? Can a person be both

optimal, agile, and stable? We do not know answers to these questions, which are obviously relevant for such diverse fields as athletics

and motor rehabilitation.

There are plenty of unsolved methodological issues related to analysis within the UCM framework. Some of them, such as

reliability of the main outcome indices, the number of trials required to reach a criterion of statistical robustness, and a few others have

been addressed recently 30,106,107. A number of issues, however, remain acknowledged but not analyzed in sufficient detail. These include

the linearization using the null-space of the J matrix in most studies, assumptions that the J matrix does not change significantly within

the selected time (or phase) window of analysis, potential interdependence among elemental variables unrelated to the task, etc.

Applied studies performed within the UCM-based framework are still few and fragmented despite the obvious functional

importance of the proper control of action stability. Very little is known about changes in the neural control of movement stability with

typical and atypical development. In contrast, this method has been applied at the other end of the spectrum, to studies of aging

demonstrating impairment in indices of both movement stability and its adjustments in preparation to quick actions (ASAs). Studies of

neurological patients have demonstrated the sensitivity of the indices quantified within the UCM framework to a variety of disorders.

However, changes in these indices with disease progression, pharmacological therapy, brain stimulation, and rehabilitation are next to

unknown with only a handful of exceptions. This field is waiting to be adequately developed.

Very little is known about changes in indices of stability with athletic training and motor rehabilitation although, obviously,

developing better stability of actions and better agility could be very beneficial in various sports and in recovery of functional everyday

movements. In laboratory conditions, practice has been shown to lead to major changes in the indices of synergies, in particular on VUCM.

In contrast, no studies have explored potential effects of practice on ASAs.

Overall, the UCM-based approach seems to be at a stage of maturity. It is considered seriously by most researchers as both a

viable theoretical framework and useful toolbox to analyze the neural control of movement stability. It is up to next generation of

researchers to address the missing pieces of the puzzle and to develop this approach and its applications. This would require deep

understanding of the main aspects of the approach and the associated fields such as linear algebra, statistics, and neurophysiology:

Challenging but not impossible.

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10.1249/JES.0000000000000002

BJMB

Brazilian Journal of Motor Behavior

Latash

2024

VOL.18

N.1

https://doi.org/10.20338/bjmb.v18i1.433

14 of 14

Special issue:

“Using the Framework of the uncontrolled manifold

(UCM) to understand motor behavior”

97. Latash ML, Shim JK, Zatsiorsky VM. Is there a timing synergy during multi-finger production of quick force pulses? Experimental Brain Research,

2004; 159: 65-71. doi: 10.1007/s00221-004-1933-y

98. Goodman SR, Shim JK, Zatsiorsky VM, Latash ML. Motor variability within a multi-effector system: Experimental and analytical studies of multi-

finger production of quick force pulses. Experimental Brain Research, 2005; 163: 75-85. doi: 10.1007/s00221-004-2147-z

99. Klishko AN, Farrell BJ, Beloozerova IN, Latash ML, Prilutsky BI. Stabilization of cat paw trajectory during locomotion. Journal of Neurophysiology,

2014; 112: 1376-1391. doi: 10.1152/jn.00663.2013

100. Mangalam M, Rein R, Fragaszy DM. Bearded capuchin monkeys use joint synergies to stabilize the hammer trajectory while cracking nuts in

bipedal stance. Proceedings of the Royal Society Biological Sciences, 2018; 285 (1889): 20181797. doi: 10.1098/rspb.2018.1797

101. Reschechtko S, Latash ML. Stability of hand force production: I. Hand level control variables and multi-finger synergies. Journal of

Neurophysiology, 2017; 118: 3152-3164. doi: 10.1152/jn.00485.2017

102. Zhang W, Scholz JP, Zatsiorsky VM, Latash ML. What do synergies do? Effects of secondary constraints on multi-digit synergies in accurate

force-production tasks. Journal of Neurophysiology, 2008; 99: 500-513. doi: 10.1152/jn.01029.2007

103. Zhang W, Sainburg RL, Zatsiorsky VM, Latash ML. Hand dominance and multi-finger synergies. Neuroscience Letters, 2006; 409: 200-204.

doi: 10.1016/j.neulet.2006.09.048

104. De Freitas PB, Freitas SMSF, Lewis MM, Huang X, Latash ML. Individual preferences in motor coordination seen across the two hands:

Relations to movement stability and optimality. Experimental Brain Research, 2019; 237: 1-13. doi: 10.1007/s00221-018-5393-1

105. Abolins V, Latash ML. Unintentional force drifts across the human fingers: Implications for the neural control of finger tasks. Experimental

Brain Research, 2022; 240: 751-761. doi: 10.1007/s00221-021-06287-2

106. Piscitelli D, Buttram A, Abernathy K, Canelón J, Knighten D, Solnik S. Clinically relevant estimation of minimal number of trials for the

uncontrolled manifold analysis. Journal of Biomechanics, 2024; 171: 112195. doi: 10.1016/j.jbiomech.2024.112195

107. Piscitelli D, Buttram A, Gibson S, Hager J, Thomas B, Solnik S. Test-Retest reliability and measurement error of the uncontrolled manifold

analysis: A step towards the clinical translation. Journal of Biomechanics, 2024; 162: 111902. doi: 10.1016/j.jbiomech.2023.111902

Editor-in-chief: Dr Fabio Augusto Barbieri - São Paulo State University (UNESP), Bauru, SP, Brazil.

Associate editors: Dr José Angelo Barela - São Paulo State University (UNESP), Rio Claro, SP, Brazil; Dr Natalia Madalena Rinaldi - Federal University of Espírito Santo

(UFES), Vitória, ES, Brazil; Dr Renato de Moraes – University of São Paulo (USP), Ribeirão Preto, SP, Brazil.

International License which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: Nothing to declare.

Competing interests: The authors have declared that no competing interests exist.

DOI: https://doi.org/10.20338/bjmb.v18i1.433

Citation: Latash ML. (2024). Brief History of the Uncontrolled Manifold Hypothesis and Its Role in Motor Control. Brazilian Journal of Motor Behavior, 18(1):e433.